{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "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": "2021-02-02T06:55:23.572634Z",
     "iopub.status.busy": "2021-02-02T06:55:23.562860Z",
     "iopub.status.idle": "2021-02-02T06:55:24.917425Z",
     "shell.execute_reply": "2021-02-02T06:55:24.918520Z"
    }
   },
   "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": "2021-02-02T06:55:24.923717Z",
     "iopub.status.busy": "2021-02-02T06:55:24.922220Z",
     "iopub.status.idle": "2021-02-02T06:55:27.287451Z",
     "shell.execute_reply": "2021-02-02T06:55:27.286760Z"
    }
   },
   "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": "2021-02-02T06:55:27.291614Z",
     "iopub.status.busy": "2021-02-02T06:55:27.291206Z",
     "iopub.status.idle": "2021-02-02T06:55:27.294358Z",
     "shell.execute_reply": "2021-02-02T06:55:27.293981Z"
    }
   },
   "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": "2021-02-02T06:55:27.297533Z",
     "iopub.status.busy": "2021-02-02T06:55:27.296945Z",
     "iopub.status.idle": "2021-02-02T06:55:27.299920Z",
     "shell.execute_reply": "2021-02-02T06:55:27.300272Z"
    }
   },
   "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": "2021-02-02T06:55:27.306396Z",
     "iopub.status.busy": "2021-02-02T06:55:27.304617Z",
     "iopub.status.idle": "2021-02-02T06:55:27.308743Z",
     "shell.execute_reply": "2021-02-02T06:55:27.309109Z"
    }
   },
   "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": "2021-02-02T06:55:27.314838Z",
     "iopub.status.busy": "2021-02-02T06:55:27.313768Z",
     "iopub.status.idle": "2021-02-02T06:55:28.611206Z",
     "shell.execute_reply": "2021-02-02T06:55:28.612437Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<AxesSubplot:xlabel='DATE'>, <AxesSubplot:xlabel='DATE'>],\n",
       "       [<AxesSubplot:xlabel='DATE'>, <AxesSubplot:xlabel='DATE'>]], dtype=object)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n",
    "\n",
    "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:28.617801Z",
     "iopub.status.busy": "2021-02-02T06:55:28.616203Z",
     "iopub.status.idle": "2021-02-02T06:55:28.643771Z",
     "shell.execute_reply": "2021-02-02T06:55:28.644924Z"
    }
   },
   "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": "2021-02-02T06:55:28.650479Z",
     "iopub.status.busy": "2021-02-02T06:55:28.648877Z",
     "iopub.status.idle": "2021-02-02T06:55:41.886505Z",
     "shell.execute_reply": "2021-02-02T06:55:41.887418Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/travis/build/statsmodels/statsmodels/statsmodels/base/model.py:568: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  ConvergenceWarning)\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": "2021-02-02T06:55:41.891831Z",
     "iopub.status.busy": "2021-02-02T06:55:41.890572Z",
     "iopub.status.idle": "2021-02-02T06:55:41.918686Z",
     "shell.execute_reply": "2021-02-02T06:55:41.919569Z"
    }
   },
   "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               -2065.023\n",
      "                                                          + AR(2) errors   AIC                           4166.047\n",
      "Date:                                                   Tue, 02 Feb 2021   BIC                           4239.237\n",
      "Time:                                                           06:55:41   HQIC                          4194.945\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              -0.8559      0.016    -52.146      0.000      -0.888      -0.824\n",
      "loading.f1.std_income               -0.2515      0.034     -7.425      0.000      -0.318      -0.185\n",
      "loading.f1.std_sales                -0.4757      0.024    -19.974      0.000      -0.522      -0.429\n",
      "loading.f1.std_emp                  -0.2721      0.027    -10.039      0.000      -0.325      -0.219\n",
      "sigma2.std_indprod                8.559e-15   1.38e-09   6.21e-06      1.000    -2.7e-09     2.7e-09\n",
      "sigma2.std_income                    0.9031      0.020     46.067      0.000       0.865       0.941\n",
      "sigma2.std_sales                     0.6022      0.035     17.302      0.000       0.534       0.670\n",
      "sigma2.std_emp                       0.3707      0.015     25.456      0.000       0.342       0.399\n",
      "L1.f1.f1                             0.2210      0.017     12.884      0.000       0.187       0.255\n",
      "L2.f1.f1                             0.2766      0.021     13.125      0.000       0.235       0.318\n",
