{
 "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": {},
   "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": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/pandas_datareader/compat/__init__.py:7: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  from pandas.util.testing import assert_frame_equal\n"
     ]
    }
   ],
   "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": {},
   "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": {},
   "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": {},
   "outputs": [],
   "source": [
    "dta = pd.concat((indprod, income, sales, emp), axis=1)\n",
    "dta.columns = ['indprod', 'income', 'sales', 'emp']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n",
    "\n",
    "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "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",
      "  \"Check mle_retvals\", 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": {},
   "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               -2065.018\n",
      "                                                          + AR(2) errors   AIC                           4166.036\n",
      "Date:                                                   Fri, 21 Feb 2020   BIC                           4239.226\n",
      "Time:                                                           13:55:46   HQIC                          4194.933\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              -0.8560      0.016    -52.137      0.000      -0.888      -0.824\n",
      "loading.f1.std_income               -0.2516      0.034     -7.427      0.000      -0.318      -0.185\n",
      "loading.f1.std_sales                -0.4757      0.024    -19.973      0.000      -0.522      -0.429\n",
      "loading.f1.std_emp                  -0.2723      0.027    -10.043      0.000      -0.325      -0.219\n",
      "sigma2.std_indprod                8.467e-15   1.38e-09   6.15e-06      1.000    -2.7e-09     2.7e-09\n",
      "sigma2.std_income                    0.9030      0.020     46.071      0.000       0.865       0.941\n",
      "sigma2.std_sales                     0.6023      0.035     17.298      0.000       0.534       0.671\n",
      "sigma2.std_emp                       0.3706      0.015     25.457      0.000       0.342       0.399\n",
      "L1.f1.f1                             0.2211      0.017     12.895      0.000       0.188       0.255\n",
      "L2.f1.f1                             0.2765      0.021     13.122      0.000       0.235       0.318\n",
      "L1.e(std_indprod).e(std_indprod)    -1.8926      0.002  -1150.429      0.000      -1.896      -1.889\n",
      "L2.e(std_indprod).e(std_indprod)    -1.0000   9.89e-06  -1.01e+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     -4.266      0.000      -0.128      -0.047\n",
      "L1.e(std_sales).e(std_sales)        -0.4418      0.031    -14.373      0.000      -0.502      -0.382\n",
      "L2.e(std_sales).e(std_sales)        -0.2077      0.021     -9.976      0.000      -0.248      -0.167\n",
      "L1.e(std_emp).e(std_emp)             0.3047      0.034      8.980      0.000       0.238       0.371\n",
      "L2.e(std_emp).e(std_emp)             0.4798      0.029     16.615      0.000       0.423       0.536\n",
      "========================================================================================================\n",
      "Ljung-Box (Q):          87.79, 34.95, 68.98, 70.65   Jarque-Bera (JB):   193.98, 9286.58, 20.13, 4165.73\n",
      "Prob(Q):                    0.00, 0.70, 0.00, 0.00   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, 25.65, 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 7.04e+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": {},
   "outputs": [
    {
     "data": {
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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": {},
   "outputs": [
    {
     "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n",
    "usphci.plot(figsize=(13,3));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "coincident_index = compute_coincident_index(mod, res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, label='Coincident index')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix 1: Extending the dynamic factor model\n",
    "\n",
    "Recall that the previous specification was described by:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Written in state space form, the previous specification of the model had the following observation equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp}     & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "and transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "the `DynamicFactor` model handles setting up the state space representation and, in the `DynamicFactor.update` method, it fills in the fitted parameter values into the appropriate locations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The extended specification is the same as in the previous example, except that we also want to allow employment to depend on lagged values of the factor. This creates a change to the $y_{\\text{emp},t}$ equation. Now we have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\qquad & i \\in \\{\\text{indprod}, \\text{income}, \\text{sales} \\}\\\\\n",
    "y_{i,t} & = \\lambda_{i,0} f_t + \\lambda_{i,1} f_{t-1} + \\lambda_{i,2} f_{t-2} + \\lambda_{i,2} f_{t-3} + u_{i,t} \\qquad & i = \\text{emp} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Now, the corresponding observation equation should look like the following:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "y_{\\text{indprod}, t} \\\\\n",
    "y_{\\text{income}, t} \\\\\n",
