{
 "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": "2026-07-30T06:35:48.017715Z",
     "iopub.status.busy": "2026-07-30T06:35:48.017199Z",
     "iopub.status.idle": "2026-07-30T06:35:50.363784Z",
     "shell.execute_reply": "2026-07-30T06:35:50.362018Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "np.set_printoptions(precision=4, suppress=True, linewidth=120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-30T06:35:50.366512Z",
     "iopub.status.busy": "2026-07-30T06:35:50.366126Z",
     "iopub.status.idle": "2026-07-30T06:35:51.660607Z",
     "shell.execute_reply": "2026-07-30T06:35:51.657222Z"
    }
   },
   "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": "2026-07-30T06:35:51.663718Z",
     "iopub.status.busy": "2026-07-30T06:35:51.663419Z",
     "iopub.status.idle": "2026-07-30T06:35:51.668803Z",
     "shell.execute_reply": "2026-07-30T06:35:51.667306Z"
    }
   },
   "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": "2026-07-30T06:35:51.671370Z",
     "iopub.status.busy": "2026-07-30T06:35:51.671123Z",
     "iopub.status.idle": "2026-07-30T06:35:51.674735Z",
     "shell.execute_reply": "2026-07-30T06:35:51.674102Z"
    }
   },
   "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": "2026-07-30T06:35:51.677300Z",
     "iopub.status.busy": "2026-07-30T06:35:51.677090Z",
     "iopub.status.idle": "2026-07-30T06:35:51.683854Z",
     "shell.execute_reply": "2026-07-30T06:35:51.682941Z"
    }
   },
   "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": "2026-07-30T06:35:51.685875Z",
     "iopub.status.busy": "2026-07-30T06:35:51.685660Z",
     "iopub.status.idle": "2026-07-30T06:35:52.460758Z",
     "shell.execute_reply": "2026-07-30T06:35:52.459018Z"
    }
   },
   "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": "2026-07-30T06:35:52.463646Z",
     "iopub.status.busy": "2026-07-30T06:35:52.463358Z",
     "iopub.status.idle": "2026-07-30T06:35:52.479107Z",
     "shell.execute_reply": "2026-07-30T06:35:52.478211Z"
    }
   },
   "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[\n",
    "    \"dln_indprod\"\n",
    "].std()\n",
    "dta[\"std_income\"] = (dta[\"dln_income\"] - dta[\"dln_income\"].mean()) / dta[\n",
    "    \"dln_income\"\n",
    "].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": "2026-07-30T06:35:52.481537Z",
     "iopub.status.busy": "2026-07-30T06:35:52.481264Z",
     "iopub.status.idle": "2026-07-30T06:37:35.411457Z",
     "shell.execute_reply": "2026-07-30T06:37:35.410679Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/tsa/statespace/mlemodel.py:736: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  mlefit = super().fit(\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": "2026-07-30T06:37:35.420941Z",
     "iopub.status.busy": "2026-07-30T06:37:35.419203Z",
     "iopub.status.idle": "2026-07-30T06:37:35.476165Z",
     "shell.execute_reply": "2026-07-30T06:37:35.475546Z"
    }
   },
   "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               -1576.859\n",
      "                                                          + AR(2) errors   AIC                           3189.717\n",
