{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dynamic factors and coincident indices\n",
    "\n",
    "Factor models generally try to find a small number of unobserved \"factors\" that influence a substantial portion of the variation in a larger number of observed variables, and they are related to dimension-reduction techniques such as principal components analysis. Dynamic factor models explicitly model the transition dynamics of the unobserved factors, and so are often applied to time-series data.\n",
    "\n",
    "Macroeconomic coincident indices are designed to capture the common component of the \"business cycle\"; such a component is assumed to simultaneously affect many macroeconomic variables. Although the estimation and use of coincident indices (for example the [Index of Coincident Economic Indicators](http://www.newyorkfed.org/research/regional_economy/coincident_summary.html)) pre-dates dynamic factor models, in several influential papers Stock and Watson (1989, 1991) used a dynamic factor model to provide a theoretical foundation for them.\n",
    "\n",
    "Below, we follow the treatment found in Kim and Nelson (1999), of the Stock and Watson (1991) model, to formulate a dynamic factor model, estimate its parameters via maximum likelihood, and create a coincident index."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Macroeconomic data\n",
    "\n",
    "The coincident index is created by considering the comovements in four macroeconomic variables (versions of these variables are available on [FRED](https://research.stlouisfed.org/fred2/); the ID of the series used below is given in parentheses):\n",
    "\n",
    "- Industrial production (IPMAN)\n",
    "- Real aggregate income (excluding transfer payments) (W875RX1)\n",
    "- Manufacturing and trade sales (CMRMTSPL)\n",
    "- Employees on non-farm payrolls (PAYEMS)\n",
    "\n",
    "In all cases, the data is at the monthly frequency and has been seasonally adjusted; the time-frame considered is 1972 - 2005."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:29.836926Z",
     "iopub.status.busy": "2022-11-02T17:11:29.834218Z",
     "iopub.status.idle": "2022-11-02T17:11:31.121614Z",
     "shell.execute_reply": "2022-11-02T17:11:31.120928Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.set_printoptions(precision=4, suppress=True, linewidth=120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:31.127038Z",
     "iopub.status.busy": "2022-11-02T17:11:31.125753Z",
     "iopub.status.idle": "2022-11-02T17:11:33.922884Z",
     "shell.execute_reply": "2022-11-02T17:11:33.922204Z"
    }
   },
   "outputs": [],
   "source": [
    "from pandas_datareader.data import DataReader\n",
    "\n",
    "# Get the datasets from FRED\n",
    "start = '1979-01-01'\n",
    "end = '2014-12-01'\n",
    "indprod = DataReader('IPMAN', 'fred', start=start, end=end)\n",
    "income = DataReader('W875RX1', 'fred', start=start, end=end)\n",
    "sales = DataReader('CMRMTSPL', 'fred', start=start, end=end)\n",
    "emp = DataReader('PAYEMS', 'fred', start=start, end=end)\n",
    "# dta = pd.concat((indprod, income, sales, emp), axis=1)\n",
    "# dta.columns = ['indprod', 'income', 'sales', 'emp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: in a recent update on FRED (8/12/15) the time series CMRMTSPL was truncated to begin in 1997; this is probably a mistake due to the fact that CMRMTSPL is a spliced series, so the earlier period is from the series HMRMT and the latter period is defined by CMRMT.\n",
    "\n",
    "This has since (02/11/16) been corrected, however the series could also be constructed by hand from HMRMT and CMRMT, as shown below (process taken from the notes in the Alfred xls file)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:33.931050Z",
     "iopub.status.busy": "2022-11-02T17:11:33.930783Z",
     "iopub.status.idle": "2022-11-02T17:11:33.935091Z",
     "shell.execute_reply": "2022-11-02T17:11:33.934275Z"
    }
   },
   "outputs": [],
   "source": [
    "# HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end)\n",
    "# CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:33.938692Z",
     "iopub.status.busy": "2022-11-02T17:11:33.938447Z",
     "iopub.status.idle": "2022-11-02T17:11:33.942649Z",
     "shell.execute_reply": "2022-11-02T17:11:33.941979Z"
    }
   },
   "outputs": [],
   "source": [
    "# HMRMT_growth = HMRMT.diff() / HMRMT.shift()\n",
    "# sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index)\n",
    "\n",
    "# # Fill in the recent entries (1997 onwards)\n",
    "# sales[CMRMT.index] = CMRMT\n",
    "\n",
    "# # Backfill the previous entries (pre 1997)\n",
    "# idx = sales.loc[:'1997-01-01'].index\n",
    "# for t in range(len(idx)-1, 0, -1):\n",
    "#     month = idx[t]\n",
    "#     prev_month = idx[t-1]\n",
    "#     sales.loc[prev_month] = sales.loc[month] / (1 + HMRMT_growth.loc[prev_month].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:33.946064Z",
     "iopub.status.busy": "2022-11-02T17:11:33.945788Z",
     "iopub.status.idle": "2022-11-02T17:11:33.953351Z",
     "shell.execute_reply": "2022-11-02T17:11:33.952678Z"
    }
   },
   "outputs": [],
   "source": [
    "dta = pd.concat((indprod, income, sales, emp), axis=1)\n",
    "dta.columns = ['indprod', 'income', 'sales', 'emp']\n",
    "dta.index.freq = dta.index.inferred_freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:33.957051Z",
     "iopub.status.busy": "2022-11-02T17:11:33.956814Z",
     "iopub.status.idle": "2022-11-02T17:11:34.790098Z",
     "shell.execute_reply": "2022-11-02T17:11:34.789377Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n",
    "\n",
    "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:34.793673Z",
     "iopub.status.busy": "2022-11-02T17:11:34.793263Z",
     "iopub.status.idle": "2022-11-02T17:11:34.808039Z",
     "shell.execute_reply": "2022-11-02T17:11:34.807357Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create log-differenced series\n",
    "dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100\n",