      "L1.e(std_indprod).e(std_indprod)    -1.8926      0.002  -1148.990      0.000      -1.896      -1.889\n",
      "L2.e(std_indprod).e(std_indprod)    -1.0000   9.78e-06  -1.02e+05      0.000      -1.000      -1.000\n",
      "L1.e(std_income).e(std_income)      -0.1542      0.019     -8.279      0.000      -0.191      -0.118\n",
      "L2.e(std_income).e(std_income)      -0.0874      0.020     -4.265      0.000      -0.128      -0.047\n",
      "L1.e(std_sales).e(std_sales)        -0.4418      0.031    -14.375      0.000      -0.502      -0.382\n",
      "L2.e(std_sales).e(std_sales)        -0.2077      0.021     -9.977      0.000      -0.248      -0.167\n",
      "L1.e(std_emp).e(std_emp)             0.3046      0.034      8.978      0.000       0.238       0.371\n",
      "L2.e(std_emp).e(std_emp)             0.4799      0.029     16.622      0.000       0.423       0.536\n",
      "====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.81, 0.05, 0.06, 5.99   Jarque-Bera (JB):   194.03, 9286.86, 20.12, 4165.97\n",
      "Prob(Q):                0.37, 0.83, 0.81, 0.01   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.80, 4.82, 0.47, 0.41   Skew:                       0.07, -0.98, 0.19, 0.86\n",
      "Prob(H) (two-sided):    0.19, 0.00, 0.00, 0.00   Kurtosis:                  6.28, 25.66, 3.99, 18.13\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 7.69e+16. 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": "2021-02-02T06:55:41.923749Z",
     "iopub.status.busy": "2021-02-02T06:55:41.922501Z",
     "iopub.status.idle": "2021-02-02T06:55:42.349590Z",
     "shell.execute_reply": "2021-02-02T06:55:42.350605Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f4e82c99710>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# 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": "2021-02-02T06:55:42.355036Z",
     "iopub.status.busy": "2021-02-02T06:55:42.353706Z",
     "iopub.status.idle": "2021-02-02T06:55:42.858813Z",
     "shell.execute_reply": "2021-02-02T06:55:42.859889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": "2021-02-02T06:55:42.865229Z",
     "iopub.status.busy": "2021-02-02T06:55:42.863831Z",
     "iopub.status.idle": "2021-02-02T06:55:43.422249Z",
     "shell.execute_reply": "2021-02-02T06:55:43.423193Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='DATE'>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n",
    "usphci.plot(figsize=(13,3));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:43.427479Z",
     "iopub.status.busy": "2021-02-02T06:55:43.426163Z",
     "iopub.status.idle": "2021-02-02T06:55:43.438036Z",
     "shell.execute_reply": "2021-02-02T06:55:43.438929Z"
    }
   },
   "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": "2021-02-02T06:55:43.443218Z",
     "iopub.status.busy": "2021-02-02T06:55:43.441862Z",
     "iopub.status.idle": "2021-02-02T06:55:43.735185Z",
     "shell.execute_reply": "2021-02-02T06:55:43.735811Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f4e82bb00d0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "coincident_index = compute_coincident_index(mod, res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, label='Coincident index')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix 1: Extending the dynamic factor model\n",
    "\n",
    "Recall that the previous specification was described by:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Written in state space form, the previous specification of the model had the following observation equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp}     & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "and transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "the `DynamicFactor` model handles setting up the state space representation and, in the `DynamicFactor.update` method, it fills in the fitted parameter values into the appropriate locations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The extended specification is the same as in the previous example, except that we also want to allow employment to depend on lagged values of the factor. This creates a change to the $y_{\\text{emp},t}$ equation. Now we have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\qquad & i \\in \\{\\text{indprod}, \\text{income}, \\text{sales} \\}\\\\\n",
