{
 "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": "2024-04-18T11:13:20.593608Z",
     "iopub.status.busy": "2024-04-18T11:13:20.593387Z",
     "iopub.status.idle": "2024-04-18T11:13:23.951972Z",
     "shell.execute_reply": "2024-04-18T11:13:23.951284Z"
    }
   },
   "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": "2024-04-18T11:13:23.955810Z",
     "iopub.status.busy": "2024-04-18T11:13:23.955292Z",
     "iopub.status.idle": "2024-04-18T11:13:25.342799Z",
     "shell.execute_reply": "2024-04-18T11:13:25.341842Z"
    }
   },
   "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": "2024-04-18T11:13:25.347286Z",
     "iopub.status.busy": "2024-04-18T11:13:25.347003Z",
     "iopub.status.idle": "2024-04-18T11:13:25.351855Z",
     "shell.execute_reply": "2024-04-18T11:13:25.351094Z"
    }
   },
   "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": "2024-04-18T11:13:25.354843Z",
     "iopub.status.busy": "2024-04-18T11:13:25.354618Z",
     "iopub.status.idle": "2024-04-18T11:13:25.358977Z",
     "shell.execute_reply": "2024-04-18T11:13:25.357424Z"
    }
   },
   "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": "2024-04-18T11:13:25.362032Z",
     "iopub.status.busy": "2024-04-18T11:13:25.361749Z",
     "iopub.status.idle": "2024-04-18T11:13:25.368936Z",
     "shell.execute_reply": "2024-04-18T11:13:25.368151Z"
    }
   },
   "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": "2024-04-18T11:13:25.371758Z",
     "iopub.status.busy": "2024-04-18T11:13:25.371431Z",
     "iopub.status.idle": "2024-04-18T11:13:27.756794Z",
     "shell.execute_reply": "2024-04-18T11:13:27.756129Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-04-18T11:13:27.760249Z",
     "iopub.status.busy": "2024-04-18T11:13:27.760004Z",
     "iopub.status.idle": "2024-04-18T11:13:27.782696Z",
     "shell.execute_reply": "2024-04-18T11:13:27.782043Z"
    }
   },
   "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": "2024-04-18T11:13:27.787265Z",
     "iopub.status.busy": "2024-04-18T11:13:27.786198Z",
     "iopub.status.idle": "2024-04-18T11:19:51.897570Z",
     "shell.execute_reply": "2024-04-18T11:19:51.896877Z"
    }
   },
   "outputs": [],
   "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": "2024-04-18T11:19:51.901206Z",
     "iopub.status.busy": "2024-04-18T11:19:51.900821Z",
     "iopub.status.idle": "2024-04-18T11:19:51.979151Z",
     "shell.execute_reply": "2024-04-18T11:19:51.978508Z"
    }
   },
   "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               -1475.297\n",
      "                                                          + AR(2) errors   AIC                           2986.594\n",
      "Date:                                                   Thu, 18 Apr 2024   BIC                           3059.784\n",
      "Time:                                                           11:19:51   HQIC                          3015.492\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              -1.0360      0.000  -4821.980      0.000      -1.036      -1.036\n",
      "loading.f1.std_income               -0.3060      0.001   -220.932      0.000      -0.309      -0.303\n",
      "loading.f1.std_sales                -0.5401      0.001   -563.326      0.000      -0.542      -0.538\n",
      "loading.f1.std_emp                  -0.3124      0.001   -238.453      0.000      -0.315      -0.310\n",
      "sigma2.std_indprod                1.038e-06   2.86e-07      3.628      0.000    4.77e-07     1.6e-06\n",
      "sigma2.std_income                    0.9014      0.010     92.547      0.000       0.882       0.920\n",
      "sigma2.std_sales                     0.5861      0.001    924.526      0.000       0.585       0.587\n",
      "sigma2.std_emp                       0.3707      0.008     49.251      0.000       0.356       0.385\n",
      "L1.f1.f1                             0.2262      0.002    104.566      0.000       0.222       0.230\n",
      "L2.f1.f1                             0.2812      0.002    147.530      0.000       0.277       0.285\n",
      "L1.e(std_indprod).e(std_indprod) -1.396e-07   3.16e-08     -4.418      0.000   -2.02e-07   -7.77e-08\n",
      "L2.e(std_indprod).e(std_indprod)     1.0000   9.23e-08   1.08e+07      0.000       1.000       1.000\n",
      "L1.e(std_income).e(std_income)      -0.1846      0.009    -20.090      0.000      -0.203      -0.167\n",
      "L2.e(std_income).e(std_income)      -0.0930      0.002    -40.120      0.000      -0.098      -0.088\n",
      "L1.e(std_sales).e(std_sales)        -0.4240      0.001   -306.301      0.000      -0.427      -0.421\n",
      "L2.e(std_sales).e(std_sales)        -0.1925      0.002    -85.336      0.000      -0.197      -0.188\n",
      "L1.e(std_emp).e(std_emp)             0.3115      0.002    139.142      0.000       0.307       0.316\n",
      "L2.e(std_emp).e(std_emp)             0.4611      0.001    501.810      0.000       0.459       0.463\n",
      "========================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.10, 0.36, 0.02, 0.58   Jarque-Bera (JB):   3285772.52, 11730.80, 56.86, 242.33\n",
      "Prob(Q):                0.75, 0.55, 0.90, 0.45   Prob(JB):                        0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.00, 4.57, 0.53, 1.07   Skew:                          20.68, -1.25, 0.40, 0.25\n",
      "Prob(H) (two-sided):    0.00, 0.00, 0.00, 0.69   Kurtosis:                     428.74, 28.43, 4.59, 6.64\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 1.09e+19. Standard errors may be unstable.\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": "2024-04-18T11:19:51.982296Z",