    "dta['dln_income'] = (np.log(dta.income)).diff() * 100\n",
    "dta['dln_sales'] = (np.log(dta.sales)).diff() * 100\n",
    "dta['dln_emp'] = (np.log(dta.emp)).diff() * 100\n",
    "\n",
    "# De-mean and standardize\n",
    "dta['std_indprod'] = (dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std()\n",
    "dta['std_income'] = (dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std()\n",
    "dta['std_sales'] = (dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std()\n",
    "dta['std_emp'] = (dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic factors\n",
    "\n",
    "A general dynamic factor model is written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\Lambda f_t + B x_t + u_t \\\\\n",
    "f_t & = A_1 f_{t-1} + \\dots + A_p f_{t-p} + \\eta_t \\qquad \\eta_t \\sim N(0, I)\\\\\n",
    "u_t & = C_1 u_{t-1} + \\dots + C_q u_{t-q} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\Sigma)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $y_t$ are observed data, $f_t$ are the unobserved factors (evolving as a vector autoregression), $x_t$ are (optional) exogenous variables, and $u_t$ is the error, or \"idiosyncratic\", process ($u_t$ is also optionally allowed to be autocorrelated). The $\\Lambda$ matrix is often referred to as the matrix of \"factor loadings\". The variance of the factor error term is set to the identity matrix to ensure identification of the unobserved factors.\n",
    "\n",
    "This model can be cast into state space form, and the unobserved factor estimated via the Kalman filter. The likelihood can be evaluated as a byproduct of the filtering recursions, and maximum likelihood estimation used to estimate the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model specification\n",
    "\n",
    "The specific dynamic factor model in this application has 1 unobserved factor which is assumed to follow an AR(2) process. The innovations $\\varepsilon_t$ are assumed to be independent (so that $\\Sigma$ is a diagonal matrix) and the error term associated with each equation, $u_{i,t}$ is assumed to follow an independent AR(2) process.\n",
    "\n",
    "Thus the specification considered here is:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n",
    "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n",
    "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $i$ is one of: `[indprod, income, sales, emp ]`.\n",
    "\n",
    "This model can be formulated using the `DynamicFactor` model built-in to statsmodels. In particular, we have the following specification:\n",
    "\n",
    "- `k_factors = 1` - (there is 1 unobserved factor)\n",
    "- `factor_order = 2` - (it follows an AR(2) process)\n",
    "- `error_var = False` - (the errors evolve as independent AR processes rather than jointly as a VAR - note that this is the default option, so it is not specified below)\n",
    "- `error_order = 2` - (the errors are autocorrelated of order 2: i.e. AR(2) processes)\n",
    "- `error_cov_type = 'diagonal'` - (the innovations are uncorrelated; this is again the default)\n",
    "\n",
    "Once the model is created, the parameters can be estimated via maximum likelihood; this is done using the `fit()` method.\n",
    "\n",
    "**Note**: recall that we have demeaned and standardized the data; this will be important in interpreting the results that follow.\n",
    "\n",
    "**Aside**: in their empirical example, Kim and Nelson (1999) actually consider a slightly different model in which the employment variable is allowed to also depend on lagged values of the factor - this model does not fit into the built-in `DynamicFactor` class, but can be accommodated by using a subclass to implement the required new parameters and restrictions - see Appendix A, below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter estimation\n",
    "\n",
    "Multivariate models can have a relatively large number of parameters, and it may be difficult to escape from local minima to find the maximized likelihood. In an attempt to mitigate this problem, I perform an initial maximization step (from the model-defined starting parameters) using the modified Powell method available in Scipy (see the minimize documentation for more information). The resulting parameters are then used as starting parameters in the standard LBFGS optimization method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:11:34.811738Z",
     "iopub.status.busy": "2022-11-02T17:11:34.811173Z",
     "iopub.status.idle": "2022-11-02T17:12:03.801398Z",
     "shell.execute_reply": "2022-11-02T17:12:03.800752Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.10.8/x64/lib/python3.10/site-packages/statsmodels/base/model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "# Get the endogenous data\n",
    "endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp']\n",
    "\n",
    "# Create the model\n",
    "mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2)\n",
    "initial_res = mod.fit(method='powell', disp=False)\n",
    "res = mod.fit(initial_res.params, disp=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimates\n",
    "\n",
    "Once the model has been estimated, there are two components that we can use for analysis or inference:\n",
    "\n",
    "- The estimated parameters\n",
    "- The estimated factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters\n",
    "\n",
    "The estimated parameters can be helpful in understanding the implications of the model, although in models with a larger number of observed variables and / or unobserved factors they can be difficult to interpret.\n",
    "\n",
    "One reason for this difficulty is due to identification issues between the factor loadings and the unobserved factors. One easy-to-see identification issue is the sign of the loadings and the factors: an equivalent model to the one displayed below would result from reversing the signs of all factor loadings and the unobserved factor.\n",
    "\n",
