dfm_coincident.ipynb

{
 "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 subtantial 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 thse 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": {
    "collapsed": false
   },
   "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",
    "import seaborn as sn\n",
    "\n",
    "np.set_printoptions(precision=4, suppress=True, linewidth=120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "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",
    "end = '2016-06-01'\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 the most 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",
    "Until this is corrected, the pre-8/12/15 dataset can be downloaded from Alfred (https://alfred.stlouisfed.org/series/downloaddata?seid=CMRMTSPL) or constructed by hand from HMRMT and CMRMT, as I do below (process taken from the notes in the Alfred xls file)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "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": {
    "collapsed": false
   },
   "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.ix[:'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.ix[prev_month] = sales.ix[month] / (1 + HMRMT_growth.ix[prev_month].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "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": {
    "collapsed": false
   },
   "outputs": [
    {
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WP0Lg+9tP8O7nZd23vyjsGrzl62v7/q+XPygC4PrJaVw3Oa1XrqUUQggh/E2N7dRgZjZX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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113dede50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dta.ix[:, '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": {
    "collapsed": true
   },
   "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",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\Lambda f_t + B x_t + u_t \\\\\n",
    "f_t & = A_1 f_{t-1} + \\dots + A_p f_{t-p} + \\eta_t \\qquad \\eta_t \\sim N(0, I)\\\\\n",
    "u_t & = C_1 u_{t-1} + \\dots + C_1 f_{t-q} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\Sigma)\n",
    "\\end{align}\n",
    "$$\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) proces. 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 de-meaned 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 accomodated 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 paramters) 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": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get the endogenous data\n",
    "endog = dta.ix['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)"
   ]
  },
  {
   "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": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                             Statespace Model Results                                            \n",
      "=================================================================================================================\n",
      "Dep. Variable:     ['std_indprod', 'std_income', 'std_sales', 'std_emp']   No. Observations:                  449\n",
      "Model:                                 DynamicFactor(factors=1, order=2)   Log Likelihood               -2123.894\n",
      "                                                          + AR(2) errors   AIC                           4283.788\n",
      "Date:                                                   Sun, 22 Jan 2017   BIC                           4357.714\n",
      "Time:                                                           14:15:55   HQIC                          4312.928\n",
      "Sample:                                                       02-01-1979                                         \n",
      "                                                            - 06-01-2016                                         \n",
      "Covariance Type:                                                     opg                                         \n",
      "====================================================================================================\n",
      "                                       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------------\n",
      "loading.f1.std_indprod              -0.6193      0.045    -13.675      0.000      -0.708      -0.531\n",
      "loading.f1.std_income               -0.2449      0.036     -6.774      0.000      -0.316      -0.174\n",
      "loading.f1.std_sales                -0.3900      0.029    -13.467      0.000      -0.447      -0.333\n",
      "loading.f1.std_emp                  -0.4205      0.042     -9.996      0.000      -0.503      -0.338\n",
      "sigma2.std_indprod                   0.2760      0.039      7.165      0.000       0.201       0.352\n",
      "sigma2.std_income                    0.8598      0.028     30.785      0.000       0.805       0.915\n",
      "sigma2.std_sales                     0.5457      0.042     13.116      0.000       0.464       0.627\n",
      "sigma2.std_emp                       0.2735      0.025     10.995      0.000       0.225       0.322\n",
      "L1.f1.f1                             0.4741      0.097      4.899      0.000       0.284       0.664\n",
