{
 "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": [],
   "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               -2066.915\n",
      "                                                          + AR(2) errors   AIC                           4169.831\n",
      "Date:                                                   Tue, 17 Dec 2019   BIC                           4243.021\n",
      "Time:                                                           23:43:20   HQIC                          4198.729\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              -0.8524      0.016    -52.173      0.000      -0.884      -0.820\n",
      "loading.f1.std_income               -0.2430      0.033     -7.351      0.000      -0.308      -0.178\n",
      "loading.f1.std_sales                -0.4731      0.024    -20.066      0.000      -0.519      -0.427\n",
      "loading.f1.std_emp                  -0.2692      0.028     -9.669      0.000      -0.324      -0.215\n",
      "sigma2.std_indprod                 2.27e-15   1.37e-09   1.66e-06      1.000   -2.68e-09    2.68e-09\n",
      "sigma2.std_income                    0.9089      0.017     53.352      0.000       0.876       0.942\n",
      "sigma2.std_sales                     0.6032      0.035     17.330      0.000       0.535       0.671\n",
      "sigma2.std_emp                       0.3725      0.014     26.623      0.000       0.345       0.400\n",
      "L1.f1.f1                             0.2190      0.019     11.537      0.000       0.182       0.256\n",
      "L2.f1.f1                             0.2814      0.023     11.999      0.000       0.235       0.327\n",
      "L1.e(std_indprod).e(std_indprod)    -1.5174      0.000  -5455.419      0.000      -1.518      -1.517\n",
      "L2.e(std_indprod).e(std_indprod)    -1.0000      0.000  -5725.669      0.000      -1.000      -1.000\n",
      "L1.e(std_income).e(std_income)      -0.1585      0.018     -8.580      0.000      -0.195      -0.122\n",
      "L2.e(std_income).e(std_income)      -0.0833      0.020     -4.204      0.000      -0.122      -0.044\n",
      "L1.e(std_sales).e(std_sales)        -0.4430      0.029    -15.054      0.000      -0.501      -0.385\n",
      "L2.e(std_sales).e(std_sales)        -0.2058      0.020    -10.476      0.000      -0.244      -0.167\n",
      "L1.e(std_emp).e(std_emp)             0.2989      0.033      9.100      0.000       0.235       0.363\n",
      "L2.e(std_emp).e(std_emp)             0.4858      0.029     16.938      0.000       0.430       0.542\n",
      "========================================================================================================\n",
      "Ljung-Box (Q):          85.11, 34.51, 68.73, 68.85   Jarque-Bera (JB):   193.87, 9396.60, 19.80, 4209.89\n",
      "Prob(Q):                    0.00, 0.72, 0.00, 0.00   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H):     0.80, 4.85, 0.47, 0.41   Skew:                       0.09, -0.98, 0.18, 0.86\n",
      "Prob(H) (two-sided):        0.18, 0.00, 0.00, 0.00   Kurtosis:                  6.28, 25.79, 3.98, 18.21\n",
      "========================================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 3.38e+17. 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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Qln0YeF27vR54Vbt9JrAW2LON6Y62/Pk0X/kJzYDi08Bhs/36jmgfXg/s3W4/sv39cOCh7fYSmrVBABYDN7TbS4G3tNu7AWuA/YA3AG9uy+cBe872a9az/voo8Jx2exFwU7t9GvBfwEOAXwF+DBzVHvs34AXt9vqB/jkR+PTWnoMj9rnpeuCI9n+Bz62qOycdfyZwWVVtqOZOfB/bxvb/tf19Nc0fFoDDgI8AVNVamj/+m9w/cI6PAM8ZODZ47mfTvEkAzhuodyhw/kB5n8xGXx0BvL+aGzFRVd8Hfhn4RlV9ra3zIZo+3WTTKpLXA1dV1V1VtQG4O8kjaRL784FrgWuAA2kS0Fww3X14BXBuklfSJGJoksPZSa4HLqK5NfZkzwdOTHIdcBXNDbaW0KwKelKS04CnVNVd2/4Ue2W6++sI4L3t674CeESSPdtjn6mqe9tzzgM+OxDD4oE2zh/4/eytPQE/t5yDquprSX6VZpT29iSXDKu2A6f4afv7/3jgv7GptjlY70dTrNfLBRlmqa8ypM2t3T55Uzv3D2xv2t+1ffzbq+qftj/U0TTdfVhVJyd5JnAMcF2SpwGvBr5DM/LbBbh7yEMDvLqqVj3oQHJY2955Sc6oOXwdxgy853YBnl1VPxksTHNH8p+257w/yb3VDsv5+ftm2Pm2em5H7HNQkscBP66qjwDvBg4G7qKZPoXmf/OHJ3l0+znPdKwGeDnwkvb8T6aZjt9kF5p7AwC8mGZ6apj/5ufLDL9koN4Vk8p7Y5b66hLg5LQXLCZ5FPA/wOKBz/deBnxhG9pcBfxhkj3aNvdO8ovTEOtOb7r7MMkTquqqalbt/C7NjbP2Ar5VVffT9M28IQ9dBbxq4LPbA9rPk/el+cjkbJplvQ/ewac80mbgPXcJcMpA+0/bjrB+f+D3lVur7Ih9bnoKcEaS+4F7aT5TfTbwmSTfqqrfaKflrgS+RTN1OuwPxbb4R+CDSdYC1wFfHjj2I+BJSa4G7uTn/4gnew1wTpI3ARuAk9ry1wIfTfJams+G+2Q2+uoDwAHA2iT30nze+N4kJwEXtQl/NfD+qTZYVZckeSJwZTtS2Qi8FLhjB2MdBdPdh2ckWUIzAv888BXgfcAnkrwIuJThM10foJnevSZNJ2wAXgAcDryp7euNNJ/jzmXT3V+vAc5q//btSjPIOXkL9YfZLclVNIOgE7ZW2SVlNeuSbKyqPWY7Dkna2SRZT3Oh8ZTv5+5UvCRJPeKIXVOW5M08+POki6rqbbMRjzbPvhp99uFo2Zn6y8QuSVKPOBUvSVKPmNglSeoRE7skST1iYpckqUdM7JIk9cj/AxceuKBOY2UwAAAAAElFTkSuQmCC\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: 4.698591\n",
      "         Iterations: 295\n",
      "         Function evaluations: 504\n",
      "                                             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               -2025.093\n",
      "                                                          + AR(2) errors   AIC                           4096.186\n",
      "Date:                                                   Tue, 17 Dec 2019   BIC                           4189.706\n",
      "Time:                                                           23:43:31   HQIC                          4133.111\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              -0.6890      0.036    -19.095      0.000      -0.760      -0.618\n",
      "loading.f1.std_income               -0.2583      0.038     -6.722      0.000      -0.334      -0.183\n",
      "loading.f1.std_sales                -0.4390      0.024    -18.550      0.000      -0.485      -0.393\n",
      "loading.f1.std_emp                  -0.4168      0.039    -10.758      0.000      -0.493      -0.341\n",
      "sigma2.std_indprod                   0.2455      0.046      5.318      0.000       0.155       0.336\n",
      "sigma2.std_income                    0.8737      0.030     29.560      0.000       0.816       0.932\n",
      "sigma2.std_sales                     0.5346      0.034     15.532      0.000       0.467       0.602\n",
      "sigma2.std_emp                       0.2530      0.024     10.497      0.000       0.206       0.300\n",
      "L1.f1.f1                             0.3048      0.059      5.172      0.000       0.189       0.420\n",
      "L2.f1.f1                             0.3767      0.062      6.077      0.000       0.255       0.498\n",
      "L3.f1.f1                                  0   6.86e-10          0      1.000   -1.34e-09    1.34e-09\n",
      "L4.f1.f1                                  0   6.86e-10          0      1.000   -1.34e-09    1.34e-09\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)    -0.2253      0.090     -2.495      0.013      -0.402      -0.048\n",
      "L1.e(std_income).e(std_income)      -0.1730      0.022     -7.836      0.000      -0.216      -0.130\n",
      "L2.e(std_income).e(std_income)      -0.0936      0.044     -2.118      0.034      -0.180      -0.007\n",
      "L1.e(std_sales).e(std_sales)        -0.4895      0.046    -10.601      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)             0.2341      0.042      5.530      0.000       0.151       0.317\n",
      "L2.e(std_emp).e(std_emp)             0.4956      0.051      9.766      0.000       0.396       0.595\n",
      "loading.L1.f1.std_emp               -0.0724      0.038     -1.895      0.058      -0.147       0.002\n",
      "loading.L2.f1.std_emp                0.0004      0.036      0.010      0.992      -0.071       0.071\n",
      "loading.L3.f1.std_emp               -0.1738      0.028     -6.168      0.000      -0.229      -0.119\n",
      "========================================================================================================\n",
      "Ljung-Box (Q):          59.19, 34.27, 68.30, 61.67   Jarque-Bera (JB):   231.73, 9688.65, 25.32, 3387.21\n",
      "Prob(Q):                    0.03, 0.73, 0.00, 0.02   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, 16.65\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 2.99e+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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}