      "Date:                                                   Thu, 30 Jul 2026   BIC                           3262.907\n",
      "Time:                                                           06:37:35   HQIC                          3218.615\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              -0.8528      0.011    -78.743      0.000      -0.874      -0.832\n",
      "loading.f1.std_income               -0.2412      0.000   -500.985      0.000      -0.242      -0.240\n",
      "loading.f1.std_sales                -0.4704      0.003   -179.723      0.000      -0.476      -0.465\n",
      "loading.f1.std_emp                  -0.2875      0.004    -77.468      0.000      -0.295      -0.280\n",
      "sigma2.std_indprod                   0.0002   4.83e-06     35.263      0.000       0.000       0.000\n",
      "sigma2.std_income                    0.8845      0.009    103.130      0.000       0.868       0.901\n",
      "sigma2.std_sales                     0.5815      0.000   1769.586      0.000       0.581       0.582\n",
      "sigma2.std_emp                       0.3534      0.007     52.131      0.000       0.340       0.367\n",
      "L1.f1.f1                             0.2638      0.002    121.887      0.000       0.260       0.268\n",
      "L2.f1.f1                             0.2255      0.002     93.718      0.000       0.221       0.230\n",
      "L1.e(std_indprod).e(std_indprod) -5.757e-10   3.47e-05  -1.66e-05      1.000    -6.8e-05     6.8e-05\n",
      "L2.e(std_indprod).e(std_indprod)     1.0000      0.000   2913.056      0.000       0.999       1.001\n",
      "L1.e(std_income).e(std_income)      -0.1741      0.008    -20.605      0.000      -0.191      -0.158\n",
      "L2.e(std_income).e(std_income)      -0.0674      0.003    -22.257      0.000      -0.073      -0.061\n",
      "L1.e(std_sales).e(std_sales)        -0.4396      0.000  -1023.862      0.000      -0.440      -0.439\n",
      "L2.e(std_sales).e(std_sales)        -0.0824      0.001   -103.851      0.000      -0.084      -0.081\n",
      "L1.e(std_emp).e(std_emp)             0.3156      0.002    134.143      0.000       0.311       0.320\n",
      "L2.e(std_emp).e(std_emp)             0.4598      0.001    548.541      0.000       0.458       0.461\n",
      "=========================================================================================================\n",
      "Ljung-Box (L1) (Q):     17.37, 0.11, 0.00, 2.80   Jarque-Bera (JB):   2790413.41, 11825.92, 7.46, 5436.27\n",
      "Prob(Q):                 0.00, 0.74, 1.00, 0.09   Prob(JB):                        0.00, 0.00, 0.02, 0.00\n",
      "Heteroskedasticity (H):  0.00, 4.82, 0.53, 0.43   Skew:                        -19.25, -1.20, -0.01, 1.26\n",
      "Prob(H) (two-sided):     0.00, 0.00, 0.00, 0.00   Kurtosis:                    395.30, 28.55, 3.64, 20.22\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 3.55e+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": "2026-07-30T06:37:35.479381Z",
     "iopub.status.busy": "2026-07-30T06:37:35.479144Z",
     "iopub.status.idle": "2026-07-30T06:37:36.132204Z",
     "shell.execute_reply": "2026-07-30T06:37:36.130557Z"
