{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic factors and coincident indices\n",
    "\n",
    "Factor models generally try to find a small number of unobserved \"factors\" that influence a substantial portion of the variation in a larger number of observed variables, and they are related to dimension-reduction techniques such as principal components analysis. Dynamic factor models explicitly model the transition dynamics of the unobserved factors, and so are often applied to time-series data.\n",
    "\n",
    "Macroeconomic coincident indices are designed to capture the common component of the \"business cycle\"; such a component is assumed to simultaneously affect many macroeconomic variables. Although the estimation and use of coincident indices (for example the [Index of Coincident Economic Indicators](http://www.newyorkfed.org/research/regional_economy/coincident_summary.html)) pre-dates dynamic factor models, in several influential papers Stock and Watson (1989, 1991) used a dynamic factor model to provide a theoretical foundation for them.\n",
    "\n",
    "Below, we follow the treatment found in Kim and Nelson (1999), of the Stock and Watson (1991) model, to formulate a dynamic factor model, estimate its parameters via maximum likelihood, and create a coincident index."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Macroeconomic data\n",
    "\n",
    "The coincident index is created by considering the comovements in four macroeconomic variables (versions of these variables are available on [FRED](https://research.stlouisfed.org/fred2/); the ID of the series used below is given in parentheses):\n",
    "\n",
    "- Industrial production (IPMAN)\n",
    "- Real aggregate income (excluding transfer payments) (W875RX1)\n",
    "- Manufacturing and trade sales (CMRMTSPL)\n",
    "- Employees on non-farm payrolls (PAYEMS)\n",
    "\n",
    "In all cases, the data is at the monthly frequency and has been seasonally adjusted; the time-frame considered is 1972 - 2005."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:27.979906Z",
     "iopub.status.busy": "2022-02-08T18:16:27.979444Z",
     "iopub.status.idle": "2022-02-08T18:16:30.599777Z",
     "shell.execute_reply": "2022-02-08T18:16:30.598984Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.set_printoptions(precision=4, suppress=True, linewidth=120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:30.606188Z",
     "iopub.status.busy": "2022-02-08T18:16:30.604877Z",
     "iopub.status.idle": "2022-02-08T18:16:32.002601Z",
     "shell.execute_reply": "2022-02-08T18:16:32.002128Z"
    }
   },
   "outputs": [],
   "source": [
    "from pandas_datareader.data import DataReader\n",
    "\n",
    "# Get the datasets from FRED\n",
    "start = '1979-01-01'\n",
    "end = '2014-12-01'\n",
    "indprod = DataReader('IPMAN', 'fred', start=start, end=end)\n",
    "income = DataReader('W875RX1', 'fred', start=start, end=end)\n",
    "sales = DataReader('CMRMTSPL', 'fred', start=start, end=end)\n",
    "emp = DataReader('PAYEMS', 'fred', start=start, end=end)\n",
    "# dta = pd.concat((indprod, income, sales, emp), axis=1)\n",
    "# dta.columns = ['indprod', 'income', 'sales', 'emp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: in a recent update on FRED (8/12/15) the time series CMRMTSPL was truncated to begin in 1997; this is probably a mistake due to the fact that CMRMTSPL is a spliced series, so the earlier period is from the series HMRMT and the latter period is defined by CMRMT.\n",
    "\n",
    "This has since (02/11/16) been corrected, however the series could also be constructed by hand from HMRMT and CMRMT, as shown below (process taken from the notes in the Alfred xls file)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:32.006046Z",
     "iopub.status.busy": "2022-02-08T18:16:32.005585Z",
     "iopub.status.idle": "2022-02-08T18:16:32.009065Z",
     "shell.execute_reply": "2022-02-08T18:16:32.008402Z"
    }
   },
   "outputs": [],
   "source": [
    "# HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end)\n",
    "# CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:32.012415Z",
     "iopub.status.busy": "2022-02-08T18:16:32.011968Z",
     "iopub.status.idle": "2022-02-08T18:16:32.015050Z",
     "shell.execute_reply": "2022-02-08T18:16:32.014685Z"
    }
   },
   "outputs": [],
   "source": [
    "# HMRMT_growth = HMRMT.diff() / HMRMT.shift()\n",
    "# sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index)\n",
    "\n",
    "# # Fill in the recent entries (1997 onwards)\n",
    "# sales[CMRMT.index] = CMRMT\n",
    "\n",
    "# # Backfill the previous entries (pre 1997)\n",
    "# idx = sales.loc[:'1997-01-01'].index\n",
    "# for t in range(len(idx)-1, 0, -1):\n",
    "#     month = idx[t]\n",
    "#     prev_month = idx[t-1]\n",
    "#     sales.loc[prev_month] = sales.loc[month] / (1 + HMRMT_growth.loc[prev_month].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:32.020877Z",
     "iopub.status.busy": "2022-02-08T18:16:32.019421Z",
     "iopub.status.idle": "2022-02-08T18:16:32.023857Z",
     "shell.execute_reply": "2022-02-08T18:16:32.023217Z"
    }
   },
   "outputs": [],
   "source": [
    "dta = pd.concat((indprod, income, sales, emp), axis=1)\n",
    "dta.columns = ['indprod', 'income', 'sales', 'emp']\n",
    "dta.index.freq = dta.index.inferred_freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:32.030228Z",
     "iopub.status.busy": "2022-02-08T18:16:32.028745Z",
     "iopub.status.idle": "2022-02-08T18:16:33.252491Z",
     "shell.execute_reply": "2022-02-08T18:16:33.252842Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n",
    "\n",
    "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:33.255793Z",
     "iopub.status.busy": "2022-02-08T18:16:33.255191Z",
     "iopub.status.idle": "2022-02-08T18:16:33.276498Z",
     "shell.execute_reply": "2022-02-08T18:16:33.277072Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create log-differenced series\n",
    "dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100\n",
    "dta['dln_income'] = (np.log(dta.income)).diff() * 100\n",
    "dta['dln_sales'] = (np.log(dta.sales)).diff() * 100\n",
    "dta['dln_emp'] = (np.log(dta.emp)).diff() * 100\n",
    "\n",
    "# De-mean and standardize\n",
    "dta['std_indprod'] = (dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std()\n",
    "dta['std_income'] = (dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std()\n",
    "dta['std_sales'] = (dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std()\n",
    "dta['std_emp'] = (dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic factors\n",
    "\n",
    "A general dynamic factor model is written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\Lambda f_t + B x_t + u_t \\\\\n",
    "f_t & = A_1 f_{t-1} + \\dots + A_p f_{t-p} + \\eta_t \\qquad \\eta_t \\sim N(0, I)\\\\\n",
    "u_t & = C_1 u_{t-1} + \\dots + C_q u_{t-q} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\Sigma)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $y_t$ are observed data, $f_t$ are the unobserved factors (evolving as a vector autoregression), $x_t$ are (optional) exogenous variables, and $u_t$ is the error, or \"idiosyncratic\", process ($u_t$ is also optionally allowed to be autocorrelated). The $\\Lambda$ matrix is often referred to as the matrix of \"factor loadings\". The variance of the factor error term is set to the identity matrix to ensure identification of the unobserved factors.\n",
    "\n",
    "This model can be cast into state space form, and the unobserved factor estimated via the Kalman filter. The likelihood can be evaluated as a byproduct of the filtering recursions, and maximum likelihood estimation used to estimate the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model specification\n",
    "\n",
    "The specific dynamic factor model in this application has 1 unobserved factor which is assumed to follow an AR(2) process. The innovations $\\varepsilon_t$ are assumed to be independent (so that $\\Sigma$ is a diagonal matrix) and the error term associated with each equation, $u_{i,t}$ is assumed to follow an independent AR(2) process.\n",
    "\n",
    "Thus the specification considered here is:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $i$ is one of: `[indprod, income, sales, emp ]`.\n",
    "\n",
    "This model can be formulated using the `DynamicFactor` model built-in to statsmodels. In particular, we have the following specification:\n",
    "\n",
    "- `k_factors = 1` - (there is 1 unobserved factor)\n",
    "- `factor_order = 2` - (it follows an AR(2) process)\n",
    "- `error_var = False` - (the errors evolve as independent AR processes rather than jointly as a VAR - note that this is the default option, so it is not specified below)\n",
    "- `error_order = 2` - (the errors are autocorrelated of order 2: i.e. AR(2) processes)\n",
    "- `error_cov_type = 'diagonal'` - (the innovations are uncorrelated; this is again the default)\n",
    "\n",
    "Once the model is created, the parameters can be estimated via maximum likelihood; this is done using the `fit()` method.\n",
    "\n",
    "**Note**: recall that we have demeaned and standardized the data; this will be important in interpreting the results that follow.\n",
    "\n",
    "**Aside**: in their empirical example, Kim and Nelson (1999) actually consider a slightly different model in which the employment variable is allowed to also depend on lagged values of the factor - this model does not fit into the built-in `DynamicFactor` class, but can be accommodated by using a subclass to implement the required new parameters and restrictions - see Appendix A, below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter estimation\n",
    "\n",
    "Multivariate models can have a relatively large number of parameters, and it may be difficult to escape from local minima to find the maximized likelihood. In an attempt to mitigate this problem, I perform an initial maximization step (from the model-defined starting parameters) using the modified Powell method available in Scipy (see the minimize documentation for more information). The resulting parameters are then used as starting parameters in the standard LBFGS optimization method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:33.279867Z",
     "iopub.status.busy": "2022-02-08T18:16:33.279251Z",
     "iopub.status.idle": "2022-02-08T18:16:43.007062Z",