     "iopub.status.busy": "2024-04-18T11:19:51.981888Z",
     "iopub.status.idle": "2024-04-18T11:19:53.482715Z",
     "shell.execute_reply": "2024-04-18T11:19:53.482076Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-04-18T11:19:53.487255Z",
     "iopub.status.busy": "2024-04-18T11:19:53.486131Z",
     "iopub.status.idle": "2024-04-18T11:19:54.530052Z",
     "shell.execute_reply": "2024-04-18T11:19:54.529388Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-04-18T11:19:54.534547Z",
     "iopub.status.busy": "2024-04-18T11:19:54.533458Z",
     "iopub.status.idle": "2024-04-18T11:19:55.731123Z",
     "shell.execute_reply": "2024-04-18T11:19:55.730016Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-04-18T11:19:55.735333Z",
     "iopub.status.busy": "2024-04-18T11:19:55.734059Z",
     "iopub.status.idle": "2024-04-18T11:19:55.758639Z",
     "shell.execute_reply": "2024-04-18T11:19:55.757916Z"
    }
   },
   "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": "2024-04-18T11:19:55.762051Z",
     "iopub.status.busy": "2024-04-18T11:19:55.761628Z",
     "iopub.status.idle": "2024-04-18T11:19:56.665561Z",
     "shell.execute_reply": "2024-04-18T11:19:56.664868Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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: 4.687046\n",
      "         Iterations: 327\n",
      "         Function evaluations: 545\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               -2020.117\n",
      "                                                          + AR(2) errors   AIC                           4086.234\n",
      "Date:                                                   Thu, 18 Apr 2024   BIC                           4179.754\n",
      "Time:                                                           11:29:40   HQIC                          4123.159\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              -0.7064      0.036    -19.667      0.000      -0.777      -0.636\n",
      "loading.f1.std_income               -0.2503      0.039     -6.459      0.000      -0.326      -0.174\n",
      "loading.f1.std_sales                -0.4504      0.023    -19.265      0.000      -0.496      -0.405\n",
      "loading.f1.std_emp                  -0.4113      0.038    -10.805      0.000      -0.486      -0.337\n",
      "sigma2.std_indprod                   0.2345      0.045      5.165      0.000       0.146       0.324\n",
      "sigma2.std_income                    0.8738      0.030     29.612      0.000       0.816       0.932\n",
      "sigma2.std_sales                     0.5227      0.035     15.101      0.000       0.455       0.591\n",
      "sigma2.std_emp                       0.2600      0.023     11.365      0.000       0.215       0.305\n",
      "L1.f1.f1                             0.2855      0.054      5.298      0.000       0.180       0.391\n",
      "L2.f1.f1                             0.3877      0.058      6.632      0.000       0.273       0.502\n",
      "L3.f1.f1                                  0   2.18e-10          0      1.000   -4.27e-10    4.27e-10\n",
      "L4.f1.f1                                  0   2.18e-10          0      1.000   -4.27e-10    4.27e-10\n",
      "L1.e(std_indprod).e(std_indprod)    -0.2212      0.120     -1.848      0.065      -0.456       0.013\n",
      "L2.e(std_indprod).e(std_indprod)    -0.1942      0.095     -2.055      0.040      -0.379      -0.009\n",
      "L1.e(std_income).e(std_income)      -0.2013      0.023     -8.926      0.000      -0.245      -0.157\n",
      "L2.e(std_income).e(std_income)      -0.0979      0.047     -2.096      0.036      -0.189      -0.006\n",
      "L1.e(std_sales).e(std_sales)        -0.4849      0.047    -10.293      0.000      -0.577      -0.393\n",
      "L2.e(std_sales).e(std_sales)        -0.2277      0.050     -4.540      0.000      -0.326      -0.129\n",
      "L1.e(std_emp).e(std_emp)             0.2315      0.041      5.701      0.000       0.152       0.311\n",
      "L2.e(std_emp).e(std_emp)             0.4903      0.049     10.085      0.000       0.395       0.586\n",
      "loading.L1.f1.std_emp               -0.0837      0.037     -2.284      0.022      -0.156      -0.012\n",
      "loading.L2.f1.std_emp               -0.0060      0.035     -0.171      0.864      -0.075       0.063\n",
      "loading.L3.f1.std_emp               -0.1729      0.028     -6.097      0.000      -0.228      -0.117\n",
      "=====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.13, 0.01, 1.04, 4.37   Jarque-Bera (JB):   274.03, 10260.89, 25.62, 3834.90\n",
      "Prob(Q):                0.72, 0.91, 0.31, 0.04   Prob(JB):                     0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.75, 4.85, 0.44, 0.44   Skew:                        0.26, -0.99, 0.26, 0.78\n",
      "Prob(H) (two-sided):    0.08, 0.00, 0.00, 0.00   Kurtosis:                   6.87, 26.82, 4.08, 17.53\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 3.28e+18. 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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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "2024-04-18T11:29:41.576149Z",
     "iopub.status.busy": "2024-04-18T11:29:41.574831Z",
     "iopub.status.idle": "2024-04-18T11:29:42.599148Z",
     "shell.execute_reply": "2024-04-18T11:29:42.598506Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}