    }
   },
   "outputs": [
    {
     "data": {
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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(\n",
    "    dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor=\"k\", alpha=0.1\n",
    ");"
   ]
  },
  {
   "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": "2026-07-30T06:37:36.134681Z",
     "iopub.status.busy": "2026-07-30T06:37:36.134391Z",
     "iopub.status.idle": "2026-07-30T06:37:36.431605Z",
     "shell.execute_reply": "2026-07-30T06:37:36.429978Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xYoTS0tLML24+AwAAcC0OD7fe3t4KCwvTihUrzLKsrCytW7dO7dq1M8uSkpJ05MgRSZK7u7sef/xxnTt3zm5f586dk7+/f659WSwW+fr62n0BAADAdTh8za0kffzxx+rSpYseeeQRNW/eXOPHj5ePj49ef/11s86oUaO0fft2xcXFmdutW7fW559/roiICEVHR2vmzJn6/vvvHXUYAAAAcDCnCLcdOnTQihUr9NVXX2np0qUKCQnRr7/+andjWOXKlXXp0iVzu2nTplq/fr3Gjh2rhQsXqnLlyvrpp5/UoUMHBxwBAAAAnIFTPOfWUXjOLQAAgHN74J5zCwAAABSU+w63V69elc1mK4ixAAAAAPclz+H26NGjqlOnjsqWLatJkyaZ5W3bttWOHTsKZXAAAABAfuQ53EZFRalbt276v//7P+3fv1/jx48vxGEBAAAA+ZfncHvy5Em1b99efn5+mjx5svbt26epU6cW5tgAAACAfMlzuO3cubNWrlxpbn/77bdatGiRDh8+XCgDAwAAAPIrz+F28ODBCggIUFZWliSpWLFi+ve//61+/fopMDCw0AYIAAAA5BXPueU5twAAAE6L59wCAADgT+uew+2mTZs0ceJErV69+pbPbDabtm/ffl8DAwAAAPKr2L00GjNmjIYPH25ud+/eXQsXLtSBAwf03XffacGCBUpPT1dmZmaBDRQAAAC4m3uauR03bpwmTJigrKws7du3T7/99pteeeUVNWzYUEuXLlXv3r21fv36gh4rAAAAcEf5vqEsKytLvr6+ysrKkrv7jWy8bds2tWjRQuPGjdO7775rljs7bigDAABwboV+Q1lOTo6KFy9uF2Dr1aunYsWKPVDBFgAAAK7nntbcWq1WffzxxwoJCVFISIjKlSsni8VCsAUAAIBD5Tvcenp6qkuXLvruu+908uRJSVKJEiWUk5OjIUOGKCwsTGFhYapevXqBDxYAAAC4k/t6iUNKSop2795t95WYmChJCg4ONv/srFhzCwAA4Nzym9fuaVnCTWXLllXHjh3VsWNHs+zChQvavXu34uLi7mfXAAAAQL7x+l1mbgEAAJxWkc7cFqScnBxt3rxZycnJCgkJUb169fLcNikpSevWrVPdunUVFhZWiKMEAACAM3OKxxukpqaqWbNmioyM1L/+9S81b95c7777bp7aZmdn69lnn9XAgQM1Z86cwh0oAAAAnJpTzNx+8MEHunr1qvbv3y9vb29FR0erefPm6tSpk5588sk7th0xYoTq1auna9euFdFoAQAA4KwcPnNrGIbmzp2ryMhIeXt7S5KaNWumZs2a3XUm9ueff9aSJUv05ZdfFsVQAQAA4OQcPnOblJSktLS0W9bY1q9fXzExMbm2O3PmjCIjI7Vo0SL5+PjkqS+r1Sqr1Wpup6en39ugAQAA4JQcPnOblpYmSSpdurRdub+/v/nZH9lsNr388st6/fXXFR4enue+oqKi5OfnZ34FBwff87gBAADgfBwebr28vCRJly9ftivPyMgwP/ujH374Qbt371ZQUJBmzJihGTNmKDU1VQcPHtSMGTOU29PNRowYobS0NPMrKSmpYA8GAAAADuXwZQmVK1eWp6enEhIS7MoTEhJUo0aN27YJDAxU9+7dtXnzZrMsMzNTJ0+e1IYNG/TKK6/Izc3tlnYWi0UWi6VAxw8AAADn4RQvcejSpYuuXbumNWvWSJKSk5NVpUoVTZw4Uf3795ckbd26VSkpKerWrdtt99GoUSO1adNG48ePz3O/vMQBAADAuT2QL3H47LPPFBERoV69eik8PFzTp09Xo0aN1KdPH7POtGnTtH379lzDLQAAAODwNbfSjScjxMbGqk6dOjpy5Ihef/11bdiwQZ6enmadiIgIde/ePdd9PP3007ydDAAA4E/OKZYlOArLEgAAAJxbfvOaU8zcAgAAAAWBcAsAAACXQbgFAACAyyDcAgAAwGUQbgEAAOAyCLcAAABwGYRbAAAAuAzCLQAAAFwG4RYAAAAug3ALAAAAl0G4BQAAgMsg3AIAAMBlEG4BAADgMgi3AAAAcBmEWwAAALgMwi0AAABcBuEWAAAALoNwCwAAAJdBuAUAAIDLKOboAdx05swZzZ49W8nJyQoJCdFLL70kT0/PXOsbhqHVq1dr69atKlasmFq2bKm2bdsW4YgBAADgbJxi5vbo0aMKCQnR+vXr5ePjo08++UQdOnTQ9evXb1vfZrOpcePGGj9+vDw8PHT58mX16NFDr732WhGPHAAAAM7EzTAMw9GDeOaZZ3Tx4kWtX79ebm5uOnnypGrUqKHvvvtOr7zyyi31DcNQXFycQkJCzLK1a9eqffv22rt3rxo2bJinftPT0+Xn56e0tDT5+voW2PEAAACgYOQ3rzl85jY7O1srV67USy+9JDc3N0lSUFCQ2rRpoyVLlty2jZubm12wlaR69epJks6ePVu4AwYAAIDTcvia28TERFmtVlWrVs2uvHr16tqyZUue9zNt2jSVLFlSoaGhudaxWq2yWq3mdnp6ev4HDAAAAKfl8Jnbq1evSpJ8fHzsyn19fXXlypU87