    "Here, one of the easy-to-interpret implications in this model is the persistence of the unobserved factor: we find that exhibits substantial persistence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:03.807188Z",
     "iopub.status.busy": "2022-11-02T17:12:03.805715Z",
     "iopub.status.idle": "2022-11-02T17:12:03.824275Z",
     "shell.execute_reply": "2022-11-02T17:12:03.823693Z"
    }
   },
   "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               -1589.814\n",
      "                                                          + AR(2) errors   AIC                           3215.628\n",
      "Date:                                                   Wed, 02 Nov 2022   BIC                           3288.818\n",
      "Time:                                                           17:12:03   HQIC                          3244.526\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              -1.0266      0.020    -52.383      0.000      -1.065      -0.988\n",
      "loading.f1.std_income               -0.3131      0.011    -27.546      0.000      -0.335      -0.291\n",
      "loading.f1.std_sales                -0.5394      0.021    -25.874      0.000      -0.580      -0.499\n",
      "loading.f1.std_emp                  -0.3050      0.014    -21.688      0.000      -0.333      -0.277\n",
      "sigma2.std_indprod                5.767e-07   1.39e-06      0.415      0.678   -2.15e-06     3.3e-06\n",
      "sigma2.std_income                    0.8754      0.016     53.989      0.000       0.844       0.907\n",
      "sigma2.std_sales                     0.5748      0.003    179.695      0.000       0.569       0.581\n",
      "sigma2.std_emp                       0.3581      0.009     39.855      0.000       0.340       0.376\n",
      "L1.f1.f1                             0.2601      0.013     19.409      0.000       0.234       0.286\n",
      "L2.f1.f1                             0.2645      0.009     28.465      0.000       0.246       0.283\n",
      "L1.e(std_indprod).e(std_indprod) -1.668e-07   1.14e-09   -145.845      0.000   -1.69e-07   -1.65e-07\n",
      "L2.e(std_indprod).e(std_indprod)     1.0000   3.72e-08   2.69e+07      0.000       1.000       1.000\n",
      "L1.e(std_income).e(std_income)      -0.1875      0.018    -10.413      0.000      -0.223      -0.152\n",
      "L2.e(std_income).e(std_income)      -0.0983      0.010     -9.415      0.000      -0.119      -0.078\n",
      "L1.e(std_sales).e(std_sales)        -0.4530      0.006    -70.375      0.000      -0.466      -0.440\n",
      "L2.e(std_sales).e(std_sales)        -0.1926      0.002    -84.558      0.000      -0.197      -0.188\n",
      "L1.e(std_emp).e(std_emp)             0.1888      0.016     11.557      0.000       0.157       0.221\n",
      "L2.e(std_emp).e(std_emp)             0.4421      0.019     23.670      0.000       0.405       0.479\n",
      "=========================================================================================================\n",
      "Ljung-Box (L1) (Q):     8.05, 0.13, 0.01, 1.92   Jarque-Bera (JB):   3050420.53, 11405.19, 10.41, 2599.40\n",
      "Prob(Q):                0.00, 0.71, 0.90, 0.17   Prob(JB):                         0.00, 0.00, 0.01, 0.00\n",
      "Heteroskedasticity (H): 0.00, 4.71, 0.53, 0.48   Skew:                          -20.05, -1.16, 0.01, 0.91\n",
      "Prob(H) (two-sided):    0.00, 0.00, 0.00, 0.00   Kurtosis:                     413.19, 28.09, 3.76, 14.89\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 2.53e+18. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "print(res.summary(separate_params=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimated factors\n",
    "\n",
    "While it can be useful to plot the unobserved factors, it is less useful here than one might think for two reasons:\n",
    "\n",
    "1. The sign-related identification issue described above.\n",
    "2. Since the data was differenced, the estimated factor explains the variation in the differenced data, not the original data.\n",
    "\n",
    "It is for these reasons that the coincident index is created (see below).\n",
    "\n",
    "With these reservations, the unobserved factor is plotted below, along with the NBER indicators for US recessions. It appears that the factor is successful at picking up some degree of business cycle activity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:03.829194Z",
     "iopub.status.busy": "2022-11-02T17:12:03.827858Z",
     "iopub.status.idle": "2022-11-02T17:12:04.375382Z",
     "shell.execute_reply": "2022-11-02T17:12:04.374764Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, res.factors.filtered[0], label='Factor')\n",
    "ax.legend()\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "rec = DataReader('USREC', 'fred', start=start, end=end)\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Post-estimation\n",
    "\n",
    "Although here we will be able to interpret the results of the model by constructing the coincident index, there is a useful and generic approach for getting a sense for what is being captured by the estimated factor. By taking the estimated factors as given, regressing them (and a constant) each (one at a time) on each of the observed variables, and recording the coefficients of determination ($R^2$ values), we can get a sense of the variables for which each factor explains a substantial portion of the variance and the variables for which it does not.\n",
    "\n",
    "In models with more variables and more factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables).\n",
    "\n",
    "In this model, with only four endogenous variables and one factor, it is easy to digest a simple table of the $R^2$ values, but in larger models it is not. For this reason, a bar plot is often employed; from the plot we can easily see that the factor explains most of the variation in industrial production index and a large portion of the variation in sales and employment, it is less helpful in explaining income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:04.379287Z",
     "iopub.status.busy": "2022-11-02T17:12:04.379026Z",