    "y_{i,t} & = \\lambda_{i,0} f_t + \\lambda_{i,1} f_{t-1} + \\lambda_{i,2} f_{t-2} + \\lambda_{i,2} f_{t-3} + u_{i,t} \\qquad & i = \\text{emp} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Now, the corresponding observation equation should look like the following:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp,1}   & \\lambda_\\text{emp,2} & \\lambda_\\text{emp,3} & \\lambda_\\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Notice that we have introduced two new state variables, $f_{t-2}$ and $f_{t-3}$, which means we need to update the  transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 1   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This model cannot be handled out-of-the-box by the `DynamicFactor` class, but it can be handled by creating a subclass when alters the state space representation in the appropriate way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, notice that if we had set `factor_order = 4`, we would almost have what we wanted. In that case, the last line of the observation equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\vdots \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\lambda_\\text{emp,1}   & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "and the first line of the transition equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Relative to what we want, we have the following differences:\n",
    "\n",
    "1. In the above situation, the $\\lambda_{\\text{emp}, j}$ are forced to be zero for $j > 0$, and we want them to be estimated as parameters.\n",
    "2. We only want the factor to transition according to an AR(2), but under the above situation it is an AR(4).\n",
    "\n",
    "Our strategy will be to subclass `DynamicFactor`, and let it do most of the work (setting up the state space representation, etc.) where it assumes that `factor_order = 4`. The only things we will actually do in the subclass will be to fix those two issues.\n",
    "\n",
    "First, here is the full code of the subclass; it is discussed below. It is important to note at the outset that none of the methods defined below could have been omitted. In fact, the methods `__init__`, `start_params`, `param_names`, `transform_params`, `untransform_params`, and `update` form the core of all state space models in statsmodels, not just the `DynamicFactor` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "from statsmodels.tsa.statespace import tools\n",
    "class ExtendedDFM(sm.tsa.DynamicFactor):\n",
    "    def __init__(self, endog, **kwargs):\n",
    "            # Setup the model as if we had a factor order of 4\n",
    "            super(ExtendedDFM, self).__init__(\n",
    "                endog, k_factors=1, factor_order=4, error_order=2,\n",
    "                **kwargs)\n",
    "\n",
    "            # Note: `self.parameters` is an ordered dict with the\n",
    "            # keys corresponding to parameter types, and the values\n",
    "            # the number of parameters of that type.\n",
    "            # Add the new parameters\n",
    "            self.parameters['new_loadings'] = 3\n",
    "\n",
    "            # Cache a slice for the location of the 4 factor AR\n",
    "            # parameters (a_1, ..., a_4) in the full parameter vector\n",
    "            offset = (self.parameters['factor_loadings'] +\n",
    "                      self.parameters['exog'] +\n",
    "                      self.parameters['error_cov'])\n",
    "            self._params_factor_ar = np.s_[offset:offset+2]\n",
    "            self._params_factor_zero = np.s_[offset+2:offset+4]\n",
    "\n",
    "    @property\n",
    "    def start_params(self):\n",
    "        # Add three new loading parameters to the end of the parameter\n",
    "        # vector, initialized to zeros (for simplicity; they could\n",
    "        # be initialized any way you like)\n",
    "        return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0]\n",
    "    \n",
    "    @property\n",
    "    def param_names(self):\n",
    "        # Add the corresponding names for the new loading parameters\n",
    "        #  (the name can be anything you like)\n",
    "        return super(ExtendedDFM, self).param_names + [\n",
    "            'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1,4)]\n",
    "\n",
    "    def transform_params(self, unconstrained):\n",
    "            # Perform the typical DFM transformation (w/o the new parameters)\n",
    "            constrained = super(ExtendedDFM, self).transform_params(\n",
    "            unconstrained[:-3])\n",
    "\n",