WPt2rX66KOPNG7cOAUEBORaLyoqSn5+fuZXcHDwvQ8cAAAATsfh4dbb21uSdOnSJbvyixcv5mldxebNm9W9e3f913/9lwYOHHjHuiNGjFBaWpr5lZSUdM/jBgAAgPNxeLitXLmyvL29dejQIbvyQ4cOqW7dundsu2XLFnXu3FlDhw7VyJEj79qXxWKRr6+v3RcAAABch8PDrbu7u3r27KkZM2aYSxT27t2rrVu36vnnnzfrzZkzR59++qm5vXXrVnXs2FFDhgzRqFGjinzcAAAAcD5O8Siwc+fOqU2bNpKkRo0a6eeff9YzzzyjqVOnmnX69++v7du3Ky4uTpmZmapUqZJKlCihnj172u2rd+/eat68eZ765VFgAAAAzi2/ec3hT0uQpHLlymnPnj1atWqVkpOTNXjwYIWHh9vV6d27t9q1aydJKlasmD755JPb7svPz6/QxwsAAADn5BQzt47CzC0AAIBze+Be4gAAAAAUFMItAAAAXAbhFgAAAC6DcAsAAACXQbgFAACAyyDcAgAAwGUQbgEAAOAyCLcAAABwGYRbAAAAuAzCLQAAAFwG4RYAAAAug3ALAAAAl0G4BQAAgMsg3AIAAMBlEG4BAADgMgi3AAAAcBmEWwAAALgMwi0AAABcBuEWAAAALsNpwu2mTZv0/PPPq02bNho0aJDOnDlTKG0AAADgupwi3K5fv17t2rVTrVq1NGzYMB07dkwRERHKyMgo0DYAAABwbW6GYRiOHkRERISCg4M1d+5cSdKVK1dUoUIFjRw5UkOHDi2wNn+Unp4uPz8/paWlydfXt2AOBgAAAAUmv3nN4TO3V65c0fbt29W1a1ezrGTJknriiSe0du3aAmsDAAAA11fM0QNISkqSzWZTxYoV7corVqyodevWFVgbSbJarbJareZ2WlqapBs/EQAAgIJV/x+rHD0EFIK4UU8WaX83c1peFxs4PNxmZ2dLkiwWi125l5eX+VlBtJGkqKgojRo16pby4ODgfI0ZAADgz8pvvGP6zcjIkJ+f313rOTzc+vv7S5JSU1Ptyi9cuKCAgIACayNJI0aM0JAhQ8xtm82m1NRUBQQEyM3N7Z7GD6Snpys4OFhJSUms3UaB4JxCQeJ8QkFyxPlkGIYyMjJu+Y19bhwebitWrKjAwEDt3LlTTz31lFkeHR2tVq1aFVgb6cZM7x9ne0uXLn1/BwD8f76+vnzjQIHinEJB4nxCQSrq8ykvM7Y3OfyGMkmKjIzUlClTdOrUKUnSwoULdfDgQUVGRpp1oqKi1Lt373y1AQAAwJ+Lw2duJWnkyJE6duyYatasqeDgYJ08eVITJ07Uo48+ataJj49XbGxsvtoAAADgz8Upwq3FYtG8efN0+vRpJScnq2bNmvLx8bGr88EHHygzMzNfbYCiYLFY9I9//OOWJS/AveKcQkHifEJBehDOJ6d4iQMAAABQEJxizS0AAABQEAi3AAAAcBmEW/xp7Nu3Txs3bsxT3ZiYGP36669F2mdhWbFiheLj4x06Bld14sQJLV26NE914+PjtXz58kIeEVxdUV5TCuo6COd38eJFzZ07Vzk5OY4eSoEg3OKBt2vXLm3ZsuWu9ebMmaOoqKg87XPatGkaO3bs/Q4tX30WliFDhmjNmjUOHcOD5tixY1qxYsVd623evFlvvvlmnva5Zs0avfPOO/c7NLiowriO3a+Cug7CcZKTkzV37ty71ouPj9eLL76orKysIhhV4SPc4oE3ZcoUffHFFwW6z6ZNm97xhSBwbatWrbJ7m2FBqFmzpt1LZ4DfK4zrGLB//369+OKLjh5GkXOKR4EBeXHixAnFxcUpICBATZo0UfHixbV//37Fx8crIyPD/Om0bdu2Kl++vKxWqzZt2iQPDw81btw4X301bNhQV65cMbejo6NlGIYaNGigPXv2KDMzU82aNbvlDXd36/PmfurXr689e/YoIyNDjz32mLy9vW+pU69ePW3btk3Z2dnq0qWLpBuvPdy6dauuXbumZs2aqXz58rf0cfbsWUVHR6tSpUpq2LBhvo77zyYlJUUxMTGyWCwKDQ2Vt7e3EhMTFRMTY3dONWnSRLVr15bNZtPWrVuVmZmZ77/batWqqX379ub2kSNHlJCQoHbt2ik2NlZnz55V48aNb/t6yRMnTig2NlYVKlRQ06ZN5e5uPy+xd+9eHT9+XJUqVVJYWJjd68Rv9tO2bVvt27dPp0+fVlhYmAIDA3Xt2jVt2bJFWVlZat68+W3f2Pjbb79p3759KlOmjJo0aSIvL698HTfsFeV1LLf+JOngwYPat2+fpBtvfgoJCVFQUFCe9nlzvMHBwWrUqJE8PDzy1CcKT0ZGhnbu3Kns7GyFhoYqICBAly5d0oYNGyTJPK9q1qyp0NBQSTeWnZw+fVp169a9pz6Tk5O1Y8cOeXt7q0mTJnZvEDt9+rS2bNmi5557Tvv371dCQoLq1aunGjVqyGazKTo6WufPn1doaKgqVKhwS7tnn33WbNewYUNVrVo1X2Mj3OKB8M9//lNjxoxRy5YtlZmZqfT0dC1cuFCHDh3Sb7/9JqvVqh9//FGSVL9+feXk5Kht27bKyclR7dq1deDAAQUHB+f5VYHTpk3TyZMn1bJlS0nS5MmTFRsbq6ysLFWpUkVnz57VmTNntHHjRtWpU0eSdOrUqbv2eXM/aWlpqlGjhk6ePKm0tDStXbvWvMDcrHP58mVVr15dderUUZcuXbR69Wr16tVLtWrVUqlSpbRjxw5NmDBBAwYMMPe/dOlSvfDCC2rUqJHc3d119epVXbp0qQD+BVzPvHnz1L9/f4WGhqpYsWL67bffNHXqVHl6eio2NlYZGRnmOeXn56fg4GB16tRJhw4dUtOmTbVv3z498sgjee5vzZo1Gjt2rPmDyrJlyzRhwgQFBgbKx8dHOTk52rVrlxYvXqwnn3xSkmSz2fTmm29q1qxZCg8PV2ZmpkqWLKnly5erZMmSunbtmnr06KFt27apWbNm2rt3rypXrqyVK1fqoYceMvsZP368fHx8FBQUpEuXLunAgQP6+uuvNWbMGAUHByslJUVnz57Vtm3bzG8iNptNb731lubPn6/w8HAlJyfr/PnzWrx4sRo1alRg/w5/JkV9Hcutvxo1aujIkSNmX6mpqdqyZYtGjhyp4