     "shell.execute_reply": "2022-02-08T18:16:43.007417Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/runner/work/statsmodels/statsmodels/statsmodels/base/model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "# Get the endogenous data\n",
    "endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp']\n",
    "\n",
    "# Create the model\n",
    "mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2)\n",
    "initial_res = mod.fit(method='powell', disp=False)\n",
    "res = mod.fit(initial_res.params, disp=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimates\n",
    "\n",
    "Once the model has been estimated, there are two components that we can use for analysis or inference:\n",
    "\n",
    "- The estimated parameters\n",
    "- The estimated factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters\n",
    "\n",
    "The estimated parameters can be helpful in understanding the implications of the model, although in models with a larger number of observed variables and / or unobserved factors they can be difficult to interpret.\n",
    "\n",
    "One reason for this difficulty is due to identification issues between the factor loadings and the unobserved factors. One easy-to-see identification issue is the sign of the loadings and the factors: an equivalent model to the one displayed below would result from reversing the signs of all factor loadings and the unobserved factor.\n",
    "\n",
    "Here, one of the easy-to-interpret implications in this model is the persistence of the unobserved factor: we find that exhibits substantial persistence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:43.009899Z",
     "iopub.status.busy": "2022-02-08T18:16:43.009423Z",
     "iopub.status.idle": "2022-02-08T18:16:43.037466Z",
     "shell.execute_reply": "2022-02-08T18:16:43.037976Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                             Statespace Model Results                                            \n",
      "=================================================================================================================\n",
      "Dep. Variable:     ['std_indprod', 'std_income', 'std_sales', 'std_emp']   No. Observations:                  431\n",
      "Model:                                 DynamicFactor(factors=1, order=2)   Log Likelihood               -2055.605\n",
      "                                                          + AR(2) errors   AIC                           4147.210\n",
      "Date:                                                   Tue, 08 Feb 2022   BIC                           4220.400\n",
      "Time:                                                           18:16:43   HQIC                          4176.108\n",
      "Sample:                                                       02-01-1979                                         \n",
      "                                                            - 12-01-2014                                         \n",
      "Covariance Type:                                                     opg                                         \n",
      "====================================================================================================\n",
      "                                       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------------\n",
      "loading.f1.std_indprod              -0.8631      0.019    -45.038      0.000      -0.901      -0.826\n",
      "loading.f1.std_income               -0.2479      0.042     -5.970      0.000      -0.329      -0.167\n",
      "loading.f1.std_sales                -0.4810      0.025    -19.312      0.000      -0.530      -0.432\n",
      "loading.f1.std_emp                  -0.2790      0.030     -9.262      0.000      -0.338      -0.220\n",
      "sigma2.std_indprod                9.342e-09   1.81e-06      0.005      0.996   -3.54e-06    3.56e-06\n",
      "sigma2.std_income                    0.9028      0.030     30.172      0.000       0.844       0.961\n",
      "sigma2.std_sales                     0.5905      0.034     17.338      0.000       0.524       0.657\n",
      "sigma2.std_emp                       0.3695      0.015     25.476      0.000       0.341       0.398\n",
      "L1.f1.f1                             0.2329      0.035      6.609      0.000       0.164       0.302\n",
      "L2.f1.f1                             0.2824      0.039      7.299      0.000       0.207       0.358\n",
      "L1.e(std_indprod).e(std_indprod)    -1.8927      0.002   -936.769      0.000      -1.897      -1.889\n",
      "L2.e(std_indprod).e(std_indprod)    -1.0000      0.001  -1260.760      0.000      -1.002      -0.998\n",
      "L1.e(std_income).e(std_income)      -0.1731      0.022     -7.888      0.000      -0.216      -0.130\n",
      "L2.e(std_income).e(std_income)      -0.0870      0.048     -1.812      0.070      -0.181       0.007\n",
      "L1.e(std_sales).e(std_sales)        -0.4250      0.042    -10.027      0.000      -0.508      -0.342\n",
      "L2.e(std_sales).e(std_sales)        -0.1979      0.050     -3.977      0.000      -0.295      -0.100\n",
      "L1.e(std_emp).e(std_emp)             0.3049      0.034      8.925      0.000       0.238       0.372\n",
      "L2.e(std_emp).e(std_emp)             0.4783      0.029     16.649      0.000       0.422       0.535\n",
      "====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.51, 0.03, 0.04, 6.07   Jarque-Bera (JB):   224.96, 9550.64, 20.39, 4450.92\n",
      "Prob(Q):                0.47, 0.86, 0.84, 0.01   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.77, 4.61, 0.47, 0.41   Skew:                       0.15, -0.98, 0.20, 0.87\n",
      "Prob(H) (two-sided):    0.11, 0.00, 0.00, 0.00   Kurtosis:                  6.53, 25.98, 3.99, 18.65\n",
      "====================================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "print(res.summary(separate_params=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimated factors\n",
    "\n",
    "While it can be useful to plot the unobserved factors, it is less useful here than one might think for two reasons:\n",
    "\n",
    "1. The sign-related identification issue described above.\n",
    "2. Since the data was differenced, the estimated factor explains the variation in the differenced data, not the original data.\n",
    "\n",
    "It is for these reasons that the coincident index is created (see below).\n",
    "\n",
    "With these reservations, the unobserved factor is plotted below, along with the NBER indicators for US recessions. It appears that the factor is successful at picking up some degree of business cycle activity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:43.040542Z",
     "iopub.status.busy": "2022-02-08T18:16:43.040012Z",
     "iopub.status.idle": "2022-02-08T18:16:43.645734Z",
     "shell.execute_reply": "2022-02-08T18:16:43.645172Z"
    }
   },
   "outputs": [
    {
     "data": {
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t4VQe8UwBy+qKSn6BPPnEPHNqJIk9p8LzfRgEQRALirSqk18MvayefEdpCU1S8okZMuMgnzG2gjH2MGPsEGPsBcbYe2pxYHNB2lTyy9l1/mfPKXzhN8eqep1STz4ALDMtNLNp2TkXSpnvJZV88uQT88+39g3gH391Zr4PgyAIYkGRyRWEkj9JCU0Z5EfS5MknZkYtlPwcgL/inG8GcBmAdzHGNtfgdWcdpeSXCfLvf6EfP3+ut6rXiZZU1wGADtNCM5vJt0+fjYIB2NrhAwCzug4F+URlBiIpbPuHB3CoNzJr7zEUyyKazitfKUEQxPnOieEkxpI5NPuMkiC/+LNRUkIzmsrPquWXWPrMOMjnnPdxzp8xf44COAxg+Uxfdy5IKSV//E0US+cQrzJIkUq+17DYdQIiyO8Lz14Zzd+fimBzuxeNXgOA9ORP7TU451V/TmLxc3Y0gWgqh1PD8Vl7j5G4uB/mohkcQRDEQodzjs88cg4Bl447d7RU7Hir6uSb1XWyBY70DPv4EOc3NfXkM8a6AOwE8GSZ597OGNvLGNs7NDRUy7edNlLJz5RR8mOpHKKpbFWvE0tn4TE06JYb1+vUUe92oG+WAp2hWBZHBhO4cnWdekyfRsfbh4+HcNvXn0d4FnMHiIVD3Nx1ktf+bDCSEPdN/xxUlyIIgljoPHgshIO9cbzziuWo8zhsSr6rjF3HCpXRJGZCzYJ8xpgfwA8BvJdzPs4LwDn/Kud8N+d8d0tLS63edkakJvDkR1M5xDPVbZXF0jmbVUfS7HdgNDE7N+jjp0Vioy3I16Zu1zk9mkIyW8CJkWRNj49YmMhdG3nt15p0rqD8pKTkEwQxHX64rxvv+/6B+T6MmnGgJwa/U8fLNzcCABxa+Y63hj4+jhiOZ/HJB89iKFad6EgQVmoS5DPGDIgA/zuc8x/V4jXngomq60TTOeQLolnWZERTOVtlHYnboc9aMLXndARtAQNrmtzqMV1jmKolX1b/OTWaquXhEQuUeGZ2lfzheHEioiCfIIjp8NiJETx4eHC+D6NmdIfT6Kx3QWNCqa+k5FubZAVcIqbYczqC+14YwVNnZy+P6nxlMLr0455aVNdhAP4bwGHO+edmfkhzRyVPfjqXR8YM7qNVbJUJJb9MkG+wqhYJ0+HkSBLbOnxgrDgoaNOw64yZOw1nKMg/L0iYdp3ZWnyOWIN8susQBDENktmcmoOXAt2hNDrrnerf0pbj1JnN5msN/lv8ItfuYE8MAGa1HPf5yImhGC79lwex78zYfB/KrFILJf8KAG8GcD1j7ID53y01eN1ZJ5UtevKtthxrImq8ihJWsVR5u47boSE1CwMV5xxDsSxa/U7b49NphiXtRKfHKMg/H4ibCV2zreTXexwYICWfIIhpkMjky+bKLRaGYlkluGXzBfRHM+g0+9kAxWDequJbHweANnN+f75fFEkYTZBdp5acHIqDc6A/vLRjn1pU1/k955xxzrdzzi80//tFLQ5utrGq7DmLAh6zqPexaoL8Ckq+a5aC/Egqj0yeq5W+RHjyJ//7cDKHveeiAICxpBg4TpOSv2R4vieM53uKzajOjMRxxScfQm8oqRats6bkm4vGre1esusQBDEtEuk88gWO3CIM9COpHO68+wX89NAIANErp8CBFfXFIF9W0XGXBPlWu06zOb9nTKfB2Czl952vSKtOMru0qwue1x1vU5Yv15p8G7FU1akmyI+mKtl1NNVwq5YMxkTw1OIrCfKrtOv88NkhvPfe44in8xhN5KAxYDieo7rmS4R/+tkh/MN9L6h/H+6LoieUxIsDUSRmWckfiWeha8CGFi9GErlZs6sRBDG/hBNZdI8lZuW1E1kx7y5GNf/4cBKZPMcz3UJI6zbLaHdagnyNMeiavXwmYFfyG70OWP45a0U8zlcGIuJ7oSB/CWMNQLKWWrTWwD5WpSe/fOLt7Cj5Q6Ylopxdp2Cx6zx5JoKfPD887u8HolkUOHBmLIVoOo8NLV4ApOYvFaKpHPosW5Dyeo6kcrOu5A/Hs2j0GFhmNoOTC1Ji5pwdSaA3RFWwiIXB5359FG/5xtOz8tpSjFiMvnxZxOJQv1gAdYdEMLncYtcBAEPTxin5hqXqjsfQEHA51L9D5Mmvmp5QEt/fe27C3xkylfw0BflLF6uSb1UMrIG9rEZSiVy+gGgqqzLhrcxWkD9oltIqteuIjrfi5+F4Fn/3y9P48mPju/ZK3/ShATEIXdTpB0BB/lIhkclhMJpCwdzVkf0eIsnsnCj5TT4D7WYzuO5Qmrow14j3ff8APvbTFyb/xUXGz5/tQyhBi8Fa8OJAdM7eayiWxkhsdpo9JhdzkD8i5tHeSAZjiSy6wxl4DQ0NHoft9wydjfPkWytouh0agm4RV6xqcJEnfwp8/+lzeP//Pauuo3IMSiV/gt9ZCpzXQb5NybcG+RYlf7LqOsMx4bdrLrHOAMKTn85xFWzViuFYFgxAk7fUkw+VePu5R84hlskjksqrwE79vRnky4SezW1eOHVGybdLhEQmj2yeY8wMnOQ1HEll1bU9GzYyQDTCavY50BEUqtVf3XcSN3z5IN7xgxex51R4kr8mJmIknkFoiU30o/EM3vW/z+Bf7z8634ey6HmhN4yX/tvv8MzZuakWEk/nZ83qUGzatwiD/NGUUugPDSTQE0pjRb3LVgkPEP57t2F/jDGmKu+4HZoSDy/qDCCUzNl26onKyLlvIpF2gDz5S59Knnxrp9vJquv0R8SFUuqPB4p+u1oPVIOxDJp8DpW8I9GZaIZ1ZiyFR06Esb7ZAwDjqpxIu8/zfSLIb/YZWNngolr5SwSpTMhrU17P4WQWidmukx/LoclnoCPoxEduWok/vbwDr9rWjHAqhw/87CR+dXR0Vt73fCCWzs3KzuB8IhX8Hz3TPWuq8Fxwajhu240Yiqbx8V+fwRu/fRj/uaenqqaKM0Uqk0NR+3lMZvJ4291P4/hgrKbvl8zkkcoWai5iAcXAa7EE+dFUFld88iE8ejKMU6MpXL22DjoTQtq5UNrmx5c4dTbOrgMUffluQ0PQ7UCzz8CqBhfyHIimlnZAWivGTDGkGiV/tqyrC4XzOsivpORH09VX15Hll0qtM0Axc77WK8WhWBbNPue4x2UJTVkC9PKuIADhwZdk8wXl7es165g3eg2sanBTrfwlAOccCfN6k4OY8uQnc7Pa8TabLyCUyqkdpls2NeEPL27He67uxH+/7gJsavPhs4901/x9zxdiqdyk/tEfPdON27+0Z46OaObIXaZ0roBvP3F2no+mPMOx9LggvVDgeO/39uOx48NI5/J41X/uwaceKO5GfOnh43jg6Cg8hoZv7xvEt/fNfmMnOW8lStTL44Mx/ObwIB49NlTT95PJsbUOxDO5gupds1jsOs/1hNETSuIbT/UhlMxhY6sXa5o8+OkLI+gJp9HV6B73Ny6HVjaXz1p55w0XteLdVy1HgzmmkmWnOkKTKPn5AsdwjBJvlzw2T37OXkLToTEEXI5Jg/yByNwH+YOxLFrLvJ/OGAqFYjlQWZe335L8OBwXn8dSqQsNHgdWN7rRF8kseX/aUiedKygPvFTyIxa7zmwq+bL6Qznrms+p4/KuIKLpvG1BXS2RVBZ3fPkxHOo9P7s+5gscyWzeNmaV4+C5EA6eCy2aPAgZ5Df7nbjn6YUX5J8bTeDSf3kQj50YsT8+lsC9B3rxhQeP4dEXhxFKZHFySCjlhQLHL5/vwxVddfjqazfgxg31+PJjvTg1MrtJ03EV5NuvETlH1boeeMIUDEoXFZPxwR89h289frri89Y5aLFU1zncJ3IhjgyK73h1oxsXLvdjNJHDyzY14nUXto77m7+9YSXecnH7uMeVXcfQsHtFADduaECj6eenhljVoew6FSoGjsTTkEPkZGPqYue8DvKtvuRST77f7YDf7Zi0uk5/JAVDZ6gvSaoBAJdp16l14Dwcz5ZdVGimJ18G+W0BAzqzdx6Vfvx1ppXHqTN4nRq6Gt3gEF3gFir7z47hli88WlWDsvMV67U2oOw6UsnPqjKps6HknzOrSHQEx+8yAVBJZNFplGrdfzaEvWfGcLA7NO3jW8xIRWqy7y1s9r2YLTtWrZFWsk0dQbXFvpA4PhQTFsgRe6lIudh88tQovvzbEwBERQ8A2Hd2DAORNK5fXw+NMbznqk4wAA8fD83qscpxsXS+GTTtO321DvLN95mqiPXQkQH87tj4qm/qdbPF8X2xKPmH+yJwWqw3a5rcePvlHfjfN23CR25aBX+Zwhw7l/vLKvzlaug3eEV8QWU0q2PMjHMqLUDlLjdAibdLGutEaPfk5+B3OeBzOSatrjMQTqE14IZWklQDFG/SyVaK8XQO/7evWwVlVoaiadvfJzI5RNP5skG+9OTLIN/p0NDid9o8+TLI375MVNRp8DrAGMMqc7BZyEH+/S/041BfpKaT1WJRPKslkS0X5Fur68yekn/YrNa0sdVb9vmgW0xUkWn4Sl/oFUm7pSrl+YIUG1KTfG8hM8hfLD5T2ZOk0edErrDwjlmWLJWLJ8mhvgg0JnZE950Zg8aAvlAKuXwBP3+2D06HhitW1wEAmnwGti/z4ZEToVk9VrmYL1UvZdOfmiv5auE5tXsykcmPO5+lz0sWU5B/2ZomrG1yw+fU0Owz4HPqZYP4yZBlNK019BtNu85CUPJf+1+P4z8ePDbfhzEhoUmUfHlPaGzyMRUA7t3fg9d8+bE5ya2pNed1kG+dCDMlQX7AbcDvckxaXac/kkJbcHxSDQC4HSLwn0jpePLkCK7414fw1z84iLsfOz3u+Vv/4/f48iMniu8ncwAqePILvGjXcWgM7QGnrfOoDPIvXOYDADR4xOCxos4FnaHmyVm15OC5EAAxuXSPJfCJXx62BenxdK7qCefkUAy3f2kPXv7vj9oeT2byizrwT1h2OWSzD3kNhywlNGcjCDw8kMCyoBN1ZXa1ACBoqlmRKnpPlCKV00QVuzicc1tDu6VAsb/BxNe3DJ4Wi89UXpuNPieyeV7TSZRzjs//5kVlo5kOFYP83gjWtvhxzYYWAMAt2zqQK3D0R1K4//l+XLuhxdYg8dq19Tg+nMLp0RR+eyKEPafCODQQx1BsZtfpiwNRXPvphzEcSxftOln7PSKV/P4yItJMUEp+ZmpjSSqbR3iCXRurslorMeK57jAeO2HfPfjGnlNq92UmZPMFHBuIYVNHAO+5uhPvubpzXCWdqWCUUfKDbh06Wxie/Od7w+PsawuJTK6AuNplmljJX97gqUrJ33dmDPvOjI1Lal8MnNdBfjqXV3VqZaIPAMTSWQRcDvhdDps15CcHejAWt1eq6Y+k0F5XfrXursKuc++BXuTyHPVeQw3GklQ2j/5ICsctk5QM8st58jWz423O/Cy6xtAWMGyJt8OxLBwaw6Y2EeQ3mtuAToeG5XUuHBuYvyA/kcnhyn99CI8cHZ+kli9wPNct1Nx4Oo/fHBrAV357EmdG4up33vKNp/DRnzw/6ftwzvEH/9+TOHguhCP9UbWLwznHzV/4Hb78yPEafaK5R068Do2pa0WqwNadIuvk+cjRQfzLLw5P+Lq5fAFH+if2wx8ZTGBTW3kVH5iZkq+C/CqC1wde6Mdl//LguHt1MROzlBScKBCWwdNi8ZnKBV+DV4gW1nF4pozEM/j8b47h/hf6p/0aPWPlg/zDfRFsXhbEu29Yjzt3deI1uzoBAE+eHEV/JIWr1jfbfv/qtfUAgD/5/lF88Oen8Dc/PYm33fMibv/683j89PRLyz5zZgynRxI4MRhTu86JUiXf4smv1SIqkysoMWkqC8psXiTVhpKV703rnFtJyX/46OCUegJ84peH8cEfPaf+HU5k8bGfHsIP9828EMCJoRgy+QI2dwSxe0UAr9jcNKPXc2jjg3yNCUvw2DzbdbL5AhKZPI7NQAwsFDje9LUn8dCRgWn9fTydK+t6kFirXFVS8qUAtqLBW9VYOWq+5snh+CS/ufA4r4P8VLaAgBl4ZHNlPPmWxNuhaBrv+d4B/GBfsYsa5xz94RTaguWDfFcVibej8TSW1buxosGrsr2Lz4kLa9ByQR81B7YVZUpyOTSGnMWu49AY2oNODMUy6rHheBZNPgda/QYMjSmvHwCsanTbFhRzzbnRJLrHknihTHLliaGYWp0nMjmlAMqFUSZXwIFzIZwenrzNeiZfQH8kheX1Ii9hxExMHktkcWYkgZNDi+9Glsggf2WjV21JSruOVO8dGrNVxPjGntP42qMnJ9zB+NmzfbjlC4/atvw/df8RfO3RkwCAkVga/dFMRasOUPTkR6aYUxFP53DKXMxVo+SfHkkgkckvaOvZVJHjEOcTJyOGk4sryBeNBB1KEJlOUnYl5H09k12r3pCZvJ7MIpcv4H33HMBDRwbQG05hc0cQO1c24NN37kBXkxBNfvqsaD64c2WD7XU6gk7sWOaDoWv4x5u78P+9dgM+/rIuAJhR6WJpXQwls2pMLLW0qTEyX1Bzykyxep2nkngr58Jydp2v//4UvvjQMdtCvtK1/sEfPofP/qp8b4Wj/VG89N9+awv2Tg7FcW40ocQNeRxyjJwJh/vEfLW5Izjj1wLsJTStNHgd8+7Jj5jf23AsPeFuzESMxDP4/fFhPHFyeuWUP/+bF/G6rzxe8Xlrbk9FT340hQavgaDbqGp8kILRYowNzusgP53LI+AWini2pOOt8uSbK0EZgPeHi4F4NJ1DIpNHe4UgvxpP/mg8g0afE81+Z8Ug37rNuv9sCK1+A62BynYdKYY5NIa2gBN5LjqRAsBQPINmnwFdY/irazvx6m0t6u9XN7pxejhe04l2KvSFhWpWbiI6YFp1ACCeyaugR67ojw/GkM1zteKeCPmdrm4WE7Mc6E8Ni6AwNIFf1Mqe48Pzdq4qIQe11c0+DMcySGXziGfy8BhF60CDz6muyWy+gKdPj6LAMWGd8p5QEgUO287Jz57tw68OCTXm2R6hRlYV5E9RyT/SH4UUIKvx5Mudi9JkyYXOwXMhXP2ph8vuQFjVzUqTEufcEuQvrOuyEsIa6YBDm3mQ/48/PYQ//p+n1b9H4rIO9vQXPD0Wu073WBI/2t+Dd3xrHwBg87JiULesXswBvz82DLehYWN7YNxrfea2tfjhWzbjxg0N2NLuw3Xr6uF2aMpCOR3kojucyFqq65TYdSJptYtmzWfinON1X3kcP3+2b8rva70Pp3J+Uxa7YOnf/Xh/D+490Fti1yl/PYSTWRzpL6/k7zszhhcHYkp1jadz6I+kzPErYTvmgcjk9otcvmCbf0o51CuSbuV8MlPK2XUAYa0dq3Jumi2si7PjQ9Prrizn7OkuOHvDKZwbS9p2paw/V6PkD0bTaAu64XHqVe1EyYWDjBEWE+d1kJ/KFuB3icGv1JPvdzsQcDuUCion3gHLyn/AHDAr2nUck9t1RuIZNPlcaPa7MFzStGpEvmekWKf5mbNj2NJefjAptetITz4A5csfjuWUn/+2rc02e8WqBhdyBY5zo/MTHMmbv1yQc/BcCNLmmEjnVE1o6a07ZKop1QwccjJc1SQ+u/TZyVV6qIqFwpmRON74tSfxqxemt+U4W8jJt8uccORnWt7gUb/T5HMq28dzPWH1N6V2MSvynPSaCzHOOQajKbUwkFaqiYJ8n1OHxqrz5HNe9GcfMpNu/S5HVUG+vGfPzNN1PF2eODmCs6OJsjaEmGWyqlQrP57Jqx27yerpLxSiqSwCbgNGGdvkVDk6EFHjAGBV8qd3LvKmxx4AQsmMGo/lMW6yKLcuh462oBg/t3fWw6GPn1p9Tt222GaModlnzCjI7zOPL5zMqoDGeo8UChxDsTS2d9YDsCffjiWyePLUKPadmXqHXOt7TMWuY/27UjW/eyyBsXjGtqAtF+Rn8wUks3mcGUmo33369Che9oVHkcjkLDuY4rlTFouFHA9lsuVEY57kR/t78Mov7ak4Lx7ui+KCtkDZ73w6ODQGjRWDfUmDd/7tOtaxe7rW3tIg/8uPnMDe09Wr+pFkFvkCV8cyEkvj8k88hPufF4vVapT8nrEk2oJuuI0qg3zzWE+RXWdxIZR8065jmVyiaaEu+Vw64pk8OOdqgLdaZ+QEUMmuozz51Sj5AZeo3WqxTIzGi1aUUCKLwWgK3WNJbK0Q5OsaA0cx8Va3BPknhkVwNhzPormMnx+AShSbrwomUmUqp8Yf7A5h6zJRrSKRySu1Vg7ocss0lMhMmjgbt6jdQDHIlzdwNUr+sBlATOQtrZZ/f/AYvvhQbaoVyAXl+lZRPenogDgv0poEiCRHaft44mQxgWoin6McOKV9IZbOIZUtqPvicF8EK+pd8JUpFSfRGEPApVel5L/v+wfxuq88gZFYGnuOj6Dea2B1s68qa4Cc3M+OjB+QJ6vWMRrP4OpPPVw2L2S2OWsGEX3hFAoFjrOWnYiYJZG4kkpvDZqqqRgxH+w9PYo9x4sJkFLJd5oBTTZfwEgsjfsO9k75taOpHEbiGbU4lEHEdIP8gUhKjSXhZFYtaN913Vq84ZIVaPbbLZOdDWKBe1GJVWcimn0GhmPTD9z6zUV3KJkp2wxrJC7Gwx0rxNjZZ7nHZVJxdBpJ6tb3mErirXUutF6viUwOY4ksxhKZST351rLW0r765MkRHO6L4NRwXAXu8nPZgnxTiZXj5GAVycjPmmV7ZZBv/eyccxzui2BTx/idm+ni1DW4Hdq45F2fU0diiknOtcam5E/Tly93T0bjGRQKHJ/51VF896lztt8pFDi+8tsT+MaeU+P+Xgb3MvC++7HT6I+k8PRpsVi1inTlYpl8gePEUAzrW/1wG9qk4wPnRYcA2XUWGTZPvqnkp3N5ZHIFBEy7Tr7AkcoWVHMF6/aeVEUq2XUm8+Tn8iJ4b/Q50eJ3IZvntptoxNLEaiCawv6zIQDA1o7yaqks4ynVD4fGsLLBhY2tHnztyX786ugoYpk82gPlg3ynqUTMVytxpeSXeP0yuQKO9kdx6epGAGKQLdp1xPchg/wCL/oGc/kCvrHn1LiGZlLxWtVUPsivxmsoq7fUosbu/c/348f7e2b8OkBxArrAtAvIhFWrkt9g7uSkcwU8fmJEdVOcaOtaKflmYCDPWSiRRTZfQF84pRaUExF0O6ry5B/ui+Cp06O44l8fwv0v9OOVFy6H16mrvIyJkMHO6RK7zpH+CDZ/9P4JJ6d7nj6Hs6MJ5Rfdf3Zszir1yCC/N5zET5/txXWffUSdb+vnrhTAWye3VLaAw30RfOE31S0eh2PpmpdYLMeHf/w8/vGnh9S/ZZBv6EW7zk8O9OLd390/5cTpSDKLTK6gJna5AE1O07okz/2qJi/CiaxaNLzx0lX4xKu3j/v9TvMe27myvur3aPI5Zqbkh61Kvt2T/3xPWH2nmzvqzGT8YjUZaUWazvVdCyU/ZBlnZYJzgdsXIuWCfGvFu6OmZUcKbr2hlBqb5O/JwKzeaxSVfPOaGIrahbVyyDG0L5zCM2fHsP0ffqVsi4PRNEbimZr58QFRJ7/Ujw8ALgdDep7toXJu9Rj6pMm3mVwB7/3e/nHjrVXJHzNFOXk+s/kCnjk7hnd8ex8+8csj+NhPD+F/n7Q3yYuaxzCayCCWzuHux88AKFpJZfzQ7HeVDfK7xxJI5wpY3+aHx9AnDfKTWRETuhwazo4mbJbCg+dC+NhPXxhntV5InOdBfh5+l92TLwNAv8uBgGnliaVzKuAeiBQrFPRPYtdx6gwMRR9iKfJilEo+ANvFYrWe9JsDjKEzbGgpH+TL3UJpPXJoIvD/8I2rEEvn8Q8PnMH6Zg9u3VI++99plvycr9rEcsIqndxPDgu//bbOOjh1TXjyLRVjpJoivy+56n7wyCA+9tNDePCw3VIjJ8MGr4F6r4Gh2Hglf7IqFHICqUWQP5bI4OxoArkaDOAyGFzX6gdjRRuTVclvMoP8eDqHvafH8LJtHWBs4iS0kFLy7UE+IK7TwUiqbO+GUoJVKvnxTA6bOoK4oC2AT9+xHX9/62Z4nXpV51sqeGdLttcP90WQs0wogFCWZWm9fIHj20+ICeP0cBzRVBZ3/tfj+GaZ0razgQryQ0k81x1GvsBVgBGzefLLnwOrQJDM5PHzZ/vwb795sSol+yM/fh7v/t7+mRz+pPSGkjg6EFW5N4AIMANuQ1kdpBUDKJ+cORHynpTjplTep6vkyyB4c0cQ0XROXfONZcoXA6JSBzC1IL/ZZ2AkMfl4U45YuliAIJSwB/lD0TRu/eLv8akHjgAA2utcaA24bDllfTLIn0btdet9mJxC4q31u7AuSrstpSy7R4s/lw3y08Xr4og5vsm5uC+cLKPkx7C83oON7QFVTlUulHOFifO4CgWuvP994SSe7wkjZyrBQHF83VTDIN/Q2Dg/PiDsv5NV1xqLZ3D3Y6cnvZ6mWzpU3pMXrqifVMk/ORzDvQd6x+2KynlmLJ5Rc6+0Vr7+q0/g1f/5GB46MoiPvHwTrr2gBX/3k+dxfLBoYbQq+fc8fQ7hZBYrG70q3yKUyMDp0NDsd5ZtnPmiaTNa3xaAx9CRzfMJc4HkeLJjRT1yBY7useK5e64njG/sOb2gy26ft0E+5xzpXFHJl4OJHBj8bgM+S5Avv+h0rqAGxd5wCo0+J9xGeYsCY2JFXknpkK8pE28BqItePm9W08JgJI39Z0PYvKxO7RCUIktvpXOmJ9/cAl/b7MGfX7kMO5b58G+vXKuC4VKkmjZfrcT7KwT5R8yW4Rvbg/C6dJsnfyiaRn8khbFEFpeuabL9vfTLl9pQpNrtdTrQ4ndhMCLUnNMjcRi6aChWqv6XIhWNako6TsZYIoNsnisrjOSzvzqKN37tiSkFAMlMHhoTi9T2oFtVKuq0KvlmucLusSSS2Ty2LAuiyefEQCSN08NxfPGhY+PyEsaUki+O0XqdDkXTGIym0eyrIsh3OyoG+dl8Qalq8XQeF62sx0/+/ErcuXsFGGPwVtGcDigGxKPxjM2KIBeRViXwQz9+Dh+7TyjLDx8ZRE8oCb/LgdMjcbw4EEWuwNE7Bwp3Ll9QamZfKKVUMvn/ahJvrTtQqVxeqVjVdIjui6TUAq4SA5EUHrNYbabKb18cAiAmaXlMpXadTI5bxuKpBZ+lQf5M7TryWt/UEQTnIhDxOfWK4/0fXr4K//Wmi9AaqL4BUovfQDJbmHS8kfzDfS/gZ2YFH+vOSziZtdl1BqMpcA48anaWbQ240V7nRn+k+B3L67qckv/YiWF8/fen8ODhgbLjj/U+rDS/7Tk+bFtQi2Mrb9fpsQRO3WMJeAwdDo0hkx//2vJ71jWGw+WU/JJO36eG41jT4sPqZr9KxrXmrExkUzwzmlDH3BdOqQBvsGQHeWMNg/yXb27EG3e1jXvc5dBQ4BPnrfz8uT78/X0v4Nxo5Xv5+GAUV3zyoSn54CXyWrloVT16QskJxxZ5fQ7H7HOJ6t+SzqnvfSiaxlg8g/1nx3DHrk48+aEb8Lar1uBDt2xCvsBtFffkMYwlsth7ehSrm324eWs7zowmUChwjCUyaPAa8Dr1skr+MXPBsK7Vr+7licYI2T1X2vCsfTekKFtp4b8QOG+DfGlJKfXky4EhYJbQBMQkaV3ty+TbvnASHRVUfInLMXmQ32TadQD7DTESz6jSbGdG4zhwLoRdE/g9y9l1JK+9sBVfvmOD6pxXDjnRzlfSnhyoo+mcTcE50h+FoTOsafHB53Qgnsmr4G0gklJq5xXrRJA/Gs8gly/gQbMO72CJDSVm2a1pCbgwFBMLhVS2gM2m7z80iWWnVnadZCavgrZTJRPigXMh7Dk+gmfOVp8Yl8jk4XOKLsYrGr3qc9iUfHNBKc9Lg9eJ1oAbg5EU7n78ND7zqxdxw2d/i/2W951IyT82KILhaoL8gFuvmHj7xq89qer1x9M5df9JvIY+rgZ4OaKpnNrutlbY6S8JagYjKbw4EMPZ0QQ457jvYC+a/U685qLlOD0Sx2FzcTkXDVD6wimVS9MbTimVTE5IVh+ynJDCiSyu/+wjKuHM5snPFtRitpoAMpzIjFtcJ818JMnXHj2Jt/zP05PaGyphVfT6zR04lXhrCgy5QkGJDBN5xc+NJvC2u5+2lQyVf1dU8qce5A9F02qB2xNKoN5rqDH+5FAMTSU+fCutQTdu3tpR9XsBQFMVVjkJ5xzfeuIM/ur7B3G4L6KuZ59Tx3Aso8bMRHp8s6mWgAsddR70WYSEiew6H/7x8/jHnx3CH9+9t2xlGZtdp4JP/N3f3W9r5AhU9uRbleXusSR8Lh1Oh4Z0mQWtnKO3LAviaH9UlbIGxPgkBYhoKgfOOU4OxbG62Ye1LT6EElmMxTO245go+VbOLS6Hhv5wSvny5ZhwuC+K5fUe1HkmH/uq5fKuOrxqW/O4x6W6P5FlR57TiSxYUuworfnOOce9+3smrLIWTmbh1DVc3CWss3snSNqWi6dSK4t1UXXUUmTgoSODKHDgugtaVb6LdEnIv0mZ1hlAiHmD0TTag26sbPQikytgICoEvwavU1RHLCMKHRuIoaPOjaDbgNspg/yCOtbSBGspcO1aJWKvz/7qRfzNDw6iUOAYjqXR4C2OXwuRhXtks8z4IF/8WwYzshkWYCr5sQx0M2iWwVFfKIVlluCpHG6HVnEQVEq+36ku6uESG0R7nRsNXgO/fK4fmVxBBbLl0LXKQX41KDXNPBfVJCXVilQ2j1AiqyZUq5J8pD+Cda0BGLpmrs6Lnvx4Jo/fvjgEQ2e4ar0oBzqWyOCp06PquywdxKX64HPpIsiPppVV5yJzq30yq0CxJnUOw7E0dn/816rCzFQYs3zO0yWDrrw+vml6DqshkcnBYw5c0j4A2D35UnWQA2edx0Br0IXBaBpH+qLoavIinSvg+3tFMhTnHKFkFm5DQzSdQySVtQW+ciKsVsmPVgjUD/VGcGIohly+gHSuAK/THuT7XI6qE2+lR9Zq2ZGTm9yF2WPadJLZPIZiaRwfjGHr8jqsa/UjlS3g0WNCea4U5J8bTeDN//3khJNitcjFyPpWP86MxFXQIytYlLPrnByO4eRQHO+95wCe7wmXBPlFJb8aRTyUzCKeyas64vF0Dpf882/wi+eKjaSGomlkcoWqytSWks0XsOf4CNa0CNGiP5xCOicaI5V68mXPkmhaKP4/3Nc9Tk1++vQofnN4EI+b36E1qFFBviqhOX78fayMygwAf/btffizbz8DQHwnHXXFAO7UcLzmip28Z6qp1x43u3GncwW863+fwWnz+C9oD6BnTFw/PqeORDZvy2uq8xhwGzqWN3jQEyqWHpzIrjMcS+PiLhHU9ISSSGRy+PQDR9R1KPtVODRWVsSSimqpipuawJMvKw+NxDPwOEWQL+cizjk++pPnse/MKGKmXefirkaEk1mcHU2o9znUF1GCXSSZxXBMJCSvafapa+/kcMx2TVjnuXyB4/rPPqLGvkN9YTg0hktWN6LXouTLhcSh3rCtlOpsInfw5U59OaxBfm8oiZf/+6PjdiqkJbl0XHvoyCDee88B/MdDlZtBRpI5BD0GLlvTBJdDw8NHKhcokNawckG+zAN70VIG9VeHxFhzQbtfPRZwOeAxdPVatvs8kcFQNI3WoEuJoaeHEwglMqg3lXyrCNcbSiKcyOLFgSjWt4mcNU+Jkv9PPzuE13/Vvnsu5+g1LT5curoRveEkfrCvG/0Rkf9RmoC/0KhJkM8Yu5kxdpQxdpwx9oFavOZsI9Vqr9MBjYnJhXOOLz18HAGXAxe0B+A3FwCxVA5jiQzWmoPEQKSoGiybRMl3Oypnb8vqOY0+J+o8BhwaG+fJb/Q50RZ04+RwHLo52FRCVtzKWEpoTgVl18kVcGo4jks/8SD