     "iopub.status.idle": "2022-11-02T17:12:04.671579Z",
     "shell.execute_reply": "2022-11-02T17:12:04.670743Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OHKmxY8fW1ksAAABALXO6++TWBu6TCwAA4Nyu6/vkAgAAANWBkAsAAACXU+mQe/bsWR0+fLhc+/fff18tBQEAAABVVamQu2LFCrVt21a9evXSrbfeqm+++cbaNmjQoGovDgAAALgalQq5f/zjH5WRkaFt27Zp0aJFGjJkiJYuXSpJ4vo1AAAAOItK3ULs/Pnz1q28IiMj9cUXX+iRRx7Rnj17ZLPZrkmBAAAAQGVV6kxukyZNtH37dut5o0aNtH79emVlZTm0AwAAALWpUiH3rbfeUpMmTRzaPDw89O677+r//u//qrUwAAAA4GpVarlC8+bNL7mtW7duVS4GAAAAqA5Vuk/uwYMH9emnnyo3N7fC7UeOHKnK7gEAAICrctUh991331WbNm30wAMP6KabbtJbb70lScrJydH06dMVHR2tFi1aVFuhAAAAwJW66pCbnJysESNG6LvvvtN9992nYcOGadKkSWrdurUWL16sqKgovffee9VZKwAAAHBFKrUm9+f27t2rkSNHqmXLlkpNTVWLFi301Vdfafv27QoLC6vOGgEAAIBKueozuefPn5e3t7ekHy9I8/Ly0owZMwi4AAAAqHVVuvBs6dKl2rVrlyTJ3d1dDRs2rJaiAAAAgKq46pB75513KikpSTfffLMCAwN17tw5vfbaa/r73/+unTt36sKFC9VZJwAAAHDFrnpN7sUvf/jhhx+UkZGhzMxMZWZm6m9/+5tOnTolDw8PtWvXjm9CAwAAQI276pB7Udu2bdW2bVs9/vjjVtv+/fu1ZcsWbd26taq7BwAAACrNZowxtV1EbSssLJSfn58KCgrk6+tb2+UAAADgFyqb16p04RkAAADgjJwy5Kampio0NFReXl6Kjo7Wpk2brmjcsmXLZLPZ1KdPn2tbIAAAAJya04Xc5cuXKzExUUlJScrMzFR4eLji4uJ07Nixy447cOCA/vCHP+jOO++soUoBAADgrJwu5M6aNUtPP/20EhIS1LFjR82bN0/16tXTwoULLzmmtLRUAwcO1NSpU3XTTTfVYLUAAABwRk4VcktKSpSRkaHY2Firzc3NTbGxsUpPT7/kuGnTpqlJkyYaMmRITZQJAAAAJ1flW4hVp/z8fJWWlsputzu02+1265vVfumf//yn/vrXv2rbtm1XfJzi4mIVFxdbzwsLC6+qXgAAADgnpzqTW1mnT5/WoEGDtGDBAgUGBl7xuJSUFPn5+VmPkJCQa1glAAAAappTnckNDAyUu7u78vLyHNrz8vIUFBRUrv/evXt14MAB9e7d22orKyuTJNWpU0fZ2dlq3bp1uXHjx49XYmKi9bywsJCgCwAA4EKcKuR6eHgoMjJSaWlp1m3AysrKlJaWpuHDh5fr36FDB3333XcObRMnTtTp06f12muvXTK4enp6ytPTs9rrBwAAgHNwqpArSYmJiRo8eLCioqLUpUsXzZ49W0VFRUpISJAkxcfHq1mzZkpJSZGXl5duueUWh/H+/v6SVK4dAAAANw6nC7n9+vXT8ePHNXnyZOXm5ioiIkLr1q2zLkbLycmRm9t1vZQYAAAA15jNGGNqu4jaVtnvQgYAAEDNqmxe45QoAAAAXA4hFwAAAC6HkAsAAACXQ8gFAACAyyHkAgAAwOUQcgEAAOByCLkAAABwOYRcAAAAuBxCLgAAAFwOIRcAAAAuh5ALAAAAl0PIBQAAgMsh5AIAAMDlEHIBAADgcgi5AAAAcDmEXAAAALgcQi4AAABcDiEXAAAALoeQCwAAAJdDyAUAAIDLccqQm5qaqtDQUHl5eSk6OlqbNm26ZN8FCxbozjvvVMOGDdWwYUPFxsZetj8AAABcn9OF3OXLlysxMVFJSUnKzMxUeHi44uLidOzYsQr7b9iwQf3799fnn3+u9PR0hYSE6P7779fhw4druHIAAAA4C5sxxtR2ET8XHR2tzp07a+7cuZKksrIyhYSEaMSIERo3btyvji8tLVXDhg01d+5cxcfHX9ExCwsL5efnp4KCAvn6+lapfgAAAFS/yuY1pzqTW1JSooyMDMXGxlptbm5uio2NVXp6+hXt4z//+Y/Onz+vRo0aXbJPcXGxCgsLHR4AAABwHU4VcvPz81VaWiq73e7QbrfblZube0X7GDt2rJo2beoQlH8pJSVFfn5+1iMkJKRKdQMAAMC5OFXIrarp06dr2bJlWr16tby8vC7Zb/z48SooKLAehw4dqsEqAQAAcK3Vqe0Cfi4wMFDu7u7Ky8tzaM/Ly1NQUNBlx86YMUPTp0/XZ599pltvvfWyfT09PeXp6VnlegEAAOCcnOpMroeHhyIjI5WWlma1lZWVKS0tTTExMZcc9/LLLys5OVnr1q1TVFRUTZQKAAAAJ+ZUZ3IlKTExUYMHD1ZUVJS6dOmi2bNnq6ioSAkJCZKk+Ph4NWvWTCkpKZKkl156SZMnT9bSpUsVGhpqrd318fGRj49Prb0OAAAA1B6nC7n9+vXT8ePHNXnyZOXm5ioiIkLr1q2zLkbLycmRm9tPJ6DffPNNlZSU6NFHH3XYT1JSkqZMmVKTpQMAAMBJON19cmsD98kFAABwbtf1fXIBAACA6kDIBQAAgMsh5AIAAMDlEHIBAADgcgi5AAAAcDmEXAAAALgcQi4AAABcDiEXAAAALoeQCwAAAJdDyAUAAIDLIeQCAADA5RByAQAA4HIIuQAAAHA5hFwAAAC4HEIuAAAAXA4hFwAAAC6HkAsAAACXQ8gFAACAyyHkAgAAwOUQcgEAAOBynDLkpqamKjQ0VF5eXoqOjtamTZsu2/+9995Thw4d5OXlpU6dOumjjz6qoUoBAADgjJwu5C5fvlyJiYlKSkpSZmamwsPDFRcXp2PHjlXYf+PGjerfv7+GDBmirVu3qk+fPurTp4927NhRw5UDAADAWdiMMaa2i/i56Ohode7cWXPnzpUklZWVKSQkRCNGjNC4cePK9e/Xr5+Kior04YcfWm133HGHIiIiNG/evCs6ZmFhofz8/FRQUCBfX9/qeSEAAECSFDpubW2XgGvkwPReNXasyua1OjVQ0xUrKSlRRkaGxo8fb7W5ubkpNjZW6enpFY5JT09XYmKiQ1tcXJzef//9Sx6nuLhYxcXF1vOCggJJP755AACgepUV/6e2S8A1UpPZ6eKxrvT8rFOF3Pz8fJWWlsputzu02+127dq1q8Ixubm5FfbPzc295HFSUlI0derUcu0hISFXUTUAAMCNyW92zR/z9OnT8vPz+9V+ThVya8r48eMdzv6WlZXpxIkTCggIkM1mq8XKcL0rLCxUSEiIDh06xNIXVBnzCdWJ+YTqVtNzyhij06dPq2nTplfU36lCbmBgoNzd3ZWXl+fQnpeXp6CgoArHBAUFVaq/JHl6esrT09Ohzd/f/+qKBirg6+vLDxFUG+YTqhPzCdWtJufUlZzBvcip7q7g4eGhyMhIpaWlWW1lZWVKS0tTTExMhWNiYmIc+kvS+vXrL9kfAAAArs+pzuRKUmJiogYPHqyoqCh16dJFs2fPVlFRkRISEiRJ8fHxatasmVJSUiRJI0eOVI8ePTRz5kz16tVLy5Yt05YtWzR//vzafBkAAACoRU4Xcvv166fjx49r8uTJys3NVUREhNatW2ddXJaTkyM3t59OQHft2lVLly7VxIkT9cILL6ht27Z6//33dcstt9TWS8ANzNPTU0lJSeWWwwBXg/mE6sR8QnVz9jnldPfJBQAAAKrKqdbkAgAAANWBkAsAAACXQ8gFAACAyyHk4oZ04MAB2Ww2bdu27Vf7btiwQTabTadOnarSMZ988kn16dOnSvuoitDQUM2ePbvWju/qamNO4cZVmflWVVOmTFFERMQ1Pw6cQ03OrWuNkAuXci2CZNeuXXX06NFK3YAaroM5hZpU2/8Zhuu6EecWIRf4FR4eHgoKCnKKr3wuKSmp7RJQDZxpTgGAqyLk4rq0YsUKderUSd7e3goICFBsbKzGjBmjJUuW6B//+IdsNptsNps2bNggSdq0aZNuu+02eXl5KSoqSlu3br3iY/3yV8uLFy+Wv7+/PvnkE4WFhcnHx0cPPPCAjh49ao0pLS1VYmKi/P39FRAQoOeff16/vFvfXXfdpeHDh2v48OHy8/NTYGCgJk2a5NAvNDRUycnJio+Pl6+vr5555hlJ0sqVK3XzzTfL09NToaGhmjlzpsO+jx07pt69e8vb21utWrXSO++8U5m394bk7HNKkhYuXGj9vQcHB2v48OHWtpycHD388MPy8fGRr6+vHnvsMYevPL/4K+eFCxeqRYsW8vHx0bPPPqvS0lK9/PLLCgoKUpMmTfSnP/3J4ZinTp3SU089pcaNG8vX11f33HOPvv3220q+u/ilmpxvJ0+e1MCBA9W4cWN5e3urbdu2WrRokbV97NixateunerVq6ebbrpJkyZN0vnz5y+7z7/85S8KCwuTl5eXOnTooDfeeMPaVlJSouHDhys4OFheXl5q2bKl9QVOuPZqcm5J0o4dO9SzZ0/5+PjIbrdr0KBBys/Pt7bfddddGjFihEaNGqWGDRvKbrdrwYIF1hd9NWjQQG3atNHHH39sjbn4Gbl27Vrdeuut8vLy0h133KEdO3ZU7s0wwHXmyJEjpk6dOmbWrFlm//79Zvv27SY1NdWcPn3aPPbYY+aBBx4wR48eNUePHjXFxcXm9OnTpnHjxmbAgAFmx44d5oMPPjA33XSTkWS2bt36q8f7/PPPjSRz8uRJY4wxixYtMnXr1jWxsbFm8+bNJiMjw4SFhZkBAwZYY1566SXTsGFDs3LlSrNz504zZMgQ06BBA/Pwww9bfXr06GF8fHzMyJEjza5du8zbb79t6tWrZ+bPn2/1admypfH19TUzZswwe/bsMXv27DFbtmwxbm5uZtq0aSY7O9ssWrTIeHt7m0WLFlnjevbsacLDw016errZsmWL6dq1q/H29javvvpqFd9913Q9zKk33njDeHl5mdmzZ5vs7GyzadMm6++ztLTUREREmO7du5stW7aYr7/+2kRGRpoePXpY45OSkoyPj4959NFHzffff2/WrFljPDw8TFxcnBkxYoTZtWuXWbhwoZFkvv76a2tcbGys6d27t9m8ebPZvXu3+f3vf28CAgLMv//97+p4629INT3fnnvuORMREWE2b95s9u/fb9avX2/WrFljbU9OTjZfffWV2b9/v1mzZo2x2+3mpZdesrYnJSWZ8PBw6/nbb79tgoODzcqVK82+ffvMypUrTaNGjczixYuNMca88sorJiQkxHzxxRfmwIED5ssvvzRLly6ttvcPl1bTc+vkyZOmcePGZvz48SYrK8tkZmaa++67z9x9991Wnx49epgGDRqY5ORks3v3bpOcnGzc3d1Nz549zfz5883u3bvNsGHDTEBAgCkqKjLG/PQZGRYWZj799FOzfft289BDD5nQ0FBTUlJyxe8HIRfXnYyMDCPJHDhwoNy2wYMHOwRJY4z585//bAICAszZs2ettjfffLNKgUSS2bNnj9UnNTXV2O1263lwcLB5+eWXrefnz583zZs3Lxdyw8LCTFlZmdU2duxYExYWZj1v2bKl6dOnj0M9AwYMMPfdd59D25gxY0zHjh2NMcZkZ2cbSWbTpk3W9qysLCOJkHsJ18Ocatq0qZkwYUKF+/v000+Nu7u7ycnJsdq+//57h3mQlJRk6tWrZwoLC60+cXFxJjQ01JSWllpt7du3NykpKcYYY7788kvj6+trzp0753C81q1bmz//+c+/+jpRsZqeb7179zYJCQlXXN8rr7xiIiMjree/DLmtW7cuF1qTk5NNTEyMMcaYESNGmHvuucfhsw01o6bnVnJysrn//vsd2g4dOmQkmezsbGPMjz/runfvbm2/cOGCqV+/vhk0aJDVdvToUSPJpKenG2N++