cOH57q/jIwM9erVS3FxcWrcuLGOHj0qHx8fLVu2TIGBgXftE4UjOjpanTt3Vu3ateXv76+DBw/qk08+UUREhLnU5ea/dfv27RUaGqq+fftq0aJFioiI0OHDh/N1LZOkMWPG6NNPP1V4eLiysrIUFxenmTNnqnPnzpJuBOfevXtr/Pjxkm48G3fTpk0aO3as5s2bJw8PD7m5uWnPnj36+eefFRERYdfu22+/1YULF+Tn56dt27Zp/PjxGjhwYN4HaABO7tq1a0bx4sWN1atXm2VHjx419u/fbxiGYbz++uvGs88+a9fmL3/5ixEREWFcvXrVMAzD2Ldvn+Hp6Wk8+eSTeerzrbfeMrp162Zu9+nTx/Dy8jIOHjxoGIZh2Gw24/HHHzciIyPz1WefPn0MScYvv/xiGIZh5OTkGE8//bTx+OOP29UpVqyYsWfPHrPs8uXLRqVKlYz333/fLJsyZYpRokQJIyEhwawTGBhojB492qwTFRVlSDImT56cp+P+M6lfv77xP//zP+Z2SkqKsWnTJsMwDOOrr74yHn74Ybv6n332mREUFGScO3fOMAzDSE5ONipWrGhUqlQpT/1NnjzZqFGjhrn9+eefG5KMn376ySx7++23jbCwMHN73Lhxhq+vr3HgwAGzbOPGjUZqaqphGIYxduxYo3z58sapU6cMwzCMS5cuGXXq1DEGDRp0Sz8rV640y5544gnDzc3NPA9tNpvRvHlz469//atZ58svvzTq1KljXLx40Sz78MMPjYYNG+bpeGGvqK9jd+vvj2JiYozixYsb8fHxZtkfr4Ovvfaa0alTJ8NqtRqGYRjXr183evToYfTu3fue+kTBeO6554zXXnvN3L5y5Yr5/33NmjXGH6PekiVLDIvFYhw6dMis/+ijjxqSjIyMjLv2t3r1asPf39/uXJk9e7ZRpkwZs/2yZcsMScYXX3xh1nnrrbdu+X7Up08fo1OnTub2zXZvvfWWWTZ9+nTDy8vLvM7lBWtu4fTc3d1lsVi0f/9+2Ww2SVKtWrVUv37929Y3DEMLFizQoEGDVKJECUlSSEiIOnXqdF/jaNOmjfnTrZubmx577DEdOXIk332Ghoaqbdu2kiQPDw+99957+uWXX3ThwgWzTqtWrexmxzZv3qzTp0/r/fffN8siIyPl7++vJUuWSJI2bdqklJQUu7Wi7777Lr8SzIWXl5eOHDkiq9UqSSpTpswd11nPmzdPffv2VdmyZSVJ5cqVU9++fe9rDMHBweZMrnTjHLt5TknS999/r8jISLtfGz722GPmrOzcuXPVp08fcymDn5+f3n777VtuIKlcubI6duxoboeHh6tWrVrmeejm5qZmzZrp6NGjZp3p06erYcOGWrt2rebPn6958+bJz89PsbGxunjx4n0d959RUV/H8tJfenq6Nm7cqPnz5+vIkSPy9fXV7t27b7u/nJwczZ49W/Xq1dPSpUs1f/58LViwQEFBQVq/fv09HSMKhpeXlxISEpSWlmZu//7/+x/NmzdPXbt2NX/r6OXlpUGDBuW5v+nTp6tu3bqKiYkxrw2SdOHCBe3fv9+s5+bmptdee83cbt68uTw8PNSvXz+7st9fd24aNmyY+ec+ffrIz89Py5Yty/MYCbdweh4eHpo1a5a+/vprlS9fXs8995wWLFiQa/2UlBRdvXr1ljU61apVu69x+Pv7221bLBbzztL89JlbnRMnTphlv1+DdPOzgIAAuzVNbm5uqlatmtkuMTFRZcuWVcmSJc06JUqUuGVfuGHy5MnauXOnypYtq06dOumbb75RdnZ2rvUTExOL9Jy62Wft2rVzbX/ixAlVr17drqxGjRpKSUmxWzN+Mwz/vp/blf2+74SEBB0/flwLFizQwoULtWjRIu3atUvPP/+8rl69mveDhKSiv47drb+FCxeqcuXKGjJkiObMmaMff/xRVqtV586du+3+zp07pytXrmjv3r1250RycrLatGlzT8eIgjF69Ghdv35dFSpUUOvWrfXZZ58pIyMj1/r3ey1LSEjQ+fPn7c6DZcuWqVevXvL09DTrFS9e3O77kcVikbe3t12dP153pBs/JFWuXNncdnNzU5UqVey+R94Na27xQOjWrZu6deumY8eOaeXKlerfv78SExNve0d76dKl5e7ufsvsUmHONuWnz9zqlClTxiz7/Q1BNz9LS0uTzWazu5koNTXVbHfzBgLDMOzaM8t2e02bNtXu3bt16tQprV27VqNGjdKOHTs0bdq029YPCAgo0nNKunFe/X5G/4/KlCmj1NRUu7LU1FSVKlXK7pvKvfD19VXHjh318ccf39d+8B9FfR27U3+DBg3S6NGj7WbsypQpI8MwbrsvHx8fubm5acCAAerVq1eBHCMKRpUqVbR27VqlpqZqw4YNioqK0pIlS7R169bb1r/fa5mvr6+CgoLy9Iixe2Gz2ZSWlmZ3g+vFixftvkfeDTO3cHpXr141/+PVqlVLgwcPVrdu3bR9+3ZJkre3t91PfsWLF1dYWJi5gF6Srly5op9//rnQxpifPrdu3aqUlBRze9GiRapSpcod71S+eQf8738tExcXp8OHD5s3vYWFhen69etatWqVWWfdunVKT0+/n0NzWadOnZIkVapUSX369NEbb7yR6zklSS1btrT79zUMQ4sXLy7UMXbo0EE//PCD3YPVMzIyzLG1bNlSixcvtgsk8+fPN2/OuB8dO3bUzJkz7WaApf/8vSF/ivo6dqf+rl+/rvPnz+vhhx8262/YsOGOP0j5+PioRYsW+t///d9bAvDNc+Jux4jCcfPv39/fXz169NDIkSO1c+dO2Ww280k8vz+3WrZsqZUrV5pLsqQb34fyqmPHjlq+fLmSkpLsys+cOZPrD0f59fvzPi4uTseOHcvXdY2ZWzi9jIwMtWjRQk8//bRCQkJ08uRJLVy40JxhCw0N1ZQpUzRp0iT5+/urbdu2+vTTT9WhQwe5u7urYcOGmjFjhrkGrLDktc+SJUuqXbt2GjhwoBISEvTFF19o5syZtzze6feCgoI0fPhwvfLKKxo+fLhKliypcePGqWfPnuY60eDgYA0ePFi9e/fW8OHD5e7urgkTJqhUqVKFdswPsi5duig0NFRhYWHKzMzU+PHj1b9/f0k3ZnWTkpL03//936pataqaNGmiv//972rUqJF69Oihjh07auXKlTp27JgsFkuhjXHUqFGKiIhQRESE/vKXvygzM1M//PCDfvnlF5UoUUL/+Mc/1LhxY3Xt2lXdunXTxo0btWbNmgJ5q9To0aO1YcMGhYWFKTIyUiVKlNC2bdt09uxZXgpyD4r6Onan/jw8PPTUU0/pnXfe0V//+lelpKRowoQJd53tnzRpktq1a6fHH39cPXv2VFZWltatW6fq1avrq6++uusxonAMHjxYHh4eat26tdzd3TVp0iT16NFD7u7uqlOnjry9vfX++++rWbNmqlWrlgYOHKhJkybpiSee0Msvv6yYmBj99NNPee7vjTfe0NKlSxUeHq633npLZcqU0d69e7V27VodPnz4lt885pe7u7s+/PBDJSYmqnTp0ho7dqx69OihZs2a5XkfhFs4vXLlymnXrl2aMWOGfv31Vz300ENavXq1WrRoIUnq1auXrl69qm3btik9PV3169dX27ZttXnzZn3//fc6cOCAhg0bJqvVmuc1O02bNrVbg9SsWbNbvqnUrVvXfGSTpDz32bFjR/Xt21crVqxQRkaGVqxYYff809v1JUkff/yxmjZtqhUrVig7O1ujR4/Wyy+/bFdnzJgxql+/vjZu3KiKFStq5cqVmj59umrWrJmn4/4z2bFjh2bPnq3o6GhZLBZNnjxZXbt2lXTjxp0lS5ZoxYoVio2NlZ+fnzp16qRdu3Zp0qRJ2r17tzp37qx3333XvJnibv74Eoc6dercctNHpUqV7H7lGxgYqD179mjq1KnatWuXgoKCtGTJEgUEBJj19+7dq2+//VabN29WUFCQ9uzZo1q1at2xn3r16tnN2kg3nu3s4+NjbpctW1YxMTGaNWuWduzYoZIlS6pz5853/JU0clfU17G79Td79mxNnjxZW7duVUBAgFatWqXZs2fbrfH+43WwQYMGOnDggGbMmKEdO3aoTJkyGjx4sHkdvFufKBw3175u2LBBNptNw4YN0wsvvCDpxvKWtWvXas6cOVq2bJnatWun0NBQbd++XV9++aV27NihevXq6ZdfftEnn3xitx42NxaLRatXr9b8+fO1ceNGnThxQk2aNNG4cePMSZo/XsukGxMwzz77rF1ZtWrV1K1bN7syT09PbdmyRdOnT1dMTIzee++9/D0GTJKbUVBzyADuqm/fvuZdxwAA4D9++uknPffcc/f9GmBmbvGnY7PZ7jjb9vjjj6tcuXJFOCK4guXLl+d6h3LTpk3tZlOB+8V1DIVl8+bNua6tr127tpo0aVLEI8o/wi3+dK5fv263WP2PGjRoUGjfFHJbcoAH35o1a3T27Nnbfubv70+4RYFy5HUMrm3btm2KiYm57WdPPvlkoYbb2y1nuBcsSwAAAIDL4FFgAAAAcBmEWwAAALgMwi0AAABcBuEWAAAALoNwCwAAAJdBuAUAAIDLINwCAADAZRBuAQAA4DIItwAAAHAZ/w/FdH3Ovb7RIAAAAABJRU5ErkJggg==",
      "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": "2026-07-30T06:37:36.434237Z",
     "iopub.status.busy": "2026-07-30T06:37:36.433938Z",
     "iopub.status.idle": "2026-07-30T06:37:37.064740Z",
     "shell.execute_reply": "2026-07-30T06:37:37.060856Z"
    }
   },
   "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": "2026-07-30T06:37:37.070166Z",
     "iopub.status.busy": "2026-07-30T06:37:37.069931Z",
     "iopub.status.idle": "2026-07-30T06:37:37.084469Z",
     "shell.execute_reply": "2026-07-30T06:37:37.082798Z"
    }
   },
   "outputs": [],
   "source": [
    "dusphci = usphci.diff()[1:].values\n",
    "\n",
    "\n",
    "def compute_coincident_index(mod, res):\n",
    "    # Estimate W(1)\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(\n",
    "        np.eye(k_states)\n",
    "        - np.dot(np.eye(k_states) - np.dot(ss_kalman_gain, design), 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(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": "2026-07-30T06:37:37.086929Z",
     "iopub.status.busy": "2026-07-30T06:37:37.086697Z",
     "iopub.status.idle": "2026-07-30T06:37:37.409075Z",
     "shell.execute_reply": "2026-07-30T06:37:37.407472Z"
    }
   },
   "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(\n",
    "    dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor=\"k\", alpha=0.1\n",
    ");"
   ]
  },
  {
   "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": {
     "iopub.execute_input": "2026-07-30T06:37:37.416896Z",
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   "source": [
    "from statsmodels.tsa.statespace import tools\n",
    "\n",