2nZlew4qpIpUY6W20TlJH+6Oq7rTX5UAsLTz58tz/4rk+bO+sV2r1aDyLX70wAJdDw+aO4LjBTK7ufS5h1xmKppWqIZvYTKrkS7tOJo9z5iSz/9zUS9FZ8y5Ky3NJZfUXz/Xh7d/ci1d+aQ++9PDxCXcPEpk8vDLIb7RbdLxOHYbO1OJV7kjVeQy0BdwYiKRwpD+Cy9Y0oTXgUsFhJJVDvsCxsV18N31mcpt8HelLbaomyHfpiKbz4zyMsXROeYzlJFRaqafS9mspsVQOW8wdmdOWQK6/xK7z+2PFykJnRhI4PSIUP1l+VNpLKiVVPXlqFI8eG8Yvn59+R1WJXIxcuqZRfcbl9R4cH4yhUOCIZ3Iq2JSLeDn5cA68954DCCWzquxeegpBfqFQTPiX131/JIVoOmc7f/KenMjeMNHni6VzeMX2ZQDEgktO2EGPYRl7uEXJz+Hnz/Xhr35wcJz/Vx7nflNltn7GYpBfWcl/1/8+g0/dP76Z0pnRBB4/OYLnusN4/MQIXrK2SZ33sURW2Sprhax0JoWj7AQNq+R3dPOWdpwciuO/fy8qj1zQHlC7Y61BN/IFrr6jloBLFYZY0eBBOldQ46G0I0VT9pyAbL6AaCqHrcvFPdQfTuGx4yP40sMn8KNnRIdYaVNs9DmVJ190En8Cv3iuD/FMDgVuFzGAolVSY+OVfGuw7DUccOpacXcik8c3Hz+DB14YUN+1XIT8zrxPHRqzNcCLpHI4Zy5+VjZ5i7viIwnbNWHd6R2JpXFyKI4HzHv6UG8E61r9WNnoRX84iW7z9QYjaaSyeZwajtfUjz8RLjNnbqIeGHIHJ5rK4fmeMF7ojajkZEncYnUFhE2xL5xU98NPD/ZW9KhHklnUeRxwGzpesrZpwipk/WWU/Gy+gOFYRp2zI/1RJU7+7sVhOHVNfU+AsDy317nVXGVdkI7GMhiMptAacKly2GdH40Ul31lU8vvCSdz8+d/hlf+5R1XWAcZXQOwNJdETSuJZi2CnxFivE/e843L82+suVK85HMugJbDEg3zGmA7gSwBeBmAzgDcwxjbP9HVnGzlRuhwaDF0oBt97+hwePzmCD718E5r8LgTNRlmhZBYj8YwKcgaiKURTwgPZMZmSb5RXOoDiJNTgdULTGJpKGmKNxNJoMoN8ANjeWaead5VDsyj5OsO4ElyToew6uQIGI8LTOVcNheSAIEuRyRsrlMigL5wqBvmGjrG46OC71rxRh2MZXLq6ER6nDrehYSyRwYFzIexcWY+uZu84lSyezkHXGFwODS0BF5LZPH734hAavAYuMFf4k5XGtCbeymBqOslMMlhhzB6QyrKtN21uA+eiwQvnHJ9+4Ci+9HBlpUUE+SL4XtkoBj5DF5816DbgdTqUD1FOblYlfyyRxUZzgStVO7mrssWchOWWeFezF05dm6KSbzbEKtkpGbD4aOXAPM6u49SRK/AJE8OlbaO9zo0mn9NWhrLPYtfhnGPP8WE12ew9PYZEJi+CfHOSsVbgKOdLlsdcmtg9Hc6MinwQa/nFW7a1I5nNoyeURCyVUzYrGaBIr+hrdnXi+GAMZ0bipmqrIZUrIJmtzq4jbA3iZxmUyfvPunNSrDA29SBfWme2qcAxqe6hoNuhFifZfEEFGNFUVv1dd8m9JcvcHjArjtmC/ERGVS4DxnvGkxmhdO8vscHlC1ztyvzFd59BrsBxx65O1FksjjVX8pVdR5zT/9lzGtd/9pGyiXwygLv9wmXY2B5QOwstlhwAGXDI5OavvHkX/uXVWwEUS3yeGxMVQgajKXidOgpc7BK8+j/34Cu/PaHO2+pmH5wODYPRtKp4c98BkQ+QzOTBmKhYI8/vmZEEHjsxgqdOjY4rcyiRlY5aA25bqeKesSS6mnwqX8xr2nUyJQvakVhGfde7VgnB65GjIsiXuROACPit10+L360Wa7F0Th2zx9BtvW/kGLH3zBjyBY7neyPY1BFER53bLPFpNpWMpfHiQBQFDmyuYfnMiXBNwa4TTeXUz6W+eTm+DsXSODEUwx/9z9O44pMP4ehAFK+8cBlG4hm1cNp3Zgxvu3uvuvbCySyC5nm8bmMrTo8kKtaOV3YdS/8fubCQsdTJoTiW1bvVdbS21T+u30Bb0KV6ElktfGdHE0hlC2gNuNFR54ahM5wekUq+08zfy6NQ4Pir7x9ENi96AKWyBWxoE7FDqZIvx70HXigKN2OJLBiD+tzL6kTM1xdOYTh2fij5lwA4zjk/yTnPAPgegNtr8LqzivxS3YauFIPvPX0OW5cH8fqLVwAQFgepDozFM1je4EHA7cBgJK0Gg8k8+W5H5Yogo/EM6iwqVrPfpbYds/kCIqkcGn1FJeaKteN9elYcFk++PkUVHwCcjqKSX1QLa18+8MRQDNd++mFbop8cEDZ31JnvK86DrGwgE5t8Ll0F7Wtbitt6coej0evESCyD44MxXNAWEIm14+w6Qu1mjKE1KG7Qh44M4roLWtU24mSfW6qQiUxeDaKlibPVIK0P61v9NrtOMptHOlfArlUNePRvr8PjH7wBP/nzK3FJV6NSmMuRyOQsSr6Y1ANuA4wx1HkM+Jy6miyUXcdroNVSBnZjR9BsBGdO1Oa5kEpbTygptkkDbjT5ner5Jm/5hG4rsvNmaS8C6yBetFOVBvkO9RkrYc2pWdVUrLiQyRXUAjqSyqEnlER/JIU7d3WCsaJffHWzD8vqPaqcbKepfkbLBMpyZ2DPiZGqbEQTcW40gRUNXrUbZegMN24SyXfHBqOIpXNo9olrNVUS+Fy1TowLj58YUdYMq10nlp74WrYqqnLhICc7a8dI+Vg1/vFS5K7lsnphP+wLp2zfldWuI8eeaCqnFph9JfdW2Hz8uR5Rhcg6+Y/GMuq+Ymy88qmSNMMpm1VjNJ6BjK1PjySwdXkQmzqCNr/1RJ786eB1avAYmjqnB7pDCCWyZS1g8nuq8xh465WrAYjyzdbjk0F+bygFt6HhopUNKhiWO3vnRpMYMDvAbjBFjbF4Bge7w3i2O6zOeYPXifag2OGTpTf3nhkzEy5F7o/H6VCBu+x6HUlm1SK+1NqVzOTAmAjc5PtIL/XyBo8q7+s1xyl5LciFx0g8jUhK+MJbAi4sr/fgsRNiR+4iS1WjlU1e0TfBPI9NfqcaT+LpYh7UikaP7XqWi6NwMosfPtONoWgaV6xrRkddUcxzGxoGoylVjtM6D80mKsgvuZ5/c2gAt3zhUWTzBUuQny0G+SXxR8yi5Ms558r1Lbh1xzL86x3b0ehz4kdmSef7DvTgN4cH8P4fHgTnHJFUVl1v125oBYCKlh05Po7EiyLJQImYl8kX0OJ3YZU5V5XrFN0edKt7Vi4eXQ5N+flbAi44dA2dDV48dnwYo/EMmv1OeE0l/8Ejg3jsxAg+eutm/N0rhP4sm8PJIF/GaGWD/HgG9R5DxVQdZnfrvlAKw+eJXWc5AGsng27zMRuMsbczxvYyxvYODVUOUuYKm5Lv0MQNkshgTbNfKeCGLlpVP3NmDLkCV6r6gKUSxaSe/EmU/CaLMiSCfDHgjFn8+m1mIPqStZX9+ABgdoZHOsenbNUBih32Mrliy/Fqur9OlSdPjuL0SAJPW7L7+8L2m1/ebLIRiVLynQ6lBkj7lK4x7DYTgRp8ThzqiyCWzmFdWwCtQTeiqZxte9aa1NniFzdsvsBxw6Y2tVoPJzL4+M8O4btPiRq9L/SGbWW8lCffEkxNVp2kHPL8XrSyAefGkkrFlApUo9eJjjqPWoBdub4Zz/eGK9YQT2Ty4zz58rMGPaL3g1TyByIp6BpDwOVAq2XLcWN7AH6XQyV7ymDygrYAHBoTSn40jRa/S6nLjT6nOsaJkEp+6XU1YOlSGbPkTFjxVtGsTf6tCPJ9ygZjVZ8jyaxa+K1u9mFZnUd1/Vzd7IOuMaw0t39lnkc5X36/ef4yOeE3nwlnRhJY0ehV40lXk08tbF8ciCGezqPZ7EOQtqhODouFbywhJmC3QwT5cuKKTWLXse5aye9aXl/WXQDV9Xs6Sr4qMuBCe50H/eGUCsytibfZPLdVOpPHYy27KY65uMg+NhhV2/gOjWE0kVHjR1vAPa6QgPW1rEmlUjy4eoP4zu+4qBMA7EF+jZV82fVWvrcMHMslg8qgLegxcNuOZWj2u7Ci0YN6y/HJ+7gnlFRVtCRKyR9NWCoHiXH17GgC+QLHUDStzl2DV8w9/eEU+sIpdf/99GAvklmR++M1dOWzf84cq0OWID+czNpKAyezeXgMHfVeJyLJLH70TDc+8KNnwTnQWe9ROyUewwGnQx8f5McyiJkVmQAxVsn59aJVxV2wtS1+RNNZdd01+pxwOTRoTIgE6WwebkNDW9BtO9dyHgKAzzxwFIbOcNOmNpuYt72zXlk8GYMaK2aboiffHuQ/fWYUh/oiGIqmbUp+pIKSL4sXDEfTKsfgs3fuwH+8YSdcDh23bu/Arw8NIJnJY/+5EDyGjgdeGMB3nxLlKqXDYWWTF2uaffi9peJWJlfAvz94DOGkaN7JGGz9f+SCamN7UHWwbwm4sNLcPZWLTittdW4MRsRCQX6mVU1edZ3Ka35VkxcHu8Oo9zrxhktWwuvUkcoWVPGCW3csw10v6cK+j9yodnBdMsjPCgtpKJlFs9+FE0NxZREcTWTU4hMQeQI+p46TwzHEM8VxeaEyZ4m3nPOvcs53c853t7S0zNXbVkReLG5D+JSzOY5oKoegx64ebmgLKN+nHPREkC8Gg2oSbyt68mMZ2/Zvs+kPB6yTohNXrm/BVeubbYNYOXRWTJx16NNQ8pVdJ68Gkkr+0Mn4u3ufr2hjkCWoXjRX4s92h/DUqVEEXA41EY3FM+geS+CLDx3HzpX16kb2uXSltrXXeeAxdGxdFlSBbKPPiSP9wj6yvtWvlC2r79LqW5fPGzrD1Rua4TZE6/nhWAbffPwMvvjQceTyBfzx/+zFX95zUL2GvH5Smbza/pxOkC/P74Ur6pG31OCVwU1DSVBx5fpmcF5MGi0laflsrQEXnA5NTYjr2wJY0+JTk8VgJI2gW1TikZawjjo36r1O+F3GOLtOo8+JlU1e7D0zhpG48CI2mepya5W+xKCrvJIvE6tilqRqX0nirddVjZJvlsB1GVjZ6EVvOIl0Lq+UIENniKZEIj0gFL6VjV7kChxOh6a2YqVl56r1QiUfLhN0DURSuKSrEQGXY8aWnZ5QEisaPWgLusEYsL7NjzqPgfagG0f7hZIvz7Wy65iTT5PfpYIQaddJZotNocrtQlix5p8oW0SJXSedyytFcFpKfkxez6JaTX8kpQLzgNuhenTY7To5W6flXL6A+5/vB+ccY4ks6s1dt4PnQup772zwYDSeUe+3vMEzTmSxLlKsQb4ce//06jX48C2b8LqLVwIQap8UQJpq7MkHhM1NlvGVY2O5RNyIRcl3Gzruecdl+IfbtqjzAECV7+wLJ8dVfHEbotDAubGEWuhI28QJy/vKc97gM1QQPBARlskdnXX41Qv9agz1OHV1fqWPOZwsqsicl3a2lUG+gZF4Bv/4s0O4d38PNAZsWR5UiyhZXUfmZ8iF6EgsrcquAsDGjmIC5QVKCNLRboo7Q9E0AqawwRgTPu10HqlsHm5DV1XFJP3hFJymjXPQVPHrvIbNlnvRygaksgU83xPG8noPXI7KXb5ribtC4q28bodj6bJKfqldz6rknxtNwGXWlJdcv6kNmZwoPHCoN4I/fMkqbGjz4/4X+k1PfvG62t3VgP1nx5RS/9iJYXzu1y/ih/u6MRzLYI2Z3yTFS3ldd9S71eK0JTC5kp8xc1XkDvrKxqJvX+7Gr23xQ9cYvvgHO7Gs3qPmjxODcQQt1RKtu3FWu85YIgPOgdfu7oSuMdzztBD4QokMGi0LZsYYOuo96no/H5T8HgArLP/uNB9bkHDO8ar/3IO//dGzAGSQLwYT2ZjFyrpWv1KWGv1OM0Exjb5wEhoD2iYJbiYroWkN4ta3+ZXPy1pD/5LVjfjWH19asT6zxFpdZzpKvkNjYKxUyZ+6XWcklsa3njiDhysk5cgk1xcHYni2O4TbvrgHDx0ZxPYVdXA6NPhdDowmMnjfPQdR4MAXXrdT7a5YK64E3A68cucyvOGSleqxBq9T+TLXt/pV8GmdNGNWJd98/tLVTeq7r/caePr0KDL5AnpCSXz5kRPoj6TwXE9YBQjKrpPNKWVkIJKasKlGOUKJLAJuBzaYg9tD5tan9fu3sn15HQJuB35/rHyQn8jm1OCmaQydpsUMAP75lVvxX2/apa6jaDqHenPwkrtFcpANuB3qM8proMHrxJ27VuCpU6PIFzhag0Ulv61C1+dSpJJfWuJPnlfOiwuycXYdowolv8Suw7mwJ0iFbnWzD5FUVlVeafQ5Ve7C6iafymu5ZkMzrljXpLbih8rYJ/rDKXQ2eLBjRb2q123l3v09KjlyIjI54R9v8bvhdGh446Ur8coLxWbojhV12HdmDPFMDvVeA5rFfjIaL04+sppQvdc53q4zqZJvteuUKvnjx4HpVN0aiWcQcDvgcuiiXntFJb9gq5MvF5j9kSQeeGEAf/rtfXjmbAjhRAbbltch6HbgwLmQ2llb1eTDWDyDYfP4l9d7kCtwm5osr4U1zT4cNNVnoBgsrWj04k+uXqN2xKTVDQAafbWf0Jt9BnrMhD8prpSW/QUsdh0zqF/b4rdV/wFgGe/StuBfsqLBg3OjSZU/JAPjE6ZqORRNFwUGb3Hnui+UQkedB1uX1+HUcNy0PIrKJ4lMDgVLLfNQImMrk2tNvk1mxU5jncdA91gSoUQW//a6C3H4n27GlmV1druOriGTs19/I2bvC79S8sV131HnVpaa1oBL2Q2HY2nbwsxjVmdLZvNwO3S0Bl22rre94RQ66twqqfeWbaIkqrTMep26qv4ia7TPFSrxtkTJtwb5EYuSH1a7XaUd380eFekcjg3G0NngseXvXdLVCKeu4b9+ewK5AsdFKxuwqSOI4wNRRFI52/W2c2UDxhJZ1V38GTNH5n4zcVkmbw9Fi7uADo2h0etUc1uL341tnaL/z5bl45OY5dwyEEkrYaDLsnsic1L+4vp1+Mm7rsBLTFuz19wJPj4YrSjGeiwlNOWcu6kjiFu2deC7T51DJJXFaDyr5klJR51bJTS3nAdB/tMA1jPGVjPGnABeD+C+GrzurMAYw4oGr2oW4XJocOoaoqkssnmutqIk69uKfrtGrxPr2vzoCSXx2IkRtAbc45JESnEbWsWgZDRht+vIbfenTo3alPxqkXF9Jj89uw5jDE5dQzpfGFfBYyrIFa61pvmZkTj+/H+fQSKTU2rVsYEoHjf9lL9491X45lsvBSAUpEeODuGp06P425svsG2HSpUaEDaUT7x6O15vCfLlwNFkKpwyiLfaLYRvXUwS9R4Dl65uxBsvLb5GncdQFWMA4AsPHlNKnvQfWhNvpZJf4FO3MowlxG7OhZ31uO6CFnziF4fxxMmRikG+Q9dw+Zom/PbFIZwciuG+g734xC8P22pkeyzn6L03bsAfX7kGgPh+GWO2ZmrSntTsd8FtaCoxMmAm3krVVCYeveGSFUr9aPG7lIohFwmToTz5pXYdq5pm/jwuyDcH7fgEtfIjJUE+ICouSE/xhraA8Opa7CPy+upqLl5nb768C99522Vlrx9ANK8ajqXRXieSxkoTiQHgK787iX+9/8ik5VjlgkO+18dfuQ0v3dIOQNRmFnX8xfUuA3hA+OcbzGRnmRRd5zHgUkH+xIm3Dx4ewBMnR+ye/ESpJ9/eYIox2BIVq8VqTewIujESz6jvIOB22DreqhKIqWKiY19ILLIB0SwplMyi0efElmV1ONIfRTQlrtEVjR6MxDMYNRdlsnSsNTAaCKcQcDtw+domPHsurAI8uZArp8zJ+6TWdh0A2NjqNeeU4sJ9IJJGOpe3XXfhZFY0uivZ4bIp+eZ9yDlQ7xl/rCsavTg3lsDzPWG0BYv5XidMm1A8k1cNiuTOdSKTx9nRBNrr3Ohs8GIskcVQLA2v2RgslS3g1EgcsbTIBwonc7b7YTRe/DkplXzzfGoMuHp9i1LDm2x2nWLirRwv0rkC+sIpBMxO9dJu1BZ0I+gWNoqWgAsBt6F2Rq3KraidLjz5bkNDW8Bl63rbH06iPejGdRe0Iuh24CYzL8bjFLsPnQ0etVsSSeXmNMiXlWBK7TryGhmIpNWuXTSVU2Nh6XhpjUcOnAup3C2Jx6nj4tUNKmDfuaIe61r86A2nkC9wm9tBdneWSezy/0+bVfm2mlXOpJLfH06jNeAShUbMBXNLwIWXbm7D0x+5sWwjuWKQL4QBQ2dqZ0UUlDDncq9TLSqA4k7w8cFY5SDfYteRFtkmnxN/ctVqxNI53PPUOYzFM2gsKSqxrM6j+poseSWfc54D8OcAHgBwGMD3OecvzPR1Z5Obt7arn6WSLyecUrvO+tbi9lGjz4k7dnXC0Bn2nRlTCRgT4XZottrAEs65efEUB+Jty+vgMXQ8dWpUTVJTqeYwUyUfgGpAMpPEW7kFbm1E8eixYfzs2T48eHgQZ80twjOjCew5MYKuJi82Lwuq42/0OnFqOA63oeGVO+3pHaVKfinSh7rOrLwjBw2r7zKWzqsAUtMY7nnH5XjZtmITm3qvAc7FAHDjpjbkChyv2rkcy+s9eOjIILL5ohUiYamuA0w9+XY0LioBaBrDF94gthk/df8RW9muUu7cvQIDkRSu/+xv8e7v7sdXfnsSv3iuTx2PdSF0245luGmzvXuidUdIqjKGruHed12Bd1yzFoAIKDkXrxdKZBB0i8Sjeq8Tr9klvhNh15maku936WAYbwOzBvnSSlDqyZeDtqwaY4Vzbpb+k30uDLWle2Ykgb5wCn6XA8vqPYgksxiNZeAxhN1AKfnN4xPo6s3StnIifez4MHZ//Nc4NhhDgYvPXecxxgXyqWwexwaiyOQKqllVJWT1iXLlGWXSpDgfZpBvqpujieL4sdkS5EuLoNxBLKfkR1JZvOd7B/CZB46qJNbWgKtYXSdhD/Klsr+q0TvtxFt5rLLBzbGBKJgZtKp8oLy94618395wEi/0iiC/N5RCKJFFvcfAikYPesaSiKTE7lyTz4VwMouBaBoaKyqw1uIH/RGh1u5c2YBoOofDpr1vMCKsHdZFskTeJ7Nh19m9Qlx3sh+GUxeJnf/58Alc/5lHVIArK5toJWN7sEziLQC1ALSyosGLvnAKDx8Zwk2bizlI1i6eLw5E4TY0eJy6uq9zBY72oFt1zj4+EDXtOmKnWvYIuXR1IyIWuw5gv9eTWTE+1Znj2o4V9bbd7EaLXadc4i0g7mc59nc1iQpA7XVuMMawqSOI9W0B9fzpkbhtYeZ1io7p0q4jP5/qfRMWvW/u2NWJpz58o+3Y1rX4saEtYDvH1nKPs41LnzjIP2krH5qtWF3HuugPJ7O2buiSK9cJS/Xyeg9ag241nwL2HJX1rSJ/a//ZEAoFjgPnQnA5NLWbLpV5q11HFnmQ12dLwAXG2DiBVSLHi/6IKLsbdBsq6JZ/Ww55H8czeSyrEKupEpqZvK1v0fbOely2phFf/u0JjMTT42yz7ZYcjfPCk885/wXnfAPnfC3n/J9r8ZqzybUXtCg1UyTeMrWKK7XrdDV7VfDZ5BedQV9uBoTL6sqvDq1UsutEkjnkCtwWxBu6hl2rGvDEyREcHRBdXku3iSZCZzMP8l0OHZn8zBJv5Ra4NfiVN9B3njyDAhfJbZwDvz82ZAtkgKIP/eYt7eO+D2vgV1piEYC6+eUOTJPPCV1jGIyKGvCZnOgEWhpA2t7fPOebOgJ4zUUioL1j1wpct7EFvz8+rK6VoNuBZDZvGzSr9eV/8EfP4ksPH0cokVVdiINuA9dvbMXR/ihG46L5WumiEwBu2tyGPR+4Hh95+SZ89c27sKbFh6/vOYVCgZuT6MRVbqxKvjVpb2N7UC1+VI+IdM6sO1z8vXddtw5vuGQlti6vUypZa5VBvkNjWFbnxHHLhAQIFUpOnrIqQ7kSmsB4ZWr/2TG88j8fw+WfeEhdZwG3A81+J3xOHWdGEugPp9BeJ9S+dK6A/khK3XtSjZPNcqxoGrMlxO87M4bhWAY/f1YE7u2WIN9aZvNIv+gCzBhw7/7eCc/JUEx83uYy1r+ty4MqoTngdpgBfLHjoxwfZF+AZr8THqduHo94jXKe/HueOoeYWQc/lMjCawZ0pXYduVCXi/2N7UEMx9I2+8tEyOZaI7GMsrrICfJwXxR+pwOaxlQ1o1y+oEoERlJZhJJZ+MwEOpkcfW4sIap8eJ1YVu/BYDSNkbhYiMog/MDZEBp9Tst2vCXID6fQFnTjmg0t0BjwwAsin2IolkZLhR2pol2n9hP62maRcPpCbwRBtwNrWnwYjKbxzNkxRNM51ZgpXOKHLj02WSa3+Hg5Jd+DvDlO3LylQwXDvZaE0xcHokpcsC7ehZIv5ry4KSZ4nQ4kM3m80BuGy6Fhd1cjMmZ5TonNrpMRwbUcd67ZYM/PU4m3TnsJTaulLJnNq3nBoWv49B3b8barRLWhb/7xJfj7WzerzxVKZG33laydnpSefPP7HoimUDD7C8gFQ6k99itv3oV/ftU2W/7R3Np1xD1i3ZXK5ovN6eRuDCB2GYrVdcbbdYIWgczaNFEic5EuXFEPABWDfF1j2LGiDvvPjeHkcAzRVA6vNhPWATFe6Jb+PwORlNr1bbQo+RPRGnCBMXHfymZcco6eKBfMmtNVScmX33Eql1fnUV6D//yqbXA5NGTzfJzYZl00NM2Cha+WnJcdb71OhxpclJJvXoTBEnXY5dDR1eSFy6GprZ27XtIFYPLymeL1NeQKfJxXWyYSlVZAuHR1I44ORPGDvd147e4VUyqFKZ1DmRyfVglNQAwk9hKaUwvyOedFu44lyJfn94mTYhvvZtOOUODFdtESeUO9ZlcnSrEGsP5ySr55g8odGBGkOfHrQwO4+fOP4t4DPYinc+OsIFbk9vfW5XW4eWs7Hvyra3DJ6kZcv7EViUxelVtsC7rBuQiI5EAlva6/eK4P77vnQNn66oBo/PHDfd0iL8NyDaxv8yOeyeP53ggavM6KKkVHnQdvu2oNXrqlHX/0ki482x1WVQ68ZZRIKw5dU4vASu3Y5SQaTWVV3WHre3/i1dvgNvSiJ38KDUHWNnlUaVRANGMajKZUg5K+sKjK4CmZZGXirVWVHY6l8bqvPoHDvREMx9LK0uE3E4pXNvlwajiOZ7vDWNnoVcrl6ZG4OvYty4L4zJ07cKvZqKmU5oBTqWWyuc79Zom19joR5OcL3Ha9y0ojd+7qxBOnRtAbSqJQ4Pj0A0dsDXuAopJfztvpcujYbm5B+5xFu47sKCrvlRWNXtz91kvwqos64XboNotEqZKfyxfwjT2nzPOXQfdYEvUeA/VeQwXzI8quU9w1AESiI+flcxRKOTYQxZaPPoBDvRGMmGXtAGCVucNydCCqvo9yHW/7QsIeICthyPN7tD9q2lEMVXL0xf4oAm6HupcePzmCW3csU9eQXGwARSW/JeDCJasb8UtzF0xWjCpHncdAwOWYlSRLjTFcblZOW9PiV0mfsv/E3Y+dQd5sWFbufnU5dHidOgJuh+3eL+/J96rnLl3TCEPXxt1nZ0YTllyd4hzXUee2WTtkz41kNo+TQ3F0NflUgHR2NKEU9HJK/somLzSGcbuM8u+9RknibSID65Rm3cW9/cLlapHrdYrvyLrYabYq+S5R0jpt2nXkTu9QJI3heBrZPK84rzf5XajzGKjzGGpR2jUvdp3inDIaz6jFvBxXPIZeknhrF0XiZj8QSWeZIH9zRxDXb2zF7ReKMXFVk0/FFKWK+84VDTjcF8XvXhTzz5svWwWnrsHp0NDgNdDkc6oxbiCSVteUVY2fCEPX0ORzYTCaMvMmHeo6KWfvkXgtQl4lQdbl0ESZ3Uy+WBzAvPbXtvjxwz97CV62tR1XrLOXL5f5H/Veo6qqcvPJwj66WeRNl63Cpo4gGnwi6UtWjijXbOqC9oBtW2jnygZ87LYteIPFx10JmRFfquZba0RbuWR1IzgXF997b9wwpc+k7Dr5Gdp1cgU1KaayhYrVgcrRPZYc5+cFoBLhJNdtbFXHuLvLHuRvXV6HTR1BlUBjxWdOYk6HVnbClQHE9s6iN6814MaLA2IAlElj5XYBJFIB27IsCMaYSr6Ufr+nTwtFUSqSw2bTsiafU7TOTmbxkXufx4/29+CpU8UyoYORlApQo6ksTg7HMRhN2bYCZQmxvadHq/b/vvqiTgTcDvx/j54EMHmQDxRVoXKBAADVlCZqdntuqPB7l3Q14g8vX6WClGpY2+zB6eF4sQFJIoNsnqsgvz+cgs/pGLfAkYm3VmXqgRf6kckV8C+v3gYA2H82BLehqaBxVaMXjx4bQk8oiTt3dRa38YeLQQhjDHfs6ixr0wBE8C2DWln9SJZXawu6i2VXLWrjcz1hNHgN/Nm168C5SEQ70B3Clx4+gf/b1217/Ym84ACwy7w/fC6Huj+jKdFR1HrtXLOhxfTta7bFeakn/5GjQ+gNp/Bqc5fq2e6QUsdKS2iW2nVkYnY1lp3D5m7GvjOjNmviyiYvfvCnl+Mfbt2svjeHaoZV7Hgrx0xrJ9R6r4HDZr5Mg89QnvsTQzGh5JvvEXA78O7r1yulLpkRr5nLi46v0sZzy7YOHBuM4dhAFMPRdMWA4/YLl+FtV62Z9DNPF9kDZW2LX4xX/VGMxDO4bE0jekJJ/ObwQMUgHxCLEJ/LYRNB6sv8rgzSb9zUpu4RuVsokxk5Lwbb1lwb2WBOBpsep64WCEf6o+hq9qr3PDuaQEvABa9Ttwf5Zonfi7sa8dSHb1TBuUQF+S57x9tQIqtsdUB5q6YV6/M2T77T9OTnRG6A/L5FLwDZ+2biHXrGmKjNbhY2mCuszSol1pyNc2a54M4Gjz3xtrQZVjqHFY1eVcKy3GfQNIavv+VilRvkdGgqxylYcl1dvaEF+QLHP/38EOo8Bja2B7B1eRDtQbEj0mTuhKayeYSTWRXk71zRgI3tgaoqs8lSrhGzhKdS8ifIBatGyWeMiV5G2TxG42mzMZ9m+7svv2mXzesvHhefYaH78YHzOMi/ekMLfvmeq+By6GpVDgB1ZewRH7h5E/79DTttj931kq6qmmDIIL/Uly8n3lI1escKUS7yvTdumHK7ZE2W0JyBku80KxpYG25MRc2XfvwNbf5xSr68IZr9LjT6nFjd7EPQ7cC6kvP41itX45fvuarsZ5BqbqBCkL6tsw6Pvv867LR0DrWex3OjCaUmVUIGvqUTUIvfhaDboZKLpIowEsvA69TRUe9GTyiJ/3jwGMYS4jFZZ/+57jCu/cwj+OyvjoJzrr7/bJ7bAugN5g5EIpMv66kth8/lEBYeU8n3TGLXAYrblJWCBptdJ54dt+Nkfe9/vH3rhJ2YS1nb5EaBFwNlObmuMxc4I/FMWTuVVGas19Uvn+vH6mYfXr6tA4yJnRTrsaxq8qLAhU3hpVvalQoVS+eqrpTSEnApJUoG+YCwHjX5nOocWoP8Z7vD2NZZj9XNPqxr9ePBIwN4xEzaLm0zPxxLw1/BCw6IxESNiYlFKvnFreXx591t6KpjqkNj44L8A+dC0DWGN1+2CoCwatR7DTT6nBiLZ5DKinKZ0hOdM8vXBdzFErfVJJhbGyiVWhMv7mrEW65YrXZUDa3YiK9011NWDgKAaze0qO+/3uNUSn7OTAiUCXnvvHYdGiwBqcxjGIqlUeCi/C4gdhQZA372bJ9Q8iuMuddvbMN7blw/6WeeLleaSuH6Nj9agy61wHn39evhdep4/MSICHAmCvKdYhEoxZNyVs/l9R78yVWr8fariwsWeU9saAuoMbdY5cahAubWgAja5DXgc+rwmOe3J5REV7NP3Qu9oRSCnuI19Y09p/CAWXrTY4jXKxcgrWnxY12rH5s7guM63lrn28mDfGsDs/GefGkbcpvlPAeiqaobXALCWrei0WsLCGcbURiDlQ3y24NuVVq6s8GDsXhGnbvS+z+eFhVy5IK4NPG2EnKeLp0zLlndiO/+yWXYtrwOt2zrgKYxfPCWTfjIyzcBEBbC4Vha5T3IIP/GzW24/71XV3UOO+rc6B5LqjLnTX4nDH3iRZZ1jp/oO/WYdsCReKbqZndy/CiXR7XQmDwaOA8wLDXlyyV/rGzyTrvhhauCkq9K/bnG1zJ+4oM3jEuuqoZaJN66DGnXKR7vWDw7qboh2XdmDG5Dw84VDXjwSLF2+Egsg92rGnCwO6QUmTdcshKxdG5Kn1XeuOWsOpLSQWtHZz36win4nLoKLCdS8q+9oAUnh2KqvJyEMYb1bQHlDZYq11AsjWX1HjQ7dTx4ZBCPHB3C6y9eAZdDw3efPoebnu3D39/3AhIZUa89nsmrARmwT8Z1XgOt5nb9VPy/N21qw4+eEZVrfVNQ8isG+RYlv9SuM1PWNIlr6Uh/FFuX1yn/7nqL77Ocncqpa9A1pqrGjMYzePzkCN5hljvsNMsDWheA8r596xWrReOvCpP/REhPfi5fQG8oqTowyioRpUF+KpvHscEYbtgkOkLeuKkNX3v0pAoixgf5mQkniyvWNWPfR25SQWvaUu6t3OLL6iVuCbjUrqHkUF9EJRFK6j1OUSXIrC0OiPvo+KBoxBVKCFuZVM6+9fgZhBIZ3LlrRcX7V/Y+eOKkqKA10fnWNAaHxmwlNCXr2/yiokadBxe0BwGIHIc6r4GOOg8YE+pzwG1gdbMPP/uLK9XCoLRtvfwO2uuKuSRXrmvGd548g2g6N2VhpVasbPLiO2+7FNs76/BDy07P1s46rG3x48RQbEIlXwTeYlDxOnVEUrmyu3SaxvDhl2+2PSYXDm1BN5r9TgxE0jbhoT3ohsuRVbaEzgYPjg/G4HHadw66mnzqtfIFUaku5cujJ5TEz5/rw47OeqSyeXiclYO6Oo+B37zvGgDChiQD2nAyi9agWzTpS+cmFRVsSr5lMe916ohn8tD1oue+NeASXexNq2V7FUH+my5dqXac5hK3oZUN8jd1BFRVss4Gr6r8Aoz35MdMu2qzX1ROqrRLW8r6Nj9+dWig7ELz8rVNuO/Pr1T/vrirmGfXEnDh+GBMHV+1ldisXLSqAb85PAiPoWPXqgZ4nQ78+J1XlM2jkshYgbGJv1OPIZX8TNVzrt/lMPO+SMlfFFhXklNRJKtBZW+X2nXMVvPlgtXpBPgAIK1hHJi+XUcXg4i1FfxUkm/3nRnDhSvqUec1bAmSYpXsxBf/YCc+equYZN565Wq8+4apqWMqyJ8gSC/lPTeuxy/efSVWNfmUb3Gi5NSN7UF86o4dZRUG666DHDiiKVE67o5dnbhhYyv+9uaN+LtXbMYbLl2JTK6Ad/3vMwA4ltd7EEnlVAUYSenAIoOvqQT5V21oUTtSlRRhK65JlHw5SQ6ai5JaBj+d9aJJ11GzqskZs8byqiavWnCXNsICxCLL69TVdfXrQ/3IF7iqZS3zMKwT/E2b2/BHV3ThdReLVh7WROZqz+/yBlEuTSrS8v3aLA2ogGKQf6gvgnyBq3KkN25qRa7AcXIojma/Cz2hpOpBAABD0dSkk4VUVmV1HdURu8xncBnF67Y14EIsbb/eDvVGsHmZSLKW36tU8gFhaQNETXVABAmjiSwafE40+1y4ZkMLnu0O4W9/+Bz+8vsHxgXlkv6ICJqktWeynRNDF/lLmVzBlhze6HNhVZMP2zvrbAlv9R7hh5Xb/fJ737q8To2hRbtOHl/57Ql8y6xg0x4sihZvu2oNhmOywlB1CeSzwRXrmhFwGyqJfWWjF0G3gXWtfhwfnDjI/+xrd+Czd14IoDi2VbLilSLz0Jr9LvX5rYvHlY1eZdUAivYOr1OH2zLWdDX5bO8Z9IgciadPjyKdK+DFwahqhlUNUsnnnCNkJv/LheJU7DrWBbTX5UAik1MlNAGxuBmIpnFqOA6PoVdlk7xz9wq88dJVVX2OWuLSNVvirbT6bbLsdlnV7TqPYStlnTPLY/ucDnTUubGqyVcx76uUN122Cp989baK12Al1rWK/j9HzeaX1VZis3LDRpG7kczm1SJj6/K6CedxKRS1BdwT7ha4DG3KQT4AfPiWTSo/cyFDQT4Aw5xQDJ2pG79WuM0GFqW18qWSP5VgdTI0y8063fwwp6Oo5MuXs5bRTOfy+Lt7n1cNce7d36MWAfF0Dof6Iri4qxFesxNivsCRN5MEm/wu7FrVOM4GMxVk8DfV88YYw/J6t6rBPVF1nYmwVhmwDlY+lwMv3dKOr/7hbvzZtWvhczmwsT2I/3zjRfjmWy/B7//2eqxt9SOczKqGHsvMILF0MpaVgcqVz6yE3+VQvvjJqusAkyv5codJNi6rtqNtNTg0hvWtfpV8e//z/Vjb4kN70K0W2ZW+H69TV3kNvz40gOX1HlUjXn431oV6a8CNv791izon1ueqHdB3dNYDAH72rFCQr97QjIDbYesyCxQ7kso8DNmheufKBvVef3RFFwCRKCoRSn5159ftsNt1yir5DquS70YqW7TAjMYz6I+klNK92iwBWOcx1G6NLMUnd8TiaVHKstEryjfe/dZLcPDvX4r333wBfnKgF1/93Ymyx9oftlt6JgueDJ0hkysgky/YzkeD18DX77oYH7tti81bK49XPlZuF1aO57F0Dp/45RH8eL/Y7bIqe1evb1a5BvOl5FuR95r8jmSQlCvwCT35skmWtLWVq5NfDhk0tQSKfUWs6u4/v2obvvD6C9W/V9jsOsVrbbXFriOPqdHnVLuWoUTWbIZV3dgtE2+jaVGJzroQnWz8Fzk94me7J19HNs8RTWUtSr4bQ5EUnj49hp0r66sOeucDoeQXVfqhaBoBt0Plpjgdmu3e6ahz2+w6MvfQ59Lx97duwedfd2HV791R57H1pKkWOX7KruBt01hIb2jzK2teJatuKS6HBo1h0lLnHkNHKpO39fKohtdfstK2Y7FQoSAfUApo0G3U/AaX1onSWrWyrN1kisRUsHrYp19CUwys6WxBVZqwevKf7wnjW0+cwSMvDqEvnMR77zmA+w6K4OfAuRDyBY7dXY2WmubFdtG18K/JCWw65225ReEopxRXgwwkGbMHBJU8/rds68DVG1rgNnQE3Q5Ek1ml5L9ixzI4NGZLKAOKSn5pbd7JkJUqypXdLEUq+ZVsODLIPmmWZZsowWk6XNAewOG+KHpCSTx5ahS3X7gcjDH1vVaaxGUJvFQ2j98fH8aNm1rVPSu/m4kCgKBtG7+687uxPQC3oeEXz4mKOisbvfj31+/En18ndqFKE28fPzGCda1+pYrqGsMt29qxpsWnqlUcsQX5lb3gpbgNUUJzIiXfateRW+Ny/JFJq1L5kwptnddQi0pZik8Gc7F0blx3bsYY3nntOqxp8alOp+JzRXDbF3+PkVga/eGU7XNNZo8ydE3ZdeTn0pgYl1c2edHkd9mCfPldqsm/zJggk/Nlads7d3Xik6/eZjtvjDG887p1YMzeSXO+kOLBpg774hWovCi3IseiapV8ed5aAi415lu/a9kESyJ/9pgdbwFxXbYFXfC7HLYqLHIRal00VKvkSyFCWlLqvU5lvZlsx13TGPwuBzRmT0CWi32h5JtBftCFgWgaR/ojCz5ocznsnvzBaMr2vdV5DNt9sLzeo/JqgOI44HM50NXsG2dJnQ1k0upjx0dEmdcq5qdSGGPK/lgpL6Xc3/icjopJtxJp1yntW7RUoCAfRU9+LQNuSbHDp33LPJbKwaHZu4/OFGtcP9NmWKlcXqldVruOTDwcjWdUMqJUMPeeHgNjogueSpJM5yyd5GYeKE5XyQeA5fXFiWqiEpoTYQ0krcdQzesFPQYiqazySN+8tR3PfPSmcSXMZJA/Vb/fa3evwJffeBEuaJt84HZPouQ7dA1ep65U3VrbGF6ythnDsTTu+vpTAKCCX3kPVjqfsgTe4ydGkMoWcP2mYgm+opI/wRau06Huk2oHdIeuYXtnvfLBL6v34LqNrarqS8AlVMNIMotsvoCnT4/i8jX2akN/f+sW/OwvrsTyeg8CLofy5WfzBVHLu1ol35J463RoZReXHptdp2gpA6DKMspOobIEoPTkAyJQB0SyMgCbJ7+UVY1e1dIeAH70TA+e7Q7j8ZMjGIymVb1tYPLzLYP8bL6gFgSyUZykLeAyA/9il1y5eC8X+Enrmhy3btjUVlaNvG3HMjz5oRuwag6bG1Wis8GDD92yEa+/RFjMph7kiwpLpXXeKyF3QFoCLrWYr5RoDxQ7Qzd4DeWv7zJtH4wVc1RE4q34+c2Xd1mOr0q7jvn9yiTveo+hhKLSUteVPlejz2W7fqw7hHLHqy3gQr7AUeDFrvMLlXF2najoICt7AYggv3iNyABXKvgyn2m68990qPOIXJlMvqB6EEyHG8yxfip2oVdftBy3bO2Y8Hfcho7BaHpccYClAgX5gKWUWG39+AAQdIuBxNrMA4CZPDS+TOBMqIWS7zSbYaWzBVV32WrXkZPlWDyD4bhQWGQAsffMKDa2BxF0GyoYj2fyqkZ+LbpFShVoosTbStiU/GnadZbXe+AxRB1mqyJVzcRV5zEQSeaUHzvodpS1GFy0sh6fumP7uBrSk+F0aHjZto6qrqmikl/5mve7HKpJTi3tOgDwmouW442XrsTxwRh2rqxXwZW0CVWyHHkNoeQ/eGQAXqeOSy2Tcjm7TilS4QOmtoi6yKzW1BZ0jQueNI0h4HIgnMzi2e4wEpn8uJKihq7Ba5YF3dAeUEG+XABX2zVRBvnCPlO+j4L1+GTQdnY0gW/sOYVHjw+jPehWFgap5Nd7Daxp8aEl4MLT5mJdBgijiQzimXzZCXBVkw9nR+KqH8RDZgWhR44OIVfg2LmiHgFzQTxZjXnDwZDKFlCwlHAsvT4duoa2oNu2A9Up7TplFEJ5LuS41TLBeZ5PP74VxhjefvVapeivaizmqlSr5Fdr1QGK816z36l2XiYKdrYsq8N33nYprtnQoirlWDu/SuU86HZgZZMPhs5w565O9V1WreQbdiW/wedUx1VN7pxsiGfFOq7IBYrMgXBoDDtX1ld1bPOFq0zibUvAbVPyrfeBtKpIBV/WzPdPc/6bLjI/aTpWHcmV65rxT7dvUYp+NXzs9q14+fbJg/wec3yYjY7W8w1V10ExyJ8NJT9g3kzhkuTVWCo3rUB1InTLhD/TZlipXH5c7WwA6DabAY3EMypAiaZzKBQ49p8N4VU7Re1tr8WmJGvkT8XvVglNE63LN7YHJ//lEqxltKarZGgaw5oWH/IFbgvsq7H/BN0GMmadbqDyRMUYw2t3r5jW8VWL2yGalUyk9vndDgxG03DqWtVb/9XCGMM/3r4VbUG3LSAu2nUqePJdou72Q4cHceW6ZtvxB90G3nPDelxzQUvZv1W/5xFVZKai2sjJv1zjGEDYXcLJrKokc+kEiuCmjgC+/cRZXPovv8Gdu8T3XO2Cw2UIJa+vxApjxRbkm7/zpYeP47ET4tiu31icJHetasCaZh82dwThdTrwqddsxx/9z9No8DrV9Snrb5dTd1c2esVCPp5BMpNX1atksN9e58G6Nr+tVnolDF1TwYg8H+Xec3m9x1Zmc1l9ZSVf7ljJcWuhd6csh0PX0NXkw7HBWFVB/ppmv61612TctLkNQ9E0ltV5cNmaJlzS1ThpJ1fZHEjulFibQgUtSv6Nm9pwcVcDOuo82NAawFOnR6sqDACUV/I3dgTR4DWqGo+6mnzQdfs8aFPyzftEWtq2TJLIuRBwOTQluokmgmk0+53qfqnzGDbhSM55xwdj+Mi9z+M1Zjfa6dpVp8v2zjrcd7B3RrZPXWO2HaFa4XfpqjDKTBYhC5WFfUXPEbI0WDlVdaYYugZfiRoOiMDY76rt+1kTyGfWDCuPdFaH29DQ7HcqPytgt+tIhT6WyiGWySGWzillUAbRCZuSX5sJ9pfvuWpaf+c2dFUOcSaD3J9ctQaJTN42IXirUEakwiK74s7GorJaXIY+acAgE5ysjeBqia6xcdWViom3FZR8p47fH4sgV+B430svGPf8X940eQO5gNuAy5Gu2jYAADvN9u6V6jLXeYpB/gVtgQmv9Xddtw7tQTfuO9iLLz58HED1Qb7boSOTK+BIf9RmhbH9jqmAaqyoyD51ahQb2vy46yVdalcCEMl0D/31terf121sxTuvXYveUFIFRLIilSw7aUVaN86MJHCoV3QbvnR1I540k4876tz4k6vWqA66E+HUNVXuTx53ufJ+H7xlk/IYAyLgfO+N68surBy6BkNn6p5rXgCJtdNhXau/6iD/716xaUqvvbbFj797hah4tqEtgO//6eVV/22jzwmPoeNC8/4AirsvQbcBXWOq/PL6Nr8I8qdQXQeAqq9e5zVw6/YO3LK1XVm1JuLzlmRhidx5AIp2HbmDc0lJU8aFiEsvJt4eHRDVirYsq4PHqcPn1G2efPlvQHRgf+jIoNrZmEu7DgBsN5Nvp1NZZ7Z513XrsHV5HZbXe3Bpic1yKUBBPoqe/NkI8gHhKy315EdT2aqzxKtFt1XXmVkJzXSuAJdDx2VrmvD1PafE8boNta01Es8odS6WzilfvjyHUq2JZ0TSXmkC1HyxvMEjgvwZbFe+0tytkBYFoHolHxALJV1jVU92s8Hrdq+Y1H8qA+65DIyKE1SlIN+BXIHjkq5GtWs0VYJuB5p85a0ulWgNuvHqi5bjpk3lLVR1HgNjiSyODUTxalMtq0RHnQd/fv16XLm+Ba/80h7x+lWeY6uFYWOFpDlpxRKNjMR3mCtwXLmupaqyf++/eSOAon/3hKnOl+uVsdLsMH1mJI6Hjgyiq8mLW3csU0F+W9A9rltkJRw6U+VRZXffconhu1bZgzG3oU/YHdzt0BFN5+A2tKp6SCxE1rf68UtAVdCZiLmsDlPnMfD0R260nVcZWJYuSGSuUdWefDPIH5CJtx5xz1Y7t5XbpbQp+eZxLK/34J3Xrp313dNa4DaKibePmztzcif03Tesx+ZlQWVHlA3SgGKTyud6RL7NXAf5W5YFUe81Ko5Z88n6tgDWV5HHtlihIB+za9cBpMpXYtdJ52ruAdVqUV3HbIaVyoqOl9dvbMVXfncSjx4bxs1b2tEdkkp+WtWWjlqSSaVararrZPIYjmXGJUDNF531Hhw8F6rJtixjTGXmVzNxyW3snrFkzfMxpsqV65txZQUlWCIni1r78SciOEnibXvQjaDbgc+9bse0LWlrWvxVWwasfO61F1Z8rs5j4OlTY8jkC+OC0EpcuKIet+1Yhl881zclJV+yocLEJH/H69RtY9olq6emVHoMHYwVOxMvKxPkr2gUzagO90Ww58QI3nTpKuW/NXQ2JYueoWuqQpFL13DHrk5ctW7ia7QaXIYI8pv9s7MjNRe8+fIurG31z5oQNRNKiyAoT35JjsRla5pQ7zWqbiwp7TrHBqJo9rtU0D8TrOO+tHJpGlML24WOy1FMvH3sxAhWNXlVdal3XLNW/Z7XqSPoMdQ4+qJZo17+fyYi13TwuRx4/AM31LTQCFEdFORjdhNvAbF9Wa66zprmWVTypxvkq2ZYou33rlUNogvh4QHsXtWgGtWMxjIYsSTelir5Vk/+SCy9YNo/X9AuOtZON0AsRfYDqEYZkcpWTyg5rTJic43MGZnLIH+yOvnvvmE9/vjK1VMuL2rl46/cigKfgmm5CmS+BTBeaZ6IT7x6G+56SVfViw6rOlmp/J2063idui0A2z3F8oCyBF0snRPJ5mWuWZdDR0fQjR/s60YmV8D/29KGC9oDcGgMbUH3lBb2hq6pxj1Oh4Z/edW2KR1vJWSCZa3sgvNBS8CF2y+c3s7VXGOtrmPlgvYADnz0pVW/jtyRenEgqnIAZko5T/5iwuUQ83O+wPHkqRG8fFv5pNKg2xBKvnn/yxyNvPlDLfvzVMt0hBVi5tCyCtY6+bNz4dd7jbLVdWqeeFsjTz4gquK4HBocuobrLmjBI0eHcNZMwNuyLIh4Jo++kEiIiqVziKRk3X+7pzphJuUtlNJU77hmDX7+7isn/8UqkQNXVUq++X2Hk9kFqciVElBB/tz5KCerk+90aDMK8AGRCzBRB8TpIAObtqCrom+/HD6XY0qLAhnAB9wOtFfwt8rgxeMU1bEYA9a0+KbVgl0GRR31lUvfrWzyIpTIotHnxO6uRrgNHZs6gkphrBarJ7+W34/c2WhZIELDUudl2zrwp9esnbEdVc7LBV5sDDZTbEr+Igzy3Q7hyT/UG0E0lRtXxUsiyqG6bYsaefsyVn2FI2Lxs/DlxDmgWCd/dgKvOk85T36u5vagmij55oSYL3ClpFy/qQ33HujFD/Z2AxBJNM+cDeGU2Q3V5sk31T6vxZM/FE0vmNJkLocOl792A5z8nNXWyZfMZ9JttchJutaNsCZ8T7UTtPDPjxX53e5a1TCrlhAZmGxsD1R8H49RXHgyxtDid+ElFYKByRC2u7StMlUpXU0+PHFyFDdualU7ZJ977Y4pnwfhyRdBfi2sGRJ5zqazyCGmzqaOoGrkNROs10AtXg+wizGLMdB1OTTkChy/Pz4MAOP6cUi++Ac74TF0W27Txasa8dTpUbMb8OK0rRFTZ3HNpLOE4Zh9u044mQHnHIyJ1u3pXKH2ibeWwH66dhTrwCr9czdtakNrwIV79p4DIMphAVD2hGjKWvvdUH+ra2LS7g+nbG3klxKyRXs1Sr41sJ+tBWUtmQ+7zvbOOuzorMOGNv/kv7yAqFNB/uw205FKfiU/vvgd++7Sd99+2bQDXLl4LZd0K5Ee6/+3pV09Np1ENkPXlK3AmGbhgHJ4KMhflLhmIcg3dFE6OJMrqHtpMeFyiPti/9kxdNS5VY3/UmTfERFzAJwDL93SJoL8OfbjE/PL4rvKZwFjtu06HgPZPEfC7Don1apa++JqadcBioOsx6njL8xShw1eAysai4lT9V4DebNeL1AMZBlj8Dp1dI8lkckX0LEAS2fVAq+lkslkuBy6zW6x0JElXufSrrOi0Yuf/PmVi84/LUvDTVQfvxZI68lE7ejlNSaD27Ut/il1ibSi7DoTLNJftrUDb7ps5aSJ3JPhtAxgtVTyZUWipdjoZikjrwGnQ8Oaltp1IpaL38Vo15Fz8gu9karOicyrcTk0XLNB9A+Z68o6xPxCQT6Kk8tsqauybrD05ctKNP4av59WgxKaVvXEOgi+bvcKrGz0YlWTz+avl4pBbygJr1O31S/2OR04OSQsPUtVyfdOwZMPWJLSFoGSf+maRty4qVV1kiUqc/3GVvz4nS+pulzkdFnV7EOz34nLJqjnLO/bWkzmcrt/IiV/dbMPH3/ltkk72k6GVb2vZRUOsussTuQ1sKHNX9McDXlNL+YgvyeUxJrm6sZlr1PH2hY/VjX5oGtszhthEfMLfdsArt7Qgndeu3bWLAKy1nMokcHyeg+iaRHs117Jn7knv5ySLx//ztsuRa7AbQ1qVjd5cfBcCL2h5LjA1evSLY10ppaEt1jwOHXoGqs6KAm6DQxE0otCyV/b4sfX7rp4vg9jUaBrDDtXVp9AO12W13uw9yM3Tfg71h24mVK068z+It0ayNUyqCO7zuJEzkWbptHdfCKKSv7i0zjdlnmm2t2NlY1ebOoIwunQsKLBQ3ad84wZRRqMsU8DuBVABsAJAH/EOQ/V4LjmlEafc1br5Mq6wTL5NqYq0dQ68bb487SDfMvk6ipROqRNp1Dg0DWGfIFblPzUuBJ7PqdDWZTmIkiYD7xOXSU4VoPM+1gMQT6xOGGMIeB2TNuiY0UF+fWzf/86ZsmuI4O5lgDZdRYTojO1NqXqU9XgdS1+JR8Q/T6q4dtvu1Tt8v/lTRsWZcIxMX1mGmn8GsAHOec5xti/AvgggL+d+WEtLYpKvhnkp2cnyGeMQWOi5FgtlHx3hYlW0xgavAaGYxnV1r4/ksJOS2tzoKgk6hpbsirajZvaynblrITM+1gMibfE4uXut16ClY3VNR2aCNnJtCM4+ztxTotKUdMSmmZQ0+RbmmPQUsXvcuDhv762YqnY6eIzd19rXUZ3LpCJtwCwprk6Jd+6mFksvRaI2jGjKJNz/ivLP58AcMfMDmdpUvTkiw6xsVlKvAVEGc0C59OurmP11ZYq+VYafU4MxzKqrX2+wMdVJ5IBQmvAVbPmUwuNl25px0stVUUmg5R8Yi64qEbWocvXNuHsaGJOmrdZgy5nDQOwOo8Bj6HXZGeDmFuWTbHXQjV4nY5Fq2ZL4c3l0Kbch4I4P6nlyP1WAPdUepIx9nYAbweAlStX1vBtFz51JXadYuJt7SdOTQNQmF0lHxBBvs+po8Wi0JcGrnJbdKkm3U6HOhXkU8BBLHxu2NSGGza1zcl7GRXygWbKH12xGjdsaptS911i6eJz6YvSjw8U74vVzT66nomqmDTKZIz9BkA5qfLDnPOfmL/zYQA5AN+p9Dqc868C+CoA7N69u7Y95Rc4bkMMKuFkiV3HVftATzTE4pjuHGmdXCdS8jvqPBiK2hNISxNv1VY/BfkKeY5IyScIO7OVeNvocy6YjtvE/HP1+pZFu6sj5+e1VfrxCWLSSINzfuNEzzPG3gLgFQBu4JyfV8H7VKj3OBFKCLtONJWFrrFZUROkLWb6dp3q1LT333wBoqmcrUxf6Za+rB3ftkRr5E8HeY5mqycDQSxWDMuYVcvEW4Kw8ppdnXjNrs75PoxpIefkWvYNIJY2M62uczOA9wO4hnOeqM0hLU3qvYatuo7fNTutpXXzNWti15lEye8wS4K7HBrSucJ4Jb+KRjrnG2ua/fA6dbTMYYMpglgMWO06izEpkiBmmyavA7s6/bh+Y+t8HwqxSJipnPhFAC4AvzYD1ic4538646NagtR5DIyZSv7J4bit1nwtkXNjrevkT0TA7UA6lhnnM5dK/lKtkT8dbtjUin0fuakmNcwJYilht+uQ35ggSnE6NPzHq9dj2bLZ78lBLA1mWl1nXa0OZKmzqSOIbz9xBj/e341Hjw3jr1+6YVbeR9bDnX7HW0t1naqDfFFOc3ydfFLyS2GMUYBPEGWQJTSdDm1WdjkJgiDON2hPdI74i+vXwevU8Zf3HESdx8BdL+malfeRXvzZtutYkaVAS+06rUE3dI3VpF43QRBLG9kMq5blMwmCIM5naDSdI5r8LrzvJqHev+3K1bNWQnHGdh196nYdFeSXVCz4f1va8eu/vJoSbwmCmBRp16GkW4IgiNpAJT7mkDdf3oVVzT5csbZ51t5jpom3hs7AmHgdR5WKml91cbVfTrrGqm69TRDE+Y304ZMfnyAIojZQkD+H6BrDdRfMblb8TO06jDE4dW1Kfx+oYNchCIKoFicp+QRBEDWFgvwlhozNp1snHxCT7FRK2AUqKPkEQRDVYpAnnyAIoqZQVLbEUEr+DLa8XQ5dVbqohjUtfqxo9FSdqEsQBFGKQ9l1KMgnCIKoBRTkLzFmatcBRMLtVLbM//DyVXjjpSun/X4EQRBSwa824Z8gCIKYGArylxgytp9JkO90aFOaaBljM9o5IAiCkB1vScknCIKoDTSaLjEcNVLyXWS9IQhiDqESmgRBELWFRtMlxkxLaAJTV/IJgiBmimHpeEsQBEHMHLLrLDG0GTbDAoDL1jTBTRMtQRBziFTyya5DEARRGyjIX2LUQsn/0C2banU4BEEQVUF2HYIgiNpCo+kSQ6tBCU2CIIi5Rtl1SMknCIKoCTSaLjGkkj+TZlgEQRBzjZOaYREEQdQUGk2XGHKnm4R8giAWEw6y6xAEQdQUGk2XGBpj0DVRu54gCGKxYFDHW4IgiJpCo+kSQ9fYjJJuCYIg5gNKvCUIgqgtNJouMTQ2s8o6BEEQ84FT16BrDB5qxEcQBFETqITmEoOUfIIgFiOaxvCVN+3C9s66+T4UgiCIJQEF+UsMr6HB6yQljCCIxceNm9vm+xAIgiCWDDWx6zDG/ooxxhljzbV4PWL6/OHF7fjky1fP92EQBEEQBEEQ88iMlXzG2AoALwVwduaHQ8yUZp+BZp8x34dBEARBEARBzCO1UPL/DcD7AfAavBZBEARBEARBEDNkRkE+Y+x2AD2c84NV/O7bGWN7GWN7h4aGZvK2BEEQBEEQBEFMwKR2HcbYbwC0l3nqwwA+BGHVmRTO+VcBfBUAdu/eTao/QRAEQRAEQcwSkwb5nPMbyz3OGNsGYDWAg2Z31U4AzzDGLuGc99f0KAmCIAiCIAiCqBrGeW1EdcbYaQC7OefDk/3u7t27+d69e2vyvgRBEARBEARxPsIY28c5313uOep4SxAEQRAEQRBLjJo1w+Kcd9XqtQiCIAiCIAiCmD6k5BMEQRAEQRDEEoOCfIIgCIIgCIJYYlCQTxAEQRAEQRBLDAryCYIgCIIgCGKJQUE+QRAEQRAEQSwxalYnf0pvytgQgDNz/sa1pxnApH0BznPoHFUHnafqoPM0OXSOqoPO0+TQOaoOOk/VQedpcqZzjlZxzlvKPTEvQf5SgTG2t1IDAkJA56g66DxVB52nyaFzVB10niaHzlF10HmqDjpPk1Prc0R2HYIgCIIgCIJYYlCQTxAEQRAEQRBLDAryZ8ZX5/sAFgF0jqqDzlN10HmaHDpH1UHnaXLoHFUHnafqoPM0OTU9R+TJJwiCIAiCIIglBin5BEEQBEEQBLHEoCDfAmPs64yxQcbY85bHdjDGHmeMPccY+yljLGg+bjDG7jYfP8wY+6Dlb25mjB1ljB1njH1gPj7LbFKr82Q+rzPG9jPGfjbXn2M2qeG19JeMsRcYY88zxr7LGHPPx+eZLaZ4npyMsW+Yjx9kjF1rPu5ljP2cMXbEPFefnJ9PM3vU4jxZnvsqY+xF83y9Zu4/zezAGFvBGHuYMXbIvA7eYz7eyBj7NWPsmPn/BvNxxhj7d3OcfpYxdpHlte4yf/8YY+yu+fpMs0Etz5P5fJAx1s0Y++J8fJ7ZoMbX0qfM1zhs/g6br89Va6ZxnjaaY1aaMfbXk73OUqBW58h8rp4x9n/m2H2YMXb5pAfAOaf/zP8AXA3gIgDPWx57GsA15s9vBfBP5s9/AOB75s9eAKcBdAHQAZwAsAaAE8BBAJvn+7MttPNk+bv3AfhfAD+b78+10M4RgOUATgHwmM99H8Bb5vuzzeN5eheAb5g/twLYByFUeAFcZz7uBPAogJfN92dbaOfJ/PfHAHzc/FkD0Dzfn62G56gDwEXmzwEALwLYDOBTAD5gPv4BAP9q/nwLgF8CYAAuA/Ck+XgjgJPm/xvMnxvm+/MttPNkeb0vmGP4F+f7sy20cwTgJQD2QMQFOoDHAVw7359vHs9TK4CLAfwzgL+e7HXm+/MtpHNkPnc3gLeZPzsB1E/2/qTkW+Cc/w7AaMnDGwD8zvz51wCk8sUB+BhjDgAeABkAEQCXADjOOT/JOc8A+B6A22f72OeSGp0nMMY6AbwcwNdm+5jnmlqdIwAOAB7zOS+A3tk87rlmiudpM4CHzL8bBBACsJtznuCcP2w+ngHwDIDO2T3yuaUW58l87q0APmE+V+CcL5nGNJzzPs75M+bPUQCHIRbKt0NMjjD//0rz59sBfJMLngBQzxjrAPD/APyacz7KOR+DOLc3z90nmV1qeJ7AGNsFoA3Ar+buE8w+NTxHHIAbIiBzATAADMzV55htpnqeOOeDnPOnAWSrfJ1FT63OEWOsDkLs+W/z9zKc89Bk709B/uS8gGKQfieAFebP/wcgDqAPwFkAn+Gcj0J8eecsf9+NJXKxTsJUzxMAfB7A+wEU5u4w55UpnSPOeQ+Az5iP9QEIc86X1GRagUrn6SCA2xhjDsbYagC7LM8BENuZAG4F8ODcHOq8MqXzZJ4bAPgnxtgzjLEfMMba5vSI5wjGWBeAnQCeBNDGOe8zn+qHCEqBymP1eTOGz+Q8McY0AJ8FYLMULDVmco44548DeBhi/O4D8ADn/PBcHPdcU+V5murrLClmeI5WAxgC8A0mLM5fY4z5JntPCvIn560A3skY2wex1ZIxH78EQB7AMoiT/1eMsTXzc4gLgimdJ8bYKwAMcs73zcvRzg9TPUcNEEHcavM5H2PsTXN/2HNOpfP0dYjJcy/EAvExiPMGADB3O74L4N855yfn8oDniameJwfEDsdjnPOLIKwDn5njY551GGN+AD8E8F7OecT6HBf73FRSDjU5T+8E8AvOefcsHeK8M9NzxBhbB2ATxH23HMD1jLGrZulw541a3XMTvc5ipwbnyAFh2fwy53wnhDA4ac6nY3qHe/7AOT8C4KUAwBjbAGEvAYSP+n7OeRbAIGNsD8SW+DnY1cVOAD1zd8TzwzTO004ItfEWiO3MIGPs25zzJRvETuMccQCnOOdD5t/8CMLj+e25Pva5pNJ54pznAPyl/D3G2GMQ/kbJVwEc45x/fs4Odh6ZxnkaAZAA8CPzqR8A+OM5PORZhzFmQEyk3+Gcy885wBjr4Jz3mRaKQfPxHpQfq3sAXFvy+COzedxzTY3O0+UArmKMvROAH4CTMRbjnC+JYhM1OkdvAvAE5zxmvuYvIc7bo3PxGeaCKZ6nqb7OkqBG56gbQDfnXO5w/B+qCPJJyZ8Exlir+X8NwEcA/Jf51FkA15vP+SCSbY5AJMOtZ4ytZow5AbwewH1zfdxzzVTPE+f8g5zzTs55F8Q5emgpB/jAtK6lswAuY6J6DANwA4Sfb0lT6TyZ58Fn/nwTgBzn/JD5748DqAPw3vk45vlgqufJVIt+imIAewOAQ3N93LOFeY/8N4DDnPPPWZ66D4CskHMXgJ9YHv9DJrgMwg7XB+ABAC9ljDWYu2kvNR9bEtTqPHHO38g5X2mO4X8N4UlfKgF+ra6lswCuMa1zBoBrsITG8Gmcp6m+zqKnVueIc94P4Bxj7ALzoerGb74Aso8Xyn8QW/19EAkP3RAq13sgVLAXAXwSxQZifggl7AXzRP+N5XVuMX//BIAPz/fnWqjnyfJ612LpVdep1bX0MYiA/3kA3wLgmu/PNo/nqQvAUYhJ8jcAVpmPd0LsehwGcMD8723z/dkW2nkyn1sFkaz7LETewsr5/mw1PEdXmtfBs5br4BYATeZnPWaej0bz9xmAL5nj9HMQSdzytd4K4Lj53x/N92dbqOfJ8ppvwdKqrlOTcwRRUecr5r14CMDn5vuzzfN5ajfHrwhEQYBuAMFKrzPfn28hnSPzuQshbJjPArgXVVT9oo63BEEQBEEQBLHEILsOQRAEQRAEQSwxKMgnCIIgCIIgiCUGBfkEQRAEQRAEscSgIJ8gCIIgCIIglhgU5BMEQRAEQRDEEoOCfIIgCIIgCIJYYlCQTxAEQRAEQRBLDAryCYIgCIIgCGKJ8f8Dq1MwBc9kftkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, res.factors.filtered[0], label='Factor')\n",
    "ax.legend()\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "rec = DataReader('USREC', 'fred', start=start, end=end)\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Post-estimation\n",
    "\n",
    "Although here we will be able to interpret the results of the model by constructing the coincident index, there is a useful and generic approach for getting a sense for what is being captured by the estimated factor. By taking the estimated factors as given, regressing them (and a constant) each (one at a time) on each of the observed variables, and recording the coefficients of determination ($R^2$ values), we can get a sense of the variables for which each factor explains a substantial portion of the variance and the variables for which it does not.\n",
    "\n",
    "In models with more variables and more factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables).\n",
    "\n",
    "In this model, with only four endogenous variables and one factor, it is easy to digest a simple table of the $R^2$ values, but in larger models it is not. For this reason, a bar plot is often employed; from the plot we can easily see that the factor explains most of the variation in industrial production index and a large portion of the variation in sales and employment, it is less helpful in explaining income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:43.650728Z",
     "iopub.status.busy": "2022-02-08T18:16:43.650284Z",
     "iopub.status.idle": "2022-02-08T18:16:44.097430Z",