    "y_{\\text{sales}, t} \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\lambda_\\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{income}  & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{sales}   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\lambda_\\text{emp,1}   & \\lambda_\\text{emp,2} & \\lambda_\\text{emp,3} & \\lambda_\\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Notice that we have introduced two new state variables, $f_{t-2}$ and $f_{t-3}$, which means we need to update the  transition equation:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "u_{\\text{indprod}, t} \\\\\n",
    "u_{\\text{income}, t} \\\\\n",
    "u_{\\text{sales}, t} \\\\\n",
    "u_{\\text{emp}, t} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "1   & 0   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 1   & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n",
    "0   & 0   & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0   & 0   & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "u_{\\text{indprod}, t-1} \\\\\n",
    "u_{\\text{income}, t-1} \\\\\n",
    "u_{\\text{sales}, t-1} \\\\\n",
    "u_{\\text{emp}, t-1} \\\\\n",
    "u_{\\text{indprod}, t-2} \\\\\n",
    "u_{\\text{income}, t-2} \\\\\n",
    "u_{\\text{sales}, t-2} \\\\\n",
    "u_{\\text{emp}, t-2} \\\\\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This model cannot be handled out-of-the-box by the `DynamicFactor` class, but it can be handled by creating a subclass when alters the state space representation in the appropriate way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, notice that if we had set `factor_order = 4`, we would almost have what we wanted. In that case, the last line of the observation equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\vdots \\\\\n",
    "y_{\\text{emp}, t} \\\\\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\lambda_\\text{emp,1}   & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "\n",
    "and the first line of the transition equation would be:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "f_t \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "\\vdots &  &  &  &  &  &  &  &  &  &  & \\vdots \\\\\n",
    "\\end{bmatrix} \n",
    "\\begin{bmatrix}\n",
    "f_{t-1} \\\\\n",
    "f_{t-2} \\\\\n",
    "f_{t-3} \\\\\n",
    "f_{t-4} \\\\\n",
    "\\vdots\n",
    "\\end{bmatrix}\n",
    "+ R \\begin{bmatrix}\n",
    "\\eta_t \\\\\n",
    "\\varepsilon_{t}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Relative to what we want, we have the following differences:\n",
    "\n",
    "1. In the above situation, the $\\lambda_{\\text{emp}, j}$ are forced to be zero for $j > 0$, and we want them to be estimated as parameters.\n",
    "2. We only want the factor to transition according to an AR(2), but under the above situation it is an AR(4).\n",
    "\n",
    "Our strategy will be to subclass `DynamicFactor`, and let it do most of the work (setting up the state space representation, etc.) where it assumes that `factor_order = 4`. The only things we will actually do in the subclass will be to fix those two issues.\n",
    "\n",
    "First, here is the full code of the subclass; it is discussed below. It is important to note at the outset that none of the methods defined below could have been omitted. In fact, the methods `__init__`, `start_params`, `param_names`, `transform_params`, `untransform_params`, and `update` form the core of all state space models in statsmodels, not just the `DynamicFactor` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/base/tsa_model.py:162: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 4.698612\n",
      "         Iterations: 268\n",
      "         Function evaluations: 459\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:                                                   Fri, 21 Feb 2020   BIC                           4189.724\n",
      "Time:                                                           13:56:02   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    -19.110      0.000      -0.760      -0.618\n",
      "loading.f1.std_income               -0.2584      0.038     -6.727      0.000      -0.334      -0.183\n",
      "loading.f1.std_sales                -0.4390      0.024    -18.549      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      5.323      0.000       0.155       0.336\n",
      "sigma2.std_income                    0.8735      0.030     29.557      0.000       0.816       0.931\n",
      "sigma2.std_sales                     0.5346      0.034     15.522      0.000       0.467       0.602\n",
      "sigma2.std_emp                       0.2531      0.024     10.487      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   1.96e-11          0      1.000   -3.85e-11    3.85e-11\n",
      "L4.f1.f1                                  0   1.96e-11          0      1.000   -3.85e-11    3.85e-11\n",
      "L1.e(std_indprod).e(std_indprod)    -0.3202      0.113     -2.828      0.005      -0.542      -0.098\n",
      "L2.e(std_indprod).e(std_indprod)    -0.2253      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    -10.597      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      9.815      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      0.014      0.989      -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 (Q):          59.16, 34.27, 68.30, 61.90   Jarque-Bera (JB):   231.63, 9689.10, 25.37, 3374.68\n",
      "Prob(Q):                    0.03, 0.73, 0.00, 0.01   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 5.31e+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,
   "metadata": {},
   "outputs": [
    {
     "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n",
    "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set(title='Coincident indices, comparison')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}