oxctmyZ1eff//638fb2NsuXL//Vui5iuQKuO+Hh4br33nvVqVMn9e3bVwsWLNDJkycv2T8rK8v6dcdFMTExVaqhXr16at26tfU8ODhYx44dkyQVFBTo6NGjio6OtrbXqVNHUVFR5fZzxx13OKzLjImJ0Q8//KDS0lKr7ZfjsrKy1K1bN4e2bt26WeOysrJUp04dRUZGWts7dOggf3//q3uxNwBnn1PHjh3TkSNHdO+9916ynpCQEIWEhFhtHTt2lL+/v7Kysqy20NBQNWjQwHput9vVsWNHh69Kt9vt1nG//fZbnTlzRgEBAfLx8bEe+/fv1969e6v0em9kNT3fhg0bpmXLlikiIkLPP/+8Nm7c6LB9+fLl6tatm4KCguTj46OJEycqJyenwn0VFRVp7969GjJkiMOc+OMf/2jNiSeffFLbtm1T+/bt9T//8z/69NNPr7hWVE1Nz61vv/1Wn3/+ucNc6NChgyQ5fEbceuut1p/d3d0VEBCgTp06WW12u12SrM+eimpp1KiR2rdv7/CZ9msIubjuuLu7a/369fr444/VsWNHzZkzR+3bt9f+/ftrrIa6des6PLfZbOXW3FaX+vXrX5P94ifOPqe8vb2v2TEqaisrK5MknTlzRsHBwdq2bZvDIzs7W2PGjKmWmm5ENT3fevbsqYMHD2r06NHWf5b+8Ic/SJLS09M1cOBAPfjgg/rwww+1detWTZgw4ZIXuZ45c0aStGDBAoc5sWPHDn399deSpNtvv1379+9XcnKyzp49q8cee0yPPvroNXltcFTTc+vMmTPq3bt3uc+IH374Qb/5zW+sfr/22XPxZM/Fz57qQsjFdclms6lbt26aOnWqtm7dKg8PD61evVoeHh4OZ0ElKSwsTNu3b9e5c+estosfxteCn5+fgoOD9c0331htFy5cUEZGRrm+P+9zsa62bdvK3d39kvsPCwvTV1995dD21VdfqV27dnJ3d1eHDh3KHS87O5t7sv4KZ55TDRo0UGhoqNLS0ircHhYWpkOHDunQoUNW286dO3Xq1Cl17Njxqo97++23Kzc3V3Xq1FGbNm0cHoGBgVe9X9T8fGvcuLEGDx6st99+W7Nnz9b8+fMlSRs3blTLli01YcIERUVFqW3btjp48OAl92O329W0aVPt27ev3Jxo1aqV1c/X11f9+vXTggULtHz5cq1cuVInTpyoVM24OjU5t26//XZ9//33Cg0NLTcfquMEzc9rOXnypHbv3q2wsLArHk/IxXXnm2++0YsvvqgtW7YoJydHq1at0vHjxxUWFqbQ0FBt375d2dnZys/P1/nz5zVgwADZbDY9/fTT2rlzpz766CPNmDHjmtY4cuRITZ8+Xe+//7527dqlZ599tsKQmZOTo8TERGVnZ+vdd9/VnDlzNHLkyMvu+/e//73S0tKUnJys3bt3a8mSJZo7d651ZqZ9+/Z64IEH9N///d/65ptvlJGRoaeeeqrazga6outhTk2ZMkUzZ87U66+/rh9++EGZmZmaM2eOJCk2NladOnXSwIEDlZmZqU2bNik+Pl49evSocJnMlYqNjVVMTIz69OmjTz/9VAcOHNDGjRs1YcIEbdmypbpe2g2npufb5MmT9Y9//EN79uzR999/rw8//NAKCm3btlVOTo6WLVumvXv36vXXX9fq1asvu7+pU6cqJSVFr7/+unbv3q3vvvtOixYt0qxZsyRJs2bN0rvvvqtdu3Zp9+7deu+99xQUFMSSqRpQ03Prueee04kTJ9S/f39t3rxZe/fu1SeffKKEhIRygfpqTJs2TWlpadqxY4eefPJJBQYGVu5ev1e8ehdwEjt37jRxcXGmcePGxtPT07Rr187MmTPHGGPMsWPHzH333Wd8fHyMJPP5558bY4xJT0834eHhxsPDw0RERJiVK1dW6SIhPz8/hz6rV682P//ndP78eTNy5Ejj6+tr/P39TWJioomPjy934dmzzz5rhg4danx9fU3Dhg3NCy+84HCxRsuWLSu8WGzFihWmY8eOpm7duqZFixbmlVdecdh+9OhR06tXL+Pp6WlatGhh/va3v11yX7g+5pQxxsybN8+0b9/e1K1b1wQHB5sRI0ZY2w4ePGj+67/+y9SvX980aNDA9O3b1+Tm5lrbf3nxkDEVX4jSo0cPM3LkSOt5YWGhGTFihGnatKmpW7euCQkJMQMHDnS4yA2VU9PzLTk52YSFhRlvb2/TqFEj8/DDD5t9+/ZZ28eMGWMCAgKMj4+P6devn3n11Vcd5mNFc+edd94xERERxsPDwzRs2ND85je/MatWrTLGGDN//nwTERFh6tevb3x9fc29995rMjMzq/Se4crU9Nwyxpjdu3ebRx55xPj7+xtvb2/ToUMHM2rUKOtn2S8/U4yp+GebJLN69WpjzE+fkR988IG5+eabjYeHh+nSpYv59ttvK/V+2P7/jgHUsLvuuksRERF81S4AAD+zYcMG3X333Tp58mSVfgPAcgUAAAC4HEIubnhDhw51uP3Jzx9Dhw6t7fJwHWJOoSYx33CtXO9zi+UKuOEdO3ZMhYWFFW7z9fVVkyZNargiXO+YU6hJzDdcK9f73CLkAgAAwOWwXAEAAAAuh5ALAAAAl0PIBQAAgMsh5AIAAMDlEHIBAADgcgi5AAAAcDmEXAAAALgcQi4AAABczv8D36OTd+egV8AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coincident Index\n",
    "\n",
    "As described above, the goal of this model was to create an interpretable series which could be used to understand the current status of the macroeconomy. This is what the coincident index is designed to do. It is constructed below. For readers interested in an explanation of the construction, see Kim and Nelson (1999) or Stock and Watson (1991).\n",
    "\n",
    "In essence, what is done is to reconstruct the mean of the (differenced) factor. We will compare it to the coincident index on published by the Federal Reserve Bank of Philadelphia (USPHCI on FRED)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:04.675296Z",
     "iopub.status.busy": "2022-11-02T17:12:04.675034Z",
     "iopub.status.idle": "2022-11-02T17:12:05.239533Z",
     "shell.execute_reply": "2022-11-02T17:12:05.238757Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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61NLSEnr9x9ntdtntLN8CAAAA4NQZhqEDjR1at7dB6/Y1aNuRVgXenysixmrWZLdDU3OcunBChuaPy1CMdWg/JpGSEKNbLxyrrxSP0qObDuvB1w5oe5VH1/7+LX3hvHx9f+EEJcfHRLvMsDEMQ1Wt3dp8sFkv767X6+WNA+aPyEuN06Ip2Vo42aUZeSln5QiSkSCs4URBQYGysrK0bt26UBjh9Xq1ZcsW3XrrrZKk4uJitbW1adu2bZo9e7Ykaf369QoGg5ozZ044ywEAAABwljIMQ7trvHpue43W7qpTZUvXgPZJ2Q7dNCdfi2e4lRQ7PP91PcFu1bcvHKfPzc7Vqhf3aU1Jtf66pVIv7arTf1wxUUtn5Qzrxxg6fX16dNNh/XVzparbuge0FaQn6IqpWVo0JVuT3Y5hfZ3od8rhREdHhyoqKkI/Hzp0SKWlpUpNTVV+fr7uuOMO/fznP1dhYWFoKVG32x1a0WPixIm6/PLL9fWvf13/8z//I7/fr9tvv1033njjSa3UAQAAAAAf98HoiK2HW7X1cIveOdSiqtYPP9DGWMwqHpumi4sydXFRpvJS46NYbXhlJsXqNzfM0A3n5unuZ3epvKFDdz29Xa/sqdP/WTJNKQnDYxRFQ3uPXt3ToCMtnWrp6NX6fQ1q7uyfiNRqNmlarlPzCzN0xdQsTXAlEUiMMKe8lOiGDRt00UUXHbN92bJlWr16tQzD0D333KM//OEPamtr0/z58/XAAw9o/PjxoX1bWlp0++236/nnn5fZbNbSpUt1//33KzEx8aRqYClRAAAAAIZh6J1DLfr7tiqt29egls6BK2rYrWYtmOjS1dOzdUFhhhLsw2LKvTPiDwT10BsH9ZtX9ssfMORy2PXzxVN16STXp794EHX6+lTR0KHyhg6V17er9Gib3jncoo9/Oh2VFq/vXlyoRVOzFB8z8v/3G4lO9vP7KYcTQwHhBAAAAHB2au7w6a0DzXqzvFFvlDep1tMTarNbzZqZn6xzR6fqnNGpmj0qRYlnQSBxPLuqPfrukyU6+P5ympdOcunuKycpP23wR4x4uv3acrBZ2460qqy+XeX1Hcc8pvGBmfnJmpmXorTEGI1OS9DCyS5ZWSp1WCOcAAAAADDs9fgDevdwq96oaNSb5U3aXeMd0J4QY9FV09y6blaOZuWnDPnJLAdTd29A968v10OvH1Rf0JDJJC2Y6NKy4tEqHpsW8Ykjq1q7tPL5PVq3t17B43zqTE+0qzAzUeNdiSp0JenCCRnKTRk5j9ugH+EEAAAAgGGpq7dPr+1r1Iu7avXavgZ19QYGtBdlJemCwnTNL8zQeaNTFRcT3SU+h7r99e2694W92ri/MbQtM8muK6dl69zRqZridiovNS4sczgYhqGDTZ1au6tO/72+Qt3+/v/txmQkaO6YNE12O1SYmaTCzMRhMxcGzgzhBAAAAIBhwzAMbdzfqL9tParXyhrU4/9wqUiXw6754zJ0QWG65o1LV0aSPYqVDl8VDe169O0j+mdptbw9fQPaHLFWTclxamqOU5NznJridig/NT70SEVfIKhuf0Bxtv4gqKq1W4ebO9XU0au2rl7VenpU0dChvbVeNbT7Qsc9b3Sq7r1uigpdSYN3oRhSCCcAAAAADHm9fUG9urdeD244oJ3VntD2/NR4LZqapSumZGtarpOVGcLI1xfQ6/ubtH5fvXZVe7Wvzit/4NiPhTaLSXkp8erxB1Tn7TnuoxnHE2Mxa9aoZC2ZlavPzcqVOcKPj2BoO9nP72fn7DAAAAAAosYwDO2q9uof71Xpn6XVau3yS5LibBbddF6+lszK0WS3g0AiQuxWiy6d5Aqt4NHbF9T++nbtqvZoV41HO6u92lfrla8vqINNncc9RqzNrNFpCcp0xMoZZ1N6Ykz/4xquRE3NcSrWxqM2ODWEEwAAAAAGRUN7j54tqdY/tlWrrL49tN3lsOv6c/L01XkFSmUegkEXYzVrSo5TU3KcoW3BoKFab4+ONHUqNsai3OQ4OeJs6vEH5A8YSkuIYUQEwopwAgAAAEDE9PgDWre3QX/fdlSvlzcp8P6zAXarWZdNztLnZudq/rj0iK8cgVNjNpuUkxynnOS4AdsZEYFIIZwAAAAAEDbBoKGjrV3aerhVG8oa9Pr+xgGTL87KT9bnZufpymnZcsbZolgpgKGEcAIAAADAGfF0+fXSrlq9sLNWJZVt6vANXAki2xmrJbNytHRWrsZkJEapSgBDGeEEAAAAgFPW3RvQq3vr9c/SGm3c3zBgtYcYq1kTsx36TGG6Pjs+QzPzU3hsA8AnIpwAAAAAcFL8gaDeKG/Uc6U1+t899erqDYTairKSdM0Mty4uytS4jERZLeYoVgpguCGcAAAAAHBCwaChrYdb9M/tNXppZ21o2U9JykuN07XTc3TNDLfGu5KiWCWA4Y5wAgAAAMAAhmFod41Xz22v0fPba1Tr6Qm1pSfaddW0bF07w60ZeckymXhcA8CZI5wAAAAAIE+3X6/vb9TbB5r19oEmHWnuCrUlxVq1aEqWrpmeo7ljUnlkA0DYEU4AAAAAZyF/IKi9tV5tO9KqDWWNevtA04BJLe1WsxZMdOnq6W5dOCFDsTZLFKsFMNIRTgAAAABniYb2Hm0oa9Rr+xr0RnnTMUt+js1I0IUTMlU8Jk1zx6Yp0c7HBQCDg7sNAAAAMEIFg4Z2Vnu0fl+DXitr0I4qz4B2R6xVs0el6NyCVF02yaVxmUxqCSA6CCcAAACAEaS9x683ypu0fl+DNpQ1qqnDN6B9Wq5TF03I1MVFmZqa45TZzISWAKKPcAIAAAAY5g41dWrd3nqt29ugrYdb1Bf8cO6IRLtVFxSm66KiTF04IUOZSbFRrBQAjo9wAgAAABhmgkFD2ypb9eqeer26t14HGjsHtI/JSNDF74+OOGd0qmKsrK4BYGgjnAAAAACGiVpPt54tqdGTWysHLPVpNZs0Z0yqLily6eKiTI1OT4hilQBw6iISTrS3t+vuu+/WmjVr1NDQoJkzZ+q3v/2tzj33XEmSYRi655579NBDD6mtrU3z5s3Tgw8+qMLCwkiUAwAAAAxLni6/Nh1s1lsVTXrrQJMOfmSERJLdqksmZuqSiS59dkKGHLG2KFYKAGcmIuHEv/3bv2nXrl36y1/+Irfbrccee0wLFizQnj17lJOTo/vuu0/333+/Hn30URUUFOjuu+/WwoULtWfPHsXG8gwcAAAAzk49/oC2HWnVmxVNeruiSTurPfrI9BEym6SZ+Sm64Zw8XTU9W/ExDIQGMDKYDMMwPn23k9fd3a2kpCT985//1JVXXhnaPnv2bC1atEg/+9nP5Ha7deedd+quu+6SJHk8HrlcLq1evVo33njjp57D6/XK6XTK4/HI4XCEs3wAAABg0Hyw1OebFU16+0CTth5uVW9fcMA+YzMSNG9cuuaNS9fcMWlyxjFCAsDwcbKf38Metfb19SkQCBwzAiIuLk5vvvmmDh06pLq6Oi1YsCDU5nQ6NWfOHG3atOm44YTP55PP9+ESSF6vN9xlAwAAABHn7fHrYGOnDjV16J1DLXplT8MxS326HHbNG5seCiSynIwsBjDyhT2cSEpKUnFxsX72s59p4sSJcrlceuKJJ7Rp0yaNGzdOdXV1kiSXyzXgdS6XK9T2catWrdLKlSvDXSoAAAAQdj3+gNp7+uTt8auqtVu7qj3aXePRrmqvKlu6jtk/0W5V8dg0zR+Xrnnj0jQ2I1EmkykKlQNA9ETkIbW//OUvuuWWW5STkyOLxaJZs2bppptu0rZt207reCtWrNDy5ctDP3u9XuXl5YWrXAAAAEBS/2MWrV296g0E5e8z5A8G1RcwtK/Oq//dU6/3jrSqL3j8p6KDQUPtvr5jHsv4OJfDroL0BBVlOXTJxEzNKUhjqU8AZ72IhBNjx47Vxo0b1dnZKa/Xq+zsbN1www0aM2aMsrKyJEn19fXKzs4Ovaa+vl4zZsw47vHsdrvsdnskSgUAAMAg6vEHdKS5S0HDUJzNolibRXE2i+w2s+xWc8RHDBiGobYuv462duloS/f737t0tLVbVS1dqmrtVm/gk8OFk2Ey9Y+IyEiya7LbqSluh6bkODXZ7VByfEwYrgQARpaITu+bkJCghIQEtba26uWXX9Z9992ngoICZWVlad26daEwwuv1asuWLbr11lsjWQ4AAAAiJBA01OHrU2N7j3ZWe7S72qvqtm7VenrU3RuQxWzqDyZauhQ4wcgDk0mKtVoUazMrzmZRepJdk7IdKspKUn5avHKS45WTEqdE+4dvYfsCQfUFDQWChrw9fjV39MrXF5TdalZf0ND++nbtr2vXkZb+EKKqtVsdvr5PvR6bxSSr2SybxSSbxayMJLsuLsrUhRMylRR7/LfQZpNJibFWJcValRhjldnMoxkAcLIiEk68/PLLMgxDEyZMUEVFhb7//e+rqKhIX/3qV2UymXTHHXfo5z//uQoLC0NLibrdbi1evDgS5QAAACCMDMPQgcZOvb6/UduOtGrbkVbVeXtO+vVJsVbZrWb1+IPq9gdCYYVhSN3+gLr9AbXKrxpPj3ZUeY55vTPOpvgYi9q6/Or2B07rGjKS7MpLiVNearzyUuKVl/rhf2c7Y2W18JgFAAymiIQTHo9HK1asUFVVlVJTU7V06VLde++9stn6lz36wQ9+oM7OTn3jG99QW1ub5s+fr7Vr1x6zwgcAAACizx8IasvBFpUebdW+unaVVLapuq37uPsmxFg0Mbv/EYbRafHKcvaPdAgYhqxmk8ZmJMrlsA94fMMf6A8pevwB9fQG1dMXUHdvQNVt3dpT41VZfbuqW7tV3dYtT7c/9PVxVrNJKQkxirWZ5e/rDzzGZCRovCtJYzISQiFEbkq8Ym2WyPyyAACnxWQYxvHH1Q1hJ7tOKgAAAE5djz+gndUe7anxqvRom9bvazgmDIixmjWnIFVzx6Rp9qgUFWYmKjHWKrs1sh/6O3x9qm7tlq8vIGecTUmxNlktJllMJsXHWFjlAgCGmJP9/B7ROScAAAAw9HX4+rSr2qOdVR69daBJmw82q8c/cFLI9MQYzR+XrqJshyZmO3Tu6BTFxwz+W8lEu1UTspIG/bwAgMginAAAADgL7ar26PntNdp0sFm7qj36+ByVmUl2Tct1amK2Q/PHpeuc0amyMMEjACBCCCcAAADOIm+WN+nBjRV6q6J5wHa3M1ZTc52alZ+iCydkarwrkUckAACDhnACAADgLLCnxqtVL+3VG+VNkiSL2aRFU7J0ycRMFY9JV5aTickBANFDOAEAADAC9fYF9e6RFm3c36iNZY3aV9cuSbJZTPrinFH6twsKlJsSH+UqAQDoRzgBAAAwQhiGoW1HWvXI24e1YV+DOnsDoTaTSbpyarZ+sLBI+WmEEgCAoYVwAgAAYJhr8PbopV11eua9Km2v8oS2pyfG6DPjM/TZ8Rm6oDBDqQkxUawSAIATI5wAAAAYhgzD0NsHmvXHNw5qw/5GGe+vthFjNeu6GTn6wpx8Tc1xyswKGwCAYYBwAgAAYJgwDEO7a7x6eXedXtpVp4qGjlDbzPxkXTk1W4tn5ig90R7FKgEAOHWEEwAAAEOYYRgqOdqm57fX6H9316u6rTvUFmez6PpzcnXzvAIVpCdEsUoAAM4M4QQAAMAQEwz2j5B4raxBz5ZW62BjZ6gtzmbRZ8dnaOEUly4ucskZZ4tipQAAhAfhBAAAwBBgGIZ2VHm0pqRa/9pRq6YOX6gtzmbR5VOytGhKlj4zPkOxNksUKwUAIPwIJwAAAKLoaEuX/llarWdKBo6QSIix6Pxx6bp0oktXTMtWop23bQCAkYu/cgAAAIPM0+3XSztr9UxJtd451BLaHmsz67JJWbpuZo7mjUtXjNUcxSoBABg8hBMAAACDoLcvqI37G7WmpEqv7m1Qb19QkmQyScVj0nTdzBxdPiVLSbHMIQEAOPsQTgAAAESIYRgqPdqmNSXVen57jVq7/KG28a5EXTczV4tnupXtjItilQAARB/hBAAAQJgdbenSmpJqPVtSrYNNH84jkZ5o17Uz3LpuZo4mux0ymUxRrBIAgKGDcAIAACAMPF1+vbCzVmtKqrT1cGtoe5zNooWTXVo8M0fzx6XLamEeCQAAPo5wAgAA4DQdburUCztrtbGsUdsqWxUIGpL655GYNzZd183M0cIpWay0AQDAp+AvJQAAwCmoau3SK3vq9fz2Gr1X2TagrSgrSdfNzNG1M3KU5YyNToEAAAxDYQ8nAoGAfvKTn+ixxx5TXV2d3G63br75Zv34xz8OPVdpGIbuuecePfTQQ2pra9O8efP04IMPqrCwMNzlAAAAnBHDMLS7xqv/3VOvV/bUa2+tN9RmNknzxqVr4eQsfXZ8hvJS46NYKQAAw1fYw4lf/OIXevDBB/Xoo49q8uTJevfdd/XVr35VTqdT3/3udyVJ9913n+6//349+uijKigo0N13362FCxdqz549io3lXxkAAED07azy6O/bjurVvQ2qbusObTebpHNGp+qySS5dM92tTAfvXQAAOFMmwzCMcB7wqquuksvl0sMPPxzatnTpUsXFxemxxx6TYRhyu9268847ddddd0mSPB6PXC6XVq9erRtvvPFTz+H1euV0OuXxeORwOMJZPgAAOIsZhqEdVR79bn2FXt1bH9oeazPrM4UZunSSS5dMdCk1ISaKVQIAMHyc7Of3sI+cOP/88/WHP/xB+/fv1/jx47V9+3a9+eab+vWvfy1JOnTokOrq6rRgwYLQa5xOp+bMmaNNmzYdN5zw+Xzy+Xyhn71e7zH7AAAAnI7evqBe39+oF3bW6o3yJjV19L/nMJukq6a5dc10t+YXpivWZolypQAAjFxhDyd+9KMfyev1qqioSBaLRYFAQPfee6+++MUvSpLq6uokSS6Xa8DrXC5XqO3jVq1apZUrV4a7VAAAcJYyDEPvVbZqTUm1XthRq9Yuf6gt1mbWwslZ+s7FhRqXmRjFKgEAOHuEPZx46qmn9Ne//lWPP/64Jk+erNLSUt1xxx1yu91atmzZaR1zxYoVWr58eehnr9ervLy8cJUMAADOEgcbO/RsSbWeLa1RZUtXaHtGkl3XTHdrwUSXZo1Klt3KKAkAAAZT2MOJ73//+/rRj34Uejxj6tSpOnLkiFatWqVly5YpKytLklRfX6/s7OzQ6+rr6zVjxozjHtNut8tut4e7VAAAcBZo6ezVc6XVWlNSre1VntD2+BiLLp+Spetm5uj8semymE1RrBIAgLNb2MOJrq4umc3mAdssFouCwaAkqaCgQFlZWVq3bl0ojPB6vdqyZYtuvfXWcJcDAADOUtVt3Xro9YN6cmulevz970MsZpM+U5iuxTNzdOkkl+Jjwv5WCAAAnIaw/0W++uqrde+99yo/P1+TJ09WSUmJfv3rX+uWW26RJJlMJt1xxx36+c9/rsLCwtBSom63W4sXLw53OQAA4CzS3uPX2wea9dTWo3qtrEHB99ckm5Tt0OfPydVV09zKSGI0JgAAQ03Yw4nf/e53uvvuu/Xtb39bDQ0Ncrvd+uY3v6n//M//DO3zgx/8QJ2dnfrGN76htrY2zZ8/X2vXrlVsLOuEAwCAk2cYhnbXeLWmpFpvlDeqvKFDH10k/fyxabr1wrGaPy5dJhOPbQAAMFSZDOOjf8KHh5NdJxUAAIxMNW3dera0Wmveq1Z5Q8eAtpzkOF01LVvXn5unsRmstgEAQDSd7Od3HrQEAADDQnuPXy/tqtOa96q1+VBzaIREjNWsSye6dNW0bM0enaLMJEZiAgAw3BBOAACAIasvENQb5U16pqRa/7u7Tr6+YKhtTkGqlszK0eVTsuWMs0WxSgAAcKYIJwAAwJBiGIZ2VXv1TEmVnt9eo6aO3lDb2IwELZmVq2tnuJWbEh/FKgEAQDgRTgAAgCGhuq1bz5ZUa01JtSo+Mo9EWkKMrp7u1pJZOZqa42RiSwAARiDCCQAAEBW9fUGVHm3TpgPNerOiUVsPt4ba7FazLp3k0pJZObqgMEM2izmKlQIAgEgjnAAAAIPmUFOnXtlTpzfKm/Tu4VZ1+wOhNpNJmluQputm5ejyKVlyxDKPBAAAZwvCCQAAEDEdvj6t21uvLYdatPlgsw42dg5oT0uI0dyxaSoek6aLijKVkxwXpUoBAEA0EU4AAICwCgYN7a3z6h/bqvX0u0fV7usLtVnNJs0dk6aLizI1vzBdhZmJzCEBAAAIJwAAwJkzDENvVjTpsc1HtOlAs7w9HwYSBekJuqQoU+cWpGrumDSW/QQAAMcgnAAAAKet1tOtF3fW6el3j2pfXXtoe0KMRcVj0/Xl4lG6YFy6zGZGRwAAgBMjnAAAACet1tOttyqa9V5lq0or27Sn1htqi4+x6Ppz8nTdzBxNdjtkZYUNAABwkggnAADAJ6pu69bT7x7Vv3bUqqKhY0CbySSdOypVV07L1uKZOTyyAQAATgvhBAAACPH1BbTtcKs2vb+yxpGWTu2u8cow+tvNJmlqbrLmFKRqZl6yZo9OUWZSbHSLBgAAwx7hBAAAZ7HGdp82H+x/TGNXtUc7qz3q8QeP2a94TJquPzdXF09wyRnP6AgAABBehBMAAJxFDMNQRUOH/rWjVi/vrhswieUHMpLsmj8uXVNynMpPjdfE7CTlpsRHoVoAAHC2IJwAAGAEa+vq1d7adpXVeVVytE3vHGpRradnwD4Tsx2aU5CqablOTct1amxGokwmVtcAAACDh3ACAIARpLnDpy2HWrTlYLM2H2xRWf2xIyNsFpM+U5ihK6dl66IJmUpJiIlCpQAAAB8inAAAYJhq7vBpQ1mj3ihvVGVLl+o8Par52KgIScpLjdMEl0OT3P0jJGbmJys+hrcAAABg6OCdCQAAw0h7j18v7arTmveqtflQc2gVjY8qykrS3DFpmjsmVecVpCmVkREAAGCII5wAAGCIa+3s1Yu7avW/u+u16UCzegMfrqYx2e3QxUWZmpTtUJYzVqPTEnhMAwAADDuEEwAADEHBoKEN+xv0xDtHtaGsQf7Ah0MkxmUm6rqZObpmult5qayiAQAAhr+whxOjR4/WkSNHjtn+7W9/W7///e/V09OjO++8U08++aR8Pp8WLlyoBx54QC6XK9ylAAAw7Bxq6tTLu+v05DuVOtzcFdo+2e3QldOyddmkLI3LTIxihQAAAOEX9nBi69atCgQCoZ937dqlSy+9VJ///OclSd/73vf0wgsv6Omnn5bT6dTtt9+uJUuW6K233gp3KQAADAtVrV36Z2mN/llarf31HaHtSbFW3XBOnq4/N0/jXUlRrBAAACCyTIZxvKm0wueOO+7Qv/71L5WXl8vr9SojI0OPP/64Pve5z0mS9u3bp4kTJ2rTpk2aO3fuSR3T6/XK6XTK4/HI4XBEsnwAACLC2+PXiztq9UxJtd451BLabjWbNHdMmq6Ymq3FM92sqgEAAIa1k/38HtF3PL29vXrssce0fPlymUwmbdu2TX6/XwsWLAjtU1RUpPz8/E8MJ3w+n3w+X+hnr9cbybIBAIgIfyCojWWNWlNSrVf21qu3r39iS5NJKh6Tputm5uiyyVlyxtmiXCkAAMDgimg48eyzz6qtrU0333yzJKmurk4xMTFKTk4esJ/L5VJdXd0Jj7Nq1SqtXLkygpUCABA5u6o9evrdo3p+R61aOntD28e7EnXdzFxdO8Mtd3JcFCsEAACIroiGEw8//LAWLVokt9t9RsdZsWKFli9fHvrZ6/UqLy/vTMsDACBiOnx9eq60Rk+8U6md1Z7Q9vREu66d4dZ1M3M02e2QyWSKYpUAAABDQ8TCiSNHjujVV1/VM888E9qWlZWl3t5etbW1DRg9UV9fr6ysrBMey263y263R6pUAADCZkdVm554p1L/LK1RV2//BNExFrMum+zS52bnav64dFkt5ihXCQAAMLRELJx45JFHlJmZqSuvvDK0bfbs2bLZbFq3bp2WLl0qSSorK1NlZaWKi4sjVQoAABFjGIYONHZq/b56Pbe9RruqP5wXaUx6gm46L19LZuUoLZGQHQAA4EQiEk4Eg0E98sgjWrZsmazWD0/hdDr1ta99TcuXL1dqaqocDoe+853vqLi4+KRX6gAAINpaO3v1yp56bT7UrC0HW1Td1h1qi7GYtWhqlm46L19zClJ5bAMAAOAkRCScePXVV1VZWalbbrnlmLbf/OY3MpvNWrp0qXw+nxYuXKgHHnggEmUAABA23b0Bvbq3Xv8srdbG/Y3yBz5ciTvGYtbcsWm6pChT10x3KyUhJoqVAgAADD8mwzCMT99taDnZdVIBADhdvX1BlVS2akeVR6VVbdpY1qgOX1+ofVK2Q5dMzNR5BamalZ+iBHtE55gGAAAYlk728zvvpAAAeF+dp0cbyhr0WlmD3ixvUuf7E1p+ICc5TotnurV4Ro4KXUlRqhIAAGDkIZwAAJy1+gJBlRxt02v7GvRaWaP21noHtKcnxuicUamamuvUnPdHSJjNzCEBAAAQboQTAICzRv/KGh3aerhVb1U06fX9jfL2fPiohskkzchL1kUTMnXRhExNdjsIIwAAAAYB4QQAYETqCwRV0dihI81dOtjYqW1HWrXtSItau/wD9kuOt+mz4zN00YRMfWZ8hlKZzBIAAGDQEU4AAEaMHn9AWw61aO2uOq3dVXtMECFJsTazZuQl67zRqfrshEzNyEuWhdERAAAAUUU4AQAYtvyBoPbVtuvNiia9WdGorYdb1dsXDLUn2a0qyEhQfmq8puU6de7oVE12OxVjNUexagAAAHwc4QQAYFgwDEPVbd3aUNaoDWWNKqv3qqatR4HgwBWxs52xunBCpq6alq05BamyWggiAAAAhjrCCQDAkNPdG9CBxg7trPaotLJNe+u8OtTYqXZf3zH7JtqtmjsmTRcUpmt+YbrGpCfIZOIxDQAAgOGEcAIAEDWebr8qGjp0oKFDFY0dKq9vV0Vjh6pau2UYx+5vNkkz81N0cVGmzh2dqlFp8cpItLOiBgAAwDBHOAEAiJi2rl4dbu5Sa1evenoDaurwqSIURHSood13wtcmx9s0McuhGfnJmp7r1NiMROWlxivWZhnEKwAAAMBgIJwAgGGivcevnVUeldW3q7cvqL6goWDQUF/QkKH+UQVmk0lmk2QymWQ2mWQx928zvb/9g3ZHnE3ZzjhlOWKV6bB/6gf+vkBQrV1+NXf61NzRq6aO/u/NnT61dPaqqaNXzR0+NXf2qqOn/9GL3kBQ7T3HPobxcS6HXYWZSRqXmaixmYkqzEzUuMxEpSXE8HgGAADAWYJwAgCGGH8gqLK6dtV6elTr6dauao9Kj7apvKHjuI86hENKvE0JdqvibBbFx1gUa7PIkNTS2R86tHX7T/vcLoddmUmxirNZ5IizamzGhyHE2MxEOWJtYb0WAAAADD+EEwAQZYZhqKy+XW+WN+ntA83acrBZnb2B4+6bkxynKTkOJditsppNsrz/ZZJJhgwFjf7jBYL9/x00DBnvf//g52DQUEtnr+q9Par19MjX1z8qorXL/4l1mkxSSnyM0hJilJYYo7REu9IT+r+nJsQo/f1tSbFWmdQ/QsOdHKcEO39qAAAA8Ml4xwgAg6wvENSBxk6VHm3VWxXNevtAs5o6Bs694IyzaVRavFyOWI13JWpGXopm5CUrI8ke1loMw1Bbl18N7T519fapuzegbn//V9BQKHxIS4xRSnyMLEw8CQAAgAggnACACOrxB1RW167dNV7trvFoV41X+2q98vUFB+wXazPrvII0zR+Xpnnj0jUxyzEoK1CYTCalJMQoJSEm4ucCAAAAToRwAgDCoNPXp3117TrQ0KEDjR060Nipg40dOtLSpUDw2MkaEmIsmuR2aO6Y/jBiZn6y7FZWoQAAAMDZiXACAE5BXyCosvr2/gkq6ztU2dKlQ02dOtzcecIJI1MTYjTZ7dAkt0NT3E5Ndjs0Oi1hUEZGAAAAAMMB4QQAfII6T4/W72vQ5oPNKm/o0MHGjmMeyfiAy2HXeFdS/2oUGQkak5GosRmJcjnsLIkJAAAAfALCCQD4mDpPj/61o0bPba/RjirPMe1Jdqum5Tk12e3UqLR4jUpNUFF2ktITwztZJQAAAHC2IJwAcNZr7ezV5oPN2nSwWZsO9I+Q+IDJJM3MS9aFEzI1KduhcZmJyk+N55EMAAAAIIwiEk5UV1frhz/8oV566SV1dXVp3LhxeuSRR3TOOedI6l+67p577tFDDz2ktrY2zZs3Tw8++KAKCwsjUQ4AHONoS5de2lWrF3bUake155j5ImaPStHiGW4tmprNiAgAAAAgwsIeTrS2tmrevHm66KKL9NJLLykjI0Pl5eVKSUkJ7XPffffp/vvv16OPPqqCggLdfffdWrhwofbs2aPY2NhwlwQACgQNbTnYrJd31+mNiiYdbOwc0F6Ymajzx6apeGya5hSksbQmAAAAMIhMhnGi+eVPz49+9CO99dZbeuONN47bbhiG3G637rzzTt11112SJI/HI5fLpdWrV+vGG2/81HN4vV45nU55PB45HI5wlg9ghGjv8eu9yjbtr2vX/vp2bdzfqIZ2X6jdbJLOK0jVldPcWjjJpUwHwSgAAAAQbif7+T3sIyeee+45LVy4UJ///Oe1ceNG5eTk6Nvf/ra+/vWvS5IOHTqkuro6LViwIPQap9OpOXPmaNOmTccNJ3w+n3y+Dz9UeL3ecJcNYARo6vDpmfeq9OLOOu2s9igQHJi9OuNsWjQlSxdOyFTx2DQ542xRqhQAAADAR4U9nDh48KAefPBBLV++XP/xH/+hrVu36rvf/a5iYmK0bNky1dXVSZJcLteA17lcrlDbx61atUorV64Md6kAhjl/IKjNB5u17Uir3qts09sVTer7SCAxKi1eU3KcGpeRqOl5Ts0fl6EYqzmKFQMAAAA4nrCHE8FgUOecc47+67/+S5I0c+ZM7dq1S//zP/+jZcuWndYxV6xYoeXLl4d+9nq9ysvLC0u9AIYXX19AWw62aO3uOr24s1ZtXf4B7dPzkvX52bm6qChTOclxUaoSAAAAwKkIeziRnZ2tSZMmDdg2ceJE/eMf/5AkZWVlSZLq6+uVnZ0d2qe+vl4zZsw47jHtdrvsdmbLB85WPf6AXtvXoOd31GhDWaO6egOhtvREuy4oTNeMvGTNHZOmCVlJUawUAAAAwOkIezgxb948lZWVDdi2f/9+jRo1SpJUUFCgrKwsrVu3LhRGeL1ebdmyRbfeemu4ywEwDPX2BfXWgSa9Vd6kHdUe7ar2DAgkMpPsurgoU1dNc2vumFRZLTyqAQAAAAxnYQ8nvve97+n888/Xf/3Xf+n666/XO++8oz/84Q/6wx/+IEkymUy644479POf/1yFhYWhpUTdbrcWL14c7nIADBPdvQFt3N+otbtqtW5fg9p7+ga0u52xunq6W1dOy9YUt1NmsylKlQIAAAAIt7CHE+eee67WrFmjFStW6Kc//akKCgr0//7f/9MXv/jF0D4/+MEP1NnZqW984xtqa2vT/PnztXbtWsXGspQfcDZp6+p9P5Co04ayRnX7PxwdkZFk14KJLs0elaKpOU4VZiYSSAAAAAAjlMkwDOPTdxtaTnadVABDS3uPX1sPt+jtimZtOtisPbVeffQOlJMcp8unZGnRlCzNyk8hjAAAAACGuZP9/B72kRMA8AHDMHSwqVNv7G/U/+6p1zuHWgYs9SlJ4zITddkklxZNydaUHIdMJgIJAAAA4GxDOAEgbAzDUFl9uzYfaNY7h1v0zqEWNXX0DthnVFq8isekqXhsmorHpCnTweNcAAAAwNmOcALAGTEMQ4ebu/TKnjo9/W6Vyhs6BrTbrWbNyk/RJRMztWCiS6PTE6JUKQAAAIChinACwCnxB4Iqr+/Qu0datOVQ/+iIxnZfqN1uNWvumDSdV5CqOQWpmprrlN1qiWLFAAAAAIY6wgkAnygQNPReZate2VOvTQeaVVbfrt6+4IB9YixmzcxP1rUzcnTV9Gw5Ym1RqhYAAADAcEQ4AWCA3r6gdtd4tPVwi9451Kqth1vk6fYP2CchxqJZo1J03uhUnVeQqul5yYq1MToCAAAAwOkhnADOcg3tPdpd41XJkVZtPdyqkqOt6vEPHBnhiLXq4qJMXVSUqRl5ycpLiWeZTwAAAABhQzgBnEX6AkE1dvi0s8qjV/bUa+P+RjV8ZL6IDyTH23TOqBSdV5Cq8wrSNNntkM1ijkLFAAAAAM4GhBPACGQYhqrburWnxqs9td7Q95q2bgWNgfuaTdKYjERNzXHq3NGpOnd0isZmJDIyAgAAAMCgIZwAhrHu3oA2H2rW1kMt6vD1qbcvqCPNXdpT6z1mnogPWM0m5abE6cIJmbp0kkuz8lMUF8N8EQAAAACih3ACGEaq27r17uEWlR5t065qj7ZXeY5ZOeMDVrNJha4kTcp2aJLboUnZDo3NSFB6op1REQAAAACGFMIJYIgyDEMHGjvfXzWj/6u6rfuY/dzOWF1QmKFMh10