     "shell.execute_reply": "2022-02-08T18:16:44.097810Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zno3XF4FXtOV5wE1t+RTgO8A2wIuBB4BD2mVfBY5sy2sGxucYJvD3zRn77HQ98Jp2tvbKqvrlmOX7AZdX1bpq7sT3pU1c/3+0z9fQ/GEBeBVwLkBVraL54z/qsYFtnAu8YmDZaPtzgZ9U1Y/a+ufadT6vbf+fan7yz93EWGe66RirA4FPVnMjJqrqHtb/+Y8avYrk9cDVVfWrqloHPJTkKTSJ/SDgOuBamnFbsImxDqvJHsPvAuckeRtNIoYmOXwqyfXAhTS3xh7rIOCYJN8Hrqa5wdYCmquCHpvkFOCFVfWrTX6H/TLZ43UgcGb7uS8Fnpxkh3bZJVX1SLvNOcClAzHMH1jHeQPPL9vYG/C45SxUVT9Ksg/NLO2DSb41yZt4qH3+PzbvZ2zw4gq/3vJwhtcQjNXY9Tw2UB6tb00zU/9QVX1yC7YxlCZ7DKvqHUn2Aw4DrknyUuB44C6amd9WwIPjvDTA8VW1/HELkle16zsnyUdrFp+HMQW/c1sB+1dzAbbfSnNH8ofabT6W5JF2cgK/+735bVjrKa93g5plkuwKPFBV5wKnA/sAv6LZfQrNf/N/kuRp7XGeybga4BXAX7fbfwHN7vhRW9HcG4C2z3fGef0twPyB40tvAv4buLltf3bbfvQkxDpjTNNYfQN4e9oTFpPszPo//4laDrxldKaSZLckT5+EWGe8yR7DJM+uqquruWrnOpobZ+0E/KyqHqMZmznjvHQ58M6BY7d7tseTn0VzyORTwKfb+GatKfid+zrNP16j6997M8L6q4HnKzfW2Rn77PRC4PQkjwGP0BxTfRlwaZI7q+pP291yVwL3Ad+fhG1+HPhskpuAm2h2/Y76NbBvkpOAu/ndD/FvVdWDSY4FLmwTzgrgE1X1UJrb+F6c5AHg2/zuF7APpmOsPg3sCaxK8gjN8cYzx/v8J7rCqvp6kucDV7YzlfuBN9KMd99N9hienmT0nJJvAT8Azga+kuarjJcy/p6uT9Ps3r02zSCsA44EDgDe2471/TTHcWezyR6vvwPOSrKKJudeAbxjwy95nKe2r3+ICUxevKSspl2S+6tqh433lKTZJckamhONJ3w/d3fFS5LUI87YNWFJ3sfjjyddWFX/NB3xaP0cq+HnGA6XmTReJnZJknrEXfGSJPWIiV2SpB4xsUuS1CMmdkmSesTELklSj/w/uJu4ZzmbvBUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coincident Index\n",
    "\n",
    "As described above, the goal of this model was to create an interpretable series which could be used to understand the current status of the macroeconomy. This is what the coincident index is designed to do. It is constructed below. For readers interested in an explanation of the construction, see Kim and Nelson (1999) or Stock and Watson (1991).\n",
    "\n",
    "In essence, what is done is to reconstruct the mean of the (differenced) factor. We will compare it to the coincident index on published by the Federal Reserve Bank of Philadelphia (USPHCI on FRED)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:44.100540Z",
     "iopub.status.busy": "2022-02-08T18:16:44.099943Z",
     "iopub.status.idle": "2022-02-08T18:16:44.810005Z",
     "shell.execute_reply": "2022-02-08T18:16:44.810699Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n",
    "usphci.plot(figsize=(13,3));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:44.813971Z",
     "iopub.status.busy": "2022-02-08T18:16:44.812994Z",
     "iopub.status.idle": "2022-02-08T18:16:44.826398Z",
     "shell.execute_reply": "2022-02-08T18:16:44.827035Z"
    }
   },
   "outputs": [],
   "source": [
    "dusphci = usphci.diff()[1:].values\n",
    "def compute_coincident_index(mod, res):\n",
    "    # Estimate W(1)\n",
    "    spec = res.specification\n",
    "    design = mod.ssm['design']\n",
    "    transition = mod.ssm['transition']\n",
    "    ss_kalman_gain = res.filter_results.kalman_gain[:,:,-1]\n",
    "    k_states = ss_kalman_gain.shape[0]\n",
    "\n",
    "    W1 = np.linalg.inv(np.eye(k_states) - np.dot(\n",
    "        np.eye(k_states) - np.dot(ss_kalman_gain, design),\n",
    "        transition\n",
    "    )).dot(ss_kalman_gain)[0]\n",
    "\n",
    "    # Compute the factor mean vector\n",
    "    factor_mean = np.dot(W1, dta.loc['1972-02-01':, 'dln_indprod':'dln_emp'].mean())\n",
    "    \n",
    "    # Normalize the factors\n",
    "    factor = res.factors.filtered[0]\n",
    "    factor *= np.std(usphci.diff()[1:]) / np.std(factor)\n",
    "\n",
    "    # Compute the coincident index\n",
    "    coincident_index = np.zeros(mod.nobs+1)\n",
    "    # The initial value is arbitrary; here it is set to\n",
    "    # facilitate comparison\n",
    "    coincident_index[0] = usphci.iloc[0] * factor_mean / dusphci.mean()\n",
    "    for t in range(0, mod.nobs):\n",
    "        coincident_index[t+1] = coincident_index[t] + factor[t] + factor_mean\n",
    "    \n",
    "    # Attach dates\n",
    "    coincident_index = pd.Series(coincident_index, index=dta.index).iloc[1:]\n",
    "    \n",
    "    # Normalize to use the same base year as USPHCI\n",
    "    coincident_index *= (usphci.loc['1992-07-01'] / coincident_index.loc['1992-07-01'])\n",
    "    \n",
    "    return coincident_index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the calculated coincident index along with the US recessions and the comparison coincident index USPHCI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:16:44.830719Z",
     "iopub.status.busy": "2022-02-08T18:16:44.829332Z",
     "iopub.status.idle": "2022-02-08T18:16:45.684105Z",
     "shell.execute_reply": "2022-02-08T18:16:45.684461Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "coincident_index = compute_coincident_index(mod, res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, label='Coincident index')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix 1: Extending the dynamic factor model\n",
    "\n",
    "Recall that the previous specification was described by:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Written in state space form, the previous specification of the model had the following observation equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp}     & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "and transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "the `DynamicFactor` model handles setting up the state space representation and, in the `DynamicFactor.update` method, it fills in the fitted parameter values into the appropriate locations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The extended specification is the same as in the previous example, except that we also want to allow employment to depend on lagged values of the factor. This creates a change to the $y_{\\text{emp},t}$ equation. Now we have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\qquad & i \\in \\{\\text{indprod}, \\text{income}, \\text{sales} \\}\\\\\n",
    "y_{i,t} & = \\lambda_{i,0} f_t + \\lambda_{i,1} f_{t-1} + \\lambda_{i,2} f_{t-2} + \\lambda_{i,2} f_{t-3} + u_{i,t} \\qquad & i = \\text{emp} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Now, the corresponding observation equation should look like the following:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp,1}   & \\lambda_\\text{emp,2} & \\lambda_\\text{emp,3} & \\lambda_\\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Notice that we have introduced two new state variables, $f_{t-2}$ and $f_{t-3}$, which means we need to update the  transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 1   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This model cannot be handled out-of-the-box by the `DynamicFactor` class, but it can be handled by creating a subclass when alters the state space representation in the appropriate way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, notice that if we had set `factor_order = 4`, we would almost have what we wanted. In that case, the last line of the observation equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\vdots \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\lambda_\\text{emp,1}   & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "and the first line of the transition equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Relative to what we want, we have the following differences:\n",
    "\n",
    "1. In the above situation, the $\\lambda_{\\text{emp}, j}$ are forced to be zero for $j > 0$, and we want them to be estimated as parameters.\n",
    "2. We only want the factor to transition according to an AR(2), but under the above situation it is an AR(4).\n",
    "\n",
    "Our strategy will be to subclass `DynamicFactor`, and let it do most of the work (setting up the state space representation, etc.) where it assumes that `factor_order = 4`. The only things we will actually do in the subclass will be to fix those two issues.\n",
    "\n",
    "First, here is the full code of the subclass; it is discussed below. It is important to note at the outset that none of the methods defined below could have been omitted. In fact, the methods `__init__`, `start_params`, `param_names`, `transform_params`, `untransform_params`, and `update` form the core of all state space models in statsmodels, not just the `DynamicFactor` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "from statsmodels.tsa.statespace import tools\n",
    "class ExtendedDFM(sm.tsa.DynamicFactor):\n",
    "    def __init__(self, endog, **kwargs):\n",
    "            # Setup the model as if we had a factor order of 4\n",
    "            super(ExtendedDFM, self).__init__(\n",
    "                endog, k_factors=1, factor_order=4, error_order=2,\n",
    "                **kwargs)\n",
    "\n",
    "            # Note: `self.parameters` is an ordered dict with the\n",
    "            # keys corresponding to parameter types, and the values\n",
    "            # the number of parameters of that type.\n",
    "            # Add the new parameters\n",
    "            self.parameters['new_loadings'] = 3\n",
    "\n",
    "            # Cache a slice for the location of the 4 factor AR\n",
    "            # parameters (a_1, ..., a_4) in the full parameter vector\n",
    "            offset = (self.parameters['factor_loadings'] +\n",
    "                      self.parameters['exog'] +\n",
    "                      self.parameters['error_cov'])\n",
    "            self._params_factor_ar = np.s_[offset:offset+2]\n",
    "            self._params_factor_zero = np.s_[offset+2:offset+4]\n",
    "\n",
    "    @property\n",
    "    def start_params(self):\n",
    "        # Add three new loading parameters to the end of the parameter\n",
    "        # vector, initialized to zeros (for simplicity; they could\n",
    "        # be initialized any way you like)\n",
    "        return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0]\n",
    "    \n",
    "    @property\n",
    "    def param_names(self):\n",
    "        # Add the corresponding names for the new loading parameters\n",
    "        #  (the name can be anything you like)\n",
    "        return super(ExtendedDFM, self).param_names + [\n",
    "            'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1,4)]\n",
    "\n",
    "    def transform_params(self, unconstrained):\n",
    "            # Perform the typical DFM transformation (w/o the new parameters)\n",
    "            constrained = super(ExtendedDFM, self).transform_params(\n",
    "            unconstrained[:-3])\n",
    "\n",
    "            # Redo the factor AR constraint, since we only want an AR(2),\n",
    "            # and the previous constraint was for an AR(4)\n",
    "            ar_params = unconstrained[self._params_factor_ar]\n",
    "            constrained[self._params_factor_ar] = (\n",