    "\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().__init__(endog, k_factors=1, factor_order=4, error_order=2, **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 = (\n",
    "            self.parameters[\"factor_loadings\"]\n",
    "            + self.parameters[\"exog\"]\n",
    "            + self.parameters[\"error_cov\"]\n",
    "        )\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().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().param_names + [\n",
    "            f\"loading.L{i}.f1.{self.endog_names[3]}\" for i in range(1, 4)\n",
    "        ]\n",
    "\n",
    "    def transform_params(self, unconstrained):\n",
    "        # Perform the typical DFM transformation (w/o the new parameters)\n",
    "        constrained = super().transform_params(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] = tools.constrain_stationary_univariate(\n",
    "            ar_params\n",
    "        )\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().untransform_params(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] = tools.unconstrain_stationary_univariate(\n",
    "            ar_params\n",
    "        )\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().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:]"
   ]
  },
  {
   "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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     "shell.execute_reply": "2026-07-30T06:39:27.511128Z"
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/base/optimizer.py:921: RuntimeWarning: Maximum number of iterations has been exceeded.\n",
      "  retvals = optimize.fmin(\n",
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/tsa/statespace/mlemodel.py:736: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  mlefit = super().fit(\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               -2036.972\n",
      "                                                          + AR(2) errors   AIC                           4119.944\n",
      "Date:                                                   Thu, 30 Jul 2026   BIC                           4213.464\n",
      "Time:                                                           06:39:27   HQIC                          4156.869\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              -0.9067      0.021    -43.970      0.000      -0.947      -0.866\n",
      "loading.f1.std_income               -0.2484      0.045     -5.575      0.000      -0.336      -0.161\n",
      "loading.f1.std_sales                -0.5058      0.027    -19.040      0.000      -0.558      -0.454\n",
      "loading.f1.std_emp                  -0.3258      0.030    -10.776      0.000      -0.385      -0.267\n",
      "sigma2.std_indprod                9.263e-11      0.013   7.34e-09      1.000      -0.025       0.025\n",
      "sigma2.std_income                    0.9059      0.029     30.711      0.000       0.848       0.964\n",
      "sigma2.std_sales                     0.5877      0.036     16.325      0.000       0.517       0.658\n",
      "sigma2.std_emp                       0.3409      0.014     24.562      0.000       0.314       0.368\n",