xFrNcjlhNcjtU6EqU3cqICAAAAABDH+EEMET0BYLaW9uudw636J1DzXr3cKuaO3sH7GMxmzTF7dDM/BRNzXFqel6yxmYkyGRiJAQAAACA4YtwAogCfyCo0qNt2l/frsqWLu2tbdd7R1rV4esbsJ/datbM/GSdNzpV5xakalZ+ihLs/N8WAAAAwMjCpxxgEHT6+rT9aJt2Vnv0XmWr3q5oVvvHgghJSoq1vr9iRqrOK0jRlBwnj2YAAAAAGPEIJ4AI6Ort046q/iDizfImbT3cIn9g4BqeqQkxmpGXrPzUeI3NSNDsUamakJUkC5NVAgAAADjLEE4AZygYNFTd1q2Khg6VHG3Tm+WN2l7lUSA4MIxwO2M1Iz9ZU3OSdf7YNE3NcbJqBgAAAACIcAI4Lf5AUNuOtOq57TV6aWetWrv8x+yT7YzVjLxknTs6VRdOyFBBOhNXAgAAAMDxEE4AJ6mqtUsv7qzV6/ubtO1Iq7r9gVCbzWLSmPREFWUnad7YdJ0/Lk25KfFRrBYAAAAAhg/CCeAEevuC2lnt0ev7G7WhrEHbqzwD2pPjbbpskkvXzsjRnIJUWS3mKFUKAAAAAMNb2MOJn/zkJ1q5cuWAbRMmTNC+ffskST09Pbrzzjv15JNPyufzaeHChXrggQfkcrnCXQpwyg40dujv26r0ZnmTyura1RsIhtpMJmlOQaoun5yl4rHpKsxMZM4IAAAAAAiDiIycmDx5sl599dUPT2L98DTf+9739MILL+jpp5+W0+nU7bffriVLluitt96KRCnAp/L2+PWv7bX6+7ajeq+ybUBbcrxN88am67PjM3RhUYYyk2KjUyQAAAAAjGARCSesVquysrKO2e7xePTwww/r8ccf18UXXyxJeuSRRzRx4kRt3rxZc+fOjUQ5wDE83X6t31evtbvqtKGsUb6+/hESFrNJF47P0DUz3JqVn6LclDgmsQQAAACACItIOFFeXi63263Y2FgVFxdr1apVys/P17Zt2+T3+7VgwYLQvkVFRcrPz9emTZsIJxBRHb4+vbijVi/srNXbB5rkD3y41GdhZqI+f06uFs/MYXQEAAAAAAyysIcTc+bM0erVqzVhwgTV1tZq5cqVuuCCC7Rr1y7V1dUpJiZGycnJA17jcrlUV1d3wmP6fD75fL7Qz16vN9xlY4QyDEM7qz164p1KPVdao87eD1fYKMxM1OVTsnT5lCxNynYwQgIAAAAAoiTs4cSiRYtC/z1t2jTNmTNHo0aN0lNPPaW4uLjTOuaqVauOmWQT+CTNHT79a0et/rb1qPbUfhhmjUlP0JJZObp8SrbGZSZGsUIAAAAAwAcivpRocnKyxo8fr4qKCl166aXq7e1VW1vbgNET9fX1x52j4gMrVqzQ8uXLQz97vV7l5eVFsmwMQ929Ab2yt17PllTr9f2N6gv2P7YRYzXriilZuvG8fM0pSGWEBAAAAAAMMREPJzo6OnTgwAF9+ctf1uzZs2Wz2bRu3TotXbpUklRWVqbKykoVFxef8Bh2u112uz3SpWIYCgQNbTrQrDUl1Vq7q3bAYxvTcp1aPCNHS2blKDk+JopVAgAAAAA+SdjDibvuuktXX321Ro0apZqaGt1zzz2yWCy66aab5HQ69bWvfU3Lly9XamqqHA6HvvOd76i4uJjJMHHKNh1o1o+f3akDjZ2hbbkpcbpuZo6unZHDYxsAAAAAMEyEPZyoqqrSTTfdpObmZmVkZGj+/PnavHmzMjIyJEm/+c1vZDabtXTpUvl8Pi1cuFAPPPBAuMvACOPrC+jZkmq9urdBFpNJ3f6ANu5vlCQ542y6enq2rpuZo1n5KTy2AQAAAADDjMkwDOPTdxtavF6vnE6nPB6PHA5HtMuJurauXu2p8WpPrVdHmrvU2xeUPxhUX8BQXzAoq9mslHibUhJilBIf8/53m1LiY5SeaFdGkl0W89D7QO/t8Wvb4VZtPtSsZ96rVmO7b0C7ySR9cU6+vr+wSM44W5SqBAAAAACcyMl+fo/4nBM4Mz3+gOo8Par19OhIc6fKGzpU09Ytf8BQbyCoivp21Xh6zugcFrNJaQkxSrBbFWezKC7GojibRcnxNuWnxsudHCfr++FFSkKMcpLjlO2MVWpCTNhGKfQFgjrQ2Kk9tR5tP+rR1sMt2lvrVfAj0Vm2M1ZfnJMvZ3yMfP6A5o5J05QcZ1jODwAAAACIHsKJIaKls1dbDjbraGuX2rr8qvP0aGe1RxWNHTqZsS15qXGalO1QYWaS4mIssppNslrMsllM6u0LqrWrVy2dfrV19aqls1dtXX41d/aqpdOnQNBQQ7tP+tjIhE9jt5qVkWQPBRdpiXblpcQpPzVeuanxykuJV15qnLKdcTJJau/p0+HmTu2o9uhAQ4d6/AH1+AM62NSpfXXt6u0LHnOO0WnxOq8gVRcUZmjh5CzFWM2nVCMAAAAAYOgjnPgEHb4+NXf45Onu/yBf29ajmrZu1Xi6VdvWI4vZpJzkOOWnxWuy26GpOU6lJX7yqiKdvj5VtnSpsqVLh5o6tb+uXXtqvdpX137C18THWJTliFVOSpwKM5M0Ki1eMVazLGaTRqXGqyjbcdqPNQSChpo6fGps96nbH1BXb0DdvQF1+/vU1N6rypYu1Xl7ZBiGgobU3OFTdVuPmjp88vUFVdXaHTrW4eYubTvSesw5LGaTgobxqSFLot2qidlJmpTt0DmjU3VeQapcjtjTui4AAAAAwPBx1oYT/kBQTR0+1Xt9qm3rVnVbt6pa+79Xv//d0+0/5eMmxVqVkxyn3JQ45STHKSnWpuq2bh1p7lRlS5eaOnpP+NoJriRNzE5ScnyM0hJiNDnHoSk5TmUk2iM2yaPFbJLLEXvKIYCvL6B6j0+NHT0yDCloSA3tPaps6dLRlm5VtXbpaEuXqlq71feRZzNSE2I0NcepouwkJdmtslnMyk+N1yS3Q3kp8TIPwbkvAAAAAACRNaLDCX8gqMNNndpf36H99e0qb2jX4aYuNbT71NzpO6nHJeJjLHLG2ZQcHyO3M1bu5DhlJ8fK7YxTX9BQdWu3DjZ1aGe1RwcbO9Xe06d9de2fOBLig7kc8lPjNcGVpAlZSZo1KkXpnzLqYiixWy3KT4tXflr8J+7X/8hIj6xmsxxxVtmtlkGqEAAAAAAwXIyYcKIvEFTj+48n7Kr26pU9dXrrQPNx5zH4gNVsUkaSXVnOWOUkxyknJU6573/PSY5XTkqcEu0n/yvq6u1TdWu3qj4y+qK9x6+c5P4gYlRavPJS48+qlSUsZpOynXHRLgMAAAAAMIQN63CipcOnLVX1enFnrV7ZU68OX98x+yTEWDTOlaTxmYka70rSmIwEZTn7H2NIjY8J62ME8TFWFbqSVOhKCtsxAQAAAAAY6YZ1OPGZX26Q2f7hYwVWs0npiXblpsTpoqJMLZjoUmFmIvMYAAAAAAAwhA3rcEKSCtITdOGEDF01LVsz81IIIgAAAAAAGGaGdTix+T8ukTsjNdplAAAAAACAM2COdgFn4lQmqwQAAAAAAEPTsA4nAAAAAADA8Ec4AQAAAAAAoopwAgAAAAAARBXhBAAAAAAAiCrCCQAAAAAAEFWEEwAAAAAAIKoIJwAAAAAAQFRZo13A6TAMQ5Lk9XqjXAkAAAAAADiRDz63f/A5/kSGZTjR3NwsScrLy4tyJQAAAAAA4NO0t7fL6XSesH1YhhOpqamSpMrKyk+8uHA699xztXXr1kE5F+cLL6/Xq7y8PB09elQOh2NQzimN7N/pSD9fNPrMSP59jvTz0V8436mgv3C+U8F7GM53qrjHcL5TMVj9xTAMtbe3y+12f+J+wzKcMJv7p8pwOp2D9n86i8UyqH8UOF/4ORyOEX2NnC/8BrPPjPTf50g/n0R/4Xynhv7C+U4F72E436niHsP5TsVg9JeTGVTAhJgn6bbbbuN8w/h80TDSf6cj/XyDbaT/Pkf6+QbbSP99jvTzDbaR/vsc6eeLhpH+Ox3p5xtsI/33OdLPN5SYjE+blWII8nq9cjqd8ng8g54qYfihv+BU0WdwKugvOBX0F5wK+gtOFX0Gp2Ko9ZdhOXLCbrfrnnvukd1uj3YpGAboLzhV9BmcCvoLTgX9BaeC/oJTRZ/BqRhq/WVYjpwAAAAAAAAjx7AcOQEAAAAAAEYOwgkAAAAAABBVhBMAAAAAACCqCCcAAAAAAEBURS2ceP3113X11VfL7XbLZDLp2WefHdBeX1+vm2++WW63W/Hx8br88stVXl4eaj98+LBMJtNxv55++unQfuvWrdP555+vpKQkZWVl6Yc//KH6+voG6zIRJmfaXySprq5OX/7yl5WVlaWEhATNmjVL//jHP457Pp/PpxkzZshkMqm0tDRCV4VIGqw+89577+nSSy9VcnKy0tLS9I1vfEMdHR2RvjyEWTj6y4EDB3TdddcpIyNDDodD119/verr6497Pu4xw9tg9RfuLyPDqlWrdO655yopKUmZmZlavHixysrKBuzT09Oj2267TWlpaUpMTNTSpUuP6Q+VlZW68sorFR8fr8zMTH3/+98/4Xvat956S1arVTNmzIjUZSFCBrO//P73v9fEiRMVFxenCRMm6M9//nPErw/hFa7+8t3vflezZ8+W3W7/1PtGRUWFkpKSlJycHOariWI40dnZqenTp+v3v//9MW2GYWjx4sU6ePCg/vnPf6qkpESjRo3SggUL1NnZKUnKy8tTbW3tgK+VK1cqMTFRixYtkiRt375dV1xxhS6//HKVlJTob3/7m5577jn96Ec/GtRrxZk70/4iSV/5yldUVlam5557Tjt37tSSJUt0/fXXq6Sk5Jhj/uAHP5Db7Y7oNSGyBqPP1NTUaMGCBRo3bpy2bNmitWvXavfu3br55psH6zIRJmfaXzo7O3XZZZfJZDJp/fr1euutt9Tb26urr75awWDwmGNyjxneBqO/cH8ZOTZu3KjbbrtNmzdv1iuvvCK/36/LLrtswN+b733ve3r++ef19NNPa+PGjaqpqdGSJUtC7YFAQFdeeaV6e3v19ttv69FHH9Xq1av1n//5n8ecr62tTV/5yld0ySWXDMr1IbwGq788+OCDWrFihX7yk59o9+7dWrlypW677TY9//zzg3q9ODPh6C8fuOWWW3TDDTd84vn8fr9uuukmXXDBBWG/FkmSMQRIMtasWRP6uayszJBk7Nq1K7QtEAgYGRkZxkMPPXTC48yYMcO45ZZbQj+vWLHCOOeccwbs89xzzxmxsbGG1+sN3wVgUJ1uf0lISDD+/Oc/DzhWamrqMX3qxRdfNIqKiozdu3cbkoySkpKIXAcGT6T6zP/3//1/RmZmphEIBELtO3bsMCQZ5eXlEboaRNrp9JeXX37ZMJvNhsfjCe3T1tZmmEwm45VXXhlwfO4xI0uk+gv3l5GroaHBkGRs3LjRMIz+/+1tNpvx9NNPh/bZu3evIcnYtGmTYRj99w2z2WzU1dWF9nnwwQcNh8Nh+Hy+Ace/4YYbjB//+MfGPffcY0yfPj3yF4SIilR/KS4uNu66664B51q+fLkxb968SF8SIuh0+stHfdp94wc/+IHxpS99yXjkkUcMp9MZ7vKNITnnhM/nkyTFxsaGtpnNZtntdr355pvHfc22bdtUWlqqr33tawOO89FjSFJcXJx6enq0bdu2CFSOaDjZ/nL++efrb3/7m1paWhQMBvXkk0+qp6dHF154YWif+vp6ff3rX9df/vIXxcfHD9o1YHCFq8/4fD7FxMTIbP7wVhoXFydJJ7xXYfg5mf7i8/lkMplkt9tD+8TGxspsNg/oC9xjRr5w9RfuLyOXx+ORJKWmpkrqfw/r9/u1YMGC0D5FRUXKz8/Xpk2bJEmbNm3S1KlT5XK5QvssXLhQXq9Xu3fvDm175JFHdPDgQd1zzz2DcSkYBJHqLyf6nPTOO+/I7/dH9JoQOafTX07W+vXr9fTTTx931GC4DMlw4oNf2IoVK9Ta2qre3l794he/UFVVlWpra4/7mocfflgTJ07U+eefH9q2cOFCvf3223riiScUCARUXV2tn/70p5J0wuNg+DnZ/vLUU0/