    "                tools.constrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[constrained, unconstrained[-3:]]\n",
    "\n",
    "    def untransform_params(self, constrained):\n",
    "            # Perform the typical DFM untransformation (w/o the new parameters)\n",
    "            unconstrained = super(ExtendedDFM, self).untransform_params(\n",
    "                constrained[:-3])\n",
    "\n",
    "            # Redo the factor AR unconstrained, since we only want an AR(2),\n",
    "            # and the previous unconstrained was for an AR(4)\n",
    "            ar_params = constrained[self._params_factor_ar]\n",
    "            unconstrained[self._params_factor_ar] = (\n",
    "                tools.unconstrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[unconstrained, constrained[-3:]]\n",
    "\n",
    "    def update(self, params, transformed=True, **kwargs):\n",
    "        # Peform the transformation, if required\n",
    "        if not transformed:\n",
    "            params = self.transform_params(params)\n",
    "        params[self._params_factor_zero] = 0\n",
    "        \n",
    "        # Now perform the usual DFM update, but exclude our new parameters\n",
    "        super(ExtendedDFM, self).update(params[:-3], transformed=True, **kwargs)\n",
    "\n",
    "        # Finally, set our new parameters in the design matrix\n",
    "        self.ssm['design', 3, 1:4] = params[-3:]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what did we just do?\n",
    "\n",
    "**`__init__`**\n",
    "\n",
    "The important step here was specifying the base dynamic factor model which we were operating with. In particular, as described above, we initialize with `factor_order=4`, even though we will only end up with an AR(2) model for the factor. We also performed some general setup-related tasks.\n",
    "\n",
    "**`start_params`**\n",
    "\n",
    "`start_params` are used as initial values in the optimizer. Since we are adding three new parameters, we need to pass those in. If we had not done this, the optimizer would use the default starting values, which would be three elements short.\n",
    "\n",
    "**`param_names`**\n",
    "\n",
    "`param_names` are used in a variety of places, but especially in the results class. Below we get a full result summary, which is only possible when all the parameters have associated names.\n",
    "\n",
    "**`transform_params`** and **`untransform_params`**\n",
    "\n",
    "The optimizer selects possibly parameter values in an unconstrained way. That's not usually desired (since variances cannot be negative, for example), and `transform_params` is used to transform the unconstrained values used by the optimizer to constrained values appropriate to the model. Variances terms are typically squared (to force them to be positive), and AR lag coefficients are often constrained to lead to a stationary model. `untransform_params` is used for the reverse operation (and is important because starting parameters are usually specified in terms of values appropriate to the model, and we need to convert them to parameters appropriate to the optimizer before we can begin the optimization routine).\n",
    "\n",
    "Even though we do not need to transform or untransform our new parameters (the loadings can in theory take on any values), we still need to modify this function for two reasons:\n",
    "\n",
    "1. The version in the `DynamicFactor` class is expecting 3 fewer parameters than we have now. At a minimum, we need to handle the three new parameters.\n",
    "2. The version in the `DynamicFactor` class constrains the factor lag coefficients to be stationary as though it was an AR(4) model. Since we actually have an AR(2) model, we need to re-do the constraint. We also set the last two autoregressive coefficients to be zero here.\n",
    "\n",
    "**`update`**\n",
    "\n",
    "The most important reason we need to specify a new `update` method is because we have three new parameters that we need to place into the state space formulation. In particular we let the parent `DynamicFactor.update` class handle placing all the parameters except the three new ones in to the state space representation, and then we put the last three in manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 4.959246\n",
      "         Iterations: 658\n",
      "         Function evaluations: 995\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                             Statespace Model Results                                            \n",
      "=================================================================================================================\n",
      "Dep. Variable:     ['std_indprod', 'std_income', 'std_sales', 'std_emp']   No. Observations:                  431\n",
      "Model:                                 DynamicFactor(factors=1, order=4)   Log Likelihood               -2137.435\n",
      "                                                          + AR(2) errors   AIC                           4320.870\n",
      "Date:                                                   Tue, 08 Feb 2022   BIC                           4414.391\n",
      "Time:                                                           18:17:00   HQIC                          4357.795\n",
      "Sample:                                                       02-01-1979                                         \n",
      "                                                            - 12-01-2014                                         \n",
      "Covariance Type:                                                     opg                                         \n",
      "====================================================================================================\n",
      "                                       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------------\n",
      "loading.f1.std_indprod              -0.4001      0.044     -9.177      0.000      -0.486      -0.315\n",
      "loading.f1.std_income               -0.2048      0.059     -3.490      0.000      -0.320      -0.090\n",
      "loading.f1.std_sales                -0.9674      0.034    -28.872      0.000      -1.033      -0.902\n",
      "loading.f1.std_emp                  -0.2093      0.037     -5.646      0.000      -0.282      -0.137\n",
      "sigma2.std_indprod                   0.6606      0.036     18.197      0.000       0.589       0.732\n",
      "sigma2.std_income                    0.9510      0.032     30.113      0.000       0.889       1.013\n",
      "sigma2.std_sales                     0.0008      0.002      0.395      0.693      -0.003       0.005\n",
      "sigma2.std_emp                       0.3960      0.020     20.050      0.000       0.357       0.435\n",
      "L1.f1.f1                            -0.1444      0.042     -3.423      0.001      -0.227      -0.062\n",
      "L2.f1.f1                             0.1483      0.051      2.892      0.004       0.048       0.249\n",
      "L3.f1.f1                                  0   4.72e-12          0      1.000   -9.25e-12    9.25e-12\n",
      "L4.f1.f1                                  0   4.72e-12          0      1.000   -9.25e-12    9.25e-12\n",
      "L1.e(std_indprod).e(std_indprod)     0.1667      0.039      4.301      0.000       0.091       0.243\n",
      "L2.e(std_indprod).e(std_indprod)     0.1981      0.046      4.290      0.000       0.108       0.289\n",
      "L1.e(std_income).e(std_income)      -0.1561      0.024     -6.532      0.000      -0.203      -0.109\n",
      "L2.e(std_income).e(std_income)      -0.0380      0.053     -0.720      0.471      -0.141       0.065\n",
      "L1.e(std_sales).e(std_sales)         0.5487      0.038     14.297      0.000       0.473       0.624\n",
      "L2.e(std_sales).e(std_sales)        -0.9705      0.053    -18.211      0.000      -1.075      -0.866\n",
      "L1.e(std_emp).e(std_emp)             0.2740      0.040      6.899      0.000       0.196       0.352\n",
      "L2.e(std_emp).e(std_emp)             0.4388      0.032     13.539      0.000       0.375       0.502\n",
      "loading.L1.f1.std_emp               -0.2129      0.033     -6.372      0.000      -0.278      -0.147\n",
      "loading.L2.f1.std_emp               -0.1638      0.033     -5.036      0.000      -0.228      -0.100\n",
      "loading.L3.f1.std_emp               -0.1538      0.033     -4.623      0.000      -0.219      -0.089\n",
      "=====================================================================================================\n",
      "Ljung-Box (L1) (Q):     9.64, 0.46, 34.75, 5.09   Jarque-Bera (JB):   234.63, 9638.32, 11.33, 4467.51\n",
      "Prob(Q):                 0.00, 0.50, 0.00, 0.02   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H):  0.80, 4.37, 0.56, 0.33   Skew:                      -0.40, -1.05, 0.18, 1.10\n",
      "Prob(H) (two-sided):     0.19, 0.00, 0.00, 0.00   Kurtosis:                  6.53, 26.07, 3.71, 18.62\n",
      "=====================================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 3.51e+17. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "# Create the model\n",
    "extended_mod = ExtendedDFM(endog)\n",
    "initial_extended_res = extended_mod.fit(maxiter=1000, disp=False)\n",
    "extended_res = extended_mod.fit(initial_extended_res.params, method='nm', maxiter=1000)\n",
    "print(extended_res.summary(separate_params=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this model increases the likelihood, it is not preferred by the AIC and BIC measures which penalize the additional three parameters.\n",
    "\n",
    "Furthermore, the qualitative results are unchanged, as we can see from the updated $R^2$ chart and the new coincident index, both of which are practically identical to the previous results."
   ]
  },
  {
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    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "extended_res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-02-08T18:17:00.308097Z",
     "iopub.status.busy": "2022-02-08T18:17:00.294814Z",
     "iopub.status.idle": "2022-02-08T18:17:00.660784Z",
     "shell.execute_reply": "2022-02-08T18:17:00.661396Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n",
    "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set(title='Coincident indices, comparison')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}