    "            # Redo the factor AR constraint, since we only want an AR(2),\n",
    "            # and the previous constraint was for an AR(4)\n",
    "            ar_params = unconstrained[self._params_factor_ar]\n",
    "            constrained[self._params_factor_ar] = (\n",
    "                tools.constrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[constrained, unconstrained[-3:]]\n",
    "\n",
    "    def untransform_params(self, constrained):\n",
    "            # Perform the typical DFM untransformation (w/o the new parameters)\n",
    "            unconstrained = super(ExtendedDFM, self).untransform_params(\n",
    "                constrained[:-3])\n",
    "\n",
    "            # Redo the factor AR unconstrained, since we only want an AR(2),\n",
    "            # and the previous unconstrained was for an AR(4)\n",
    "            ar_params = constrained[self._params_factor_ar]\n",
    "            unconstrained[self._params_factor_ar] = (\n",
    "                tools.unconstrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[unconstrained, constrained[-3:]]\n",
    "\n",
    "    def update(self, params, transformed=True, **kwargs):\n",
    "        # Peform the transformation, if required\n",
    "        if not transformed:\n",
    "            params = self.transform_params(params)\n",
    "        params[self._params_factor_zero] = 0\n",
    "        \n",
    "        # Now perform the usual DFM update, but exclude our new parameters\n",
    "        super(ExtendedDFM, self).update(params[:-3], transformed=True, **kwargs)\n",
    "\n",
    "        # Finally, set our new parameters in the design matrix\n",
    "        self.ssm['design', 3, 1:4] = params[-3:]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what did we just do?\n",
    "\n",
    "**`__init__`**\n",
    "\n",
    "The important step here was specifying the base dynamic factor model which we were operating with. In particular, as described above, we initialize with `factor_order=4`, even though we will only end up with an AR(2) model for the factor. We also performed some general setup-related tasks.\n",
    "\n",
    "**`start_params`**\n",
    "\n",
    "`start_params` are used as initial values in the optimizer. Since we are adding three new parameters, we need to pass those in. If we had not done this, the optimizer would use the default starting values, which would be three elements short.\n",
    "\n",
    "**`param_names`**\n",
    "\n",
    "`param_names` are used in a variety of places, but especially in the results class. Below we get a full result summary, which is only possible when all the parameters have associated names.\n",
    "\n",
    "**`transform_params`** and **`untransform_params`**\n",
    "\n",
    "The optimizer selects possibly parameter values in an unconstrained way. That's not usually desired (since variances cannot be negative, for example), and `transform_params` is used to transform the unconstrained values used by the optimizer to constrained values appropriate to the model. Variances terms are typically squared (to force them to be positive), and AR lag coefficients are often constrained to lead to a stationary model. `untransform_params` is used for the reverse operation (and is important because starting parameters are usually specified in terms of values appropriate to the model, and we need to convert them to parameters appropriate to the optimizer before we can begin the optimization routine).\n",
    "\n",
    "Even though we do not need to transform or untransform our new parameters (the loadings can in theory take on any values), we still need to modify this function for two reasons:\n",
    "\n",
    "1. The version in the `DynamicFactor` class is expecting 3 fewer parameters than we have now. At a minimum, we need to handle the three new parameters.\n",
    "2. The version in the `DynamicFactor` class constrains the factor lag coefficients to be stationary as though it was an AR(4) model. Since we actually have an AR(2) model, we need to re-do the constraint. We also set the last two autoregressive coefficients to be zero here.\n",
    "\n",
    "**`update`**\n",
    "\n",
    "The most important reason we need to specify a new `update` method is because we have three new parameters that we need to place into the state space formulation. In particular we let the parent `DynamicFactor.update` class handle placing all the parameters except the three new ones in to the state space representation, and then we put the last three in manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 4.698612\n",
      "         Iterations: 271\n",
      "         Function evaluations: 471\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               -2025.102\n",
      "                                                          + AR(2) errors   AIC                           4096.203\n",
      "Date:                                                   Tue, 02 Feb 2021   BIC                           4189.724\n",
      "Time:                                                           06:56:16   HQIC                          4133.128\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              -0.6889      0.036    -19.109      0.000      -0.760      -0.618\n",
      "loading.f1.std_income               -0.2584      0.038     -6.726      0.000      -0.334      -0.183\n",
      "loading.f1.std_sales                -0.4390      0.024    -18.548      0.000      -0.485      -0.393\n",
      "loading.f1.std_emp                  -0.4166      0.039    -10.761      0.000      -0.493      -0.341\n",
      "sigma2.std_indprod                   0.2456      0.046      5.322      0.000       0.155       0.336\n",
      "sigma2.std_income                    0.8736      0.030     29.557      0.000       0.816       0.932\n",
      "sigma2.std_sales                     0.5347      0.034     15.522      0.000       0.467       0.602\n",
      "sigma2.std_emp                       0.2531      0.024     10.488      0.000       0.206       0.300\n",
      "L1.f1.f1                             0.3047      0.059      5.169      0.000       0.189       0.420\n",
      "L2.f1.f1                             0.3768      0.062      6.076      0.000       0.255       0.498\n",
      "L3.f1.f1                                  0   3.44e-10          0      1.000   -6.75e-10    6.75e-10\n",
      "L4.f1.f1                                  0   3.44e-10          0      1.000   -6.75e-10    6.75e-10\n",
      "L1.e(std_indprod).e(std_indprod)    -0.3203      0.113     -2.828      0.005      -0.542      -0.098\n",
      "L2.e(std_indprod).e(std_indprod)    -0.2254      0.090     -2.497      0.013      -0.402      -0.048\n",
      "L1.e(std_income).e(std_income)      -0.1730      0.022     -7.835      0.000      -0.216      -0.130\n",
      "L2.e(std_income).e(std_income)      -0.0936      0.044     -2.120      0.034      -0.180      -0.007\n",
      "L1.e(std_sales).e(std_sales)        -0.4896      0.046    -10.596      0.000      -0.580      -0.399\n",
      "L2.e(std_sales).e(std_sales)        -0.2268      0.050     -4.540      0.000      -0.325      -0.129\n",
      "L1.e(std_emp).e(std_emp)             0.2334      0.042      5.523      0.000       0.151       0.316\n",
      "L2.e(std_emp).e(std_emp)             0.4965      0.051      9.814      0.000       0.397       0.596\n",
      "loading.L1.f1.std_emp               -0.0725      0.038     -1.898      0.058      -0.147       0.002\n",
      "loading.L2.f1.std_emp                0.0005      0.036      0.013      0.990      -0.070       0.071\n",
      "loading.L3.f1.std_emp               -0.1737      0.028     -6.168      0.000      -0.229      -0.119\n",
      "====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.11, 0.00, 1.04, 3.83   Jarque-Bera (JB):   231.63, 9688.75, 25.36, 3374.73\n",
      "Prob(Q):                0.74, 0.95, 0.31, 0.05   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.76, 5.03, 0.44, 0.45   Skew:                       0.22, -0.97, 0.24, 0.75\n",
      "Prob(H) (two-sided):    0.11, 0.00, 0.00, 0.00   Kurtosis:                  6.56, 26.15, 4.08, 16.63\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 1.35e+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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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "extended_res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:56:17.701736Z",
     "iopub.status.busy": "2021-02-02T06:56:17.700917Z",
     "iopub.status.idle": "2021-02-02T06:56:18.813887Z",
     "shell.execute_reply": "2021-02-02T06:56:18.814536Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f4e823d3150>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n",
    "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set(title='Coincident indices, comparison')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  }
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