      "L1.f1.f1                             0.2282      0.037      6.243      0.000       0.157       0.300\n",
      "L2.f1.f1                             0.2853      0.045      6.327      0.000       0.197       0.374\n",
      "L3.f1.f1                                  0   7.25e-12          0      1.000   -1.42e-11    1.42e-11\n",
      "L4.f1.f1                                  0   7.25e-12          0      1.000   -1.42e-11    1.42e-11\n",
      "L1.e(std_indprod).e(std_indprod)     0.0769   5.68e-11   1.35e+09      0.000       0.077       0.077\n",
      "L2.e(std_indprod).e(std_indprod)     0.6960    3.8e-11   1.83e+10      0.000       0.696       0.696\n",
      "L1.e(std_income).e(std_income)      -0.1841      0.022     -8.349      0.000      -0.227      -0.141\n",
      "L2.e(std_income).e(std_income)      -0.0897      0.047     -1.901      0.057      -0.182       0.003\n",
      "L1.e(std_sales).e(std_sales)        -0.4257      0.045     -9.382      0.000      -0.515      -0.337\n",
      "L2.e(std_sales).e(std_sales)        -0.1960      0.050     -3.930      0.000      -0.294      -0.098\n",
      "L1.e(std_emp).e(std_emp)             0.2417      0.034      7.051      0.000       0.174       0.309\n",
      "L2.e(std_emp).e(std_emp)             0.4463      0.035     12.802      0.000       0.378       0.515\n",
      "loading.L1.f1.std_emp               -0.1224      0.031     -3.996      0.000      -0.182      -0.062\n",
      "loading.L2.f1.std_emp               -0.1089      0.028     -3.844      0.000      -0.164      -0.053\n",
      "loading.L3.f1.std_emp               -0.1221      0.030     -4.126      0.000      -0.180      -0.064\n",
      "====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.44, 0.03, 0.04, 6.03   Jarque-Bera (JB):   262.91, 9952.23, 20.34, 4828.90\n",
      "Prob(Q):                0.50, 0.85, 0.85, 0.01   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.75, 4.66, 0.47, 0.38   Skew:                       0.12, -1.01, 0.21, 0.84\n",
      "Prob(H) (two-sided):    0.09, 0.00, 0.00, 0.00   Kurtosis:                  6.82, 26.45, 3.97, 19.31\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 4.58e+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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
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     "iopub.execute_input": "2026-07-30T06:39:27.526831Z",
     "iopub.status.busy": "2026-07-30T06:39:27.526583Z",
     "iopub.status.idle": "2026-07-30T06:39:27.979470Z",
     "shell.execute_reply": "2026-07-30T06:39:27.978463Z"
    }
   },
   "outputs": [
    {
     "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": "2026-07-30T06:39:27.982120Z",
     "iopub.status.busy": "2026-07-30T06:39:27.981688Z",
     "iopub.status.idle": "2026-07-30T06:39:28.578499Z",
     "shell.execute_reply": "2026-07-30T06:39:28.577558Z"
    }
   },
   "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(\n",
    "    dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor=\"k\", alpha=0.1\n",
    ");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.14.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}