      "L2.f1.f1                             0.2398      0.084      2.843      0.004       0.074       0.405\n",
      "L1.e(std_indprod).e(std_indprod)    -0.4335      0.106     -4.099      0.000      -0.641      -0.226\n",
      "L2.e(std_indprod).e(std_indprod)    -0.1852      0.079     -2.354      0.019      -0.339      -0.031\n",
      "L1.e(std_income).e(std_income)      -0.1987      0.023     -8.639      0.000      -0.244      -0.154\n",
      "L2.e(std_income).e(std_income)      -0.0945      0.045     -2.086      0.037      -0.183      -0.006\n",
      "L1.e(std_sales).e(std_sales)        -0.6220      0.050    -12.348      0.000      -0.721      -0.523\n",
      "L2.e(std_sales).e(std_sales)        -0.2900      0.052     -5.613      0.000      -0.391      -0.189\n",
      "L1.e(std_emp).e(std_emp)             0.2820      0.040      7.120      0.000       0.204       0.360\n",
      "L2.e(std_emp).e(std_emp)             0.4970      0.046     10.772      0.000       0.407       0.587\n",
      "=========================================================================================================\n",
      "Ljung-Box (Q):          72.03, 26.97, 49.92, 77.45   Jarque-Bera (JB):   271.75, 15618.63, 13.51, 4946.36\n",
      "Prob(Q):                    0.00, 0.94, 0.14, 0.00   Prob(JB):                     0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H):     0.71, 4.54, 0.48, 0.40   Skew:                        0.35, -1.24, 0.06, 0.96\n",
      "Prob(H) (two-sided):        0.04, 0.00, 0.00, 0.00   Kurtosis:                   6.74, 31.79, 3.84, 19.15\n",
      "=========================================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cS+etiAMAGo5DfZUB7mByWkK0X04KD5ZR1Lx5ZAjP7e7LEpuVgCcQx9cf2IsT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152a0890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, res.factors.filtered[0], label='Factor')\n",
    "ax.legend()\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "rec = DataReader('USREC', 'fred', start=start, end=end)\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:len(rec)], ylim[0], ylim[1], rec.values[:,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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11418a590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coincident Index\n",
    "\n",
    "As described above, the goal of this model was to create an interpretable series which could be used to understand the current status of the macroeconomy. This is what the coincident index is designed to do. It is constructed below. For readers interested in an explanation of the construction, see Kim and Nelson (1999) or Stock and Watson (1991).\n",
    "\n",
    "In essense, 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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PKMc7RjhyaoihsUkA7DYLdZV5NNQUcvv1Kwn4Jk2uVEREZPYp7ItIUpkIRWnr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\nG9vNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11418a750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2016-06-01')['USPHCI']\n",
    "usphci.plot(figsize=(13,3));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "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.ix['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.ix['1992-07-01'] / coincident_index.ix['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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JRumPDdI3Uwn3E6lgdZtapabJ2sAqZwuN1nq85hpqTTVYdObZCy1dMDk5cd3jJQpJjsRO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\nhCg1+yIiIiIiIUrNvoiIiIhIiPp/sjNZA2nKut0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1141add90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "coincident_index = compute_coincident_index(mod, res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, label='Coincident index')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:len(rec)], ylim[0], ylim[1], rec.values[:,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": {
    "collapsed": false
   },
   "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 unconstraint, since we only want an AR(2),\n",
    "            # and the previous unconstraint 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['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 hadn't 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 can't 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 don't 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": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                             Statespace Model Results                                            \n",
      "=================================================================================================================\n",
      "Dep. Variable:     ['std_indprod', 'std_income', 'std_sales', 'std_emp']   No. Observations:                  449\n",
      "Model:                                 DynamicFactor(factors=1, order=4)   Log Likelihood               -2109.326\n",
      "                                                          + AR(2) errors   AIC                           4264.653\n",
      "Date:                                                   Sun, 22 Jan 2017   BIC                           4359.114\n",
      "Time:                                                           14:16:07   HQIC                          4301.887\n",
      "Sample:                                                       02-01-1979                                         \n",
      "                                                            - 06-01-2016                                         \n",
      "Covariance Type:                                                     opg                                         \n",
      "====================================================================================================\n",
      "                                       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------------------\n",
      "loading.f1.std_indprod              -0.5990      0.051    -11.745      0.000      -0.699      -0.499\n",
      "loading.f1.std_income               -0.2349      0.037     -6.409      0.000      -0.307      -0.163\n",
      "loading.f1.std_sales                -0.3794      0.032    -11.835      0.000      -0.442      -0.317\n",
      "loading.f1.std_emp                  -0.4353      0.038    -11.322      0.000      -0.511      -0.360\n",
      "sigma2.std_indprod                   0.2757      0.043      6.460      0.000       0.192       0.359\n",
      "sigma2.std_income                    0.8634      0.028     30.776      0.000       0.808       0.918\n",
      "sigma2.std_sales                     0.5352      0.041     13.189      0.000       0.456       0.615\n",
      "sigma2.std_emp                       0.2471      0.024     10.196      0.000       0.200       0.295\n",
      "L1.f1.f1                             0.5473      0.113      4.842      0.000       0.326       0.769\n",
      "L2.f1.f1                             0.1707      0.098      1.733      0.083      -0.022       0.364\n",
      "L3.f1.f1                                  0   1.73e-10          0      1.000   -3.39e-10    3.39e-10\n",
      "L4.f1.f1                                  0   1.73e-10          0      1.000   -3.39e-10    3.39e-10\n",
      "L1.e(std_indprod).e(std_indprod)    -0.4763      0.110     -4.349      0.000      -0.691      -0.262\n",
      "L2.e(std_indprod).e(std_indprod)    -0.2078      0.077     -2.694      0.007      -0.359      -0.057\n",
      "L1.e(std_income).e(std_income)      -0.2016      0.023     -8.690      0.000      -0.247      -0.156\n",
      "L2.e(std_income).e(std_income)      -0.0958      0.045     -2.123      0.034      -0.184      -0.007\n",
      "L1.e(std_sales).e(std_sales)        -0.6285      0.051    -12.422      0.000      -0.728      -0.529\n",
      "L2.e(std_sales).e(std_sales)        -0.2896      0.051     -5.730      0.000      -0.389      -0.191\n",
      "L1.e(std_emp).e(std_emp)             0.2661      0.052      5.133      0.000       0.165       0.368\n",
      "L2.e(std_emp).e(std_emp)             0.4662      0.057      8.200      0.000       0.355       0.578\n",
      "loading.L1.f1.std_emp                0.0601      0.056      1.077      0.282      -0.049       0.170\n",
      "loading.L2.f1.std_emp               -0.0651      0.051     -1.269      0.204      -0.166       0.035\n",
      "loading.L3.f1.std_emp               -0.1378      0.033     -4.146      0.000      -0.203      -0.073\n",
      "=========================================================================================================\n",
      "Ljung-Box (Q):          67.73, 27.16, 51.11, 67.55   Jarque-Bera (JB):   250.10, 15507.40, 12.37, 3968.45\n",
      "Prob(Q):                    0.00, 0.94, 0.11, 0.00   Prob(JB):                     0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H):     0.74, 4.54, 0.49, 0.41   Skew:                        0.32, -1.23, 0.05, 0.80\n",
      "Prob(H) (two-sided):        0.07, 0.00, 0.00, 0.00   Kurtosis:                   6.60, 31.69, 3.81, 17.48\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 2.79e+19. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "# Create the model\n",
    "extended_mod = ExtendedDFM(endog)\n",
    "initial_extended_res = extended_mod.fit(method='powell', disp=False)\n",
    "extended_res = extended_mod.fit(initial_extended_res.params, 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 mesaures 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": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8tLQUcXFxMJlMOHjwoNzlERERKZrswV5SUgKbzYb8/HykpqYiJyfHMXb79m1kZ2fjk08+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\ndiIiIhVhsBMREanIfwAPHNPwcXlXUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11418a810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "extended_res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mrree2t56DvTW0eRt4bbR38bj1tLRG6DWU8sBc81J6/niwrF4u/3ElaI+5GaD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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ffd550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n",
    "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set(title='Coincident indices, comparison')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:len(rec)], ylim[0], ylim[1], rec.values[:,0], facecolor='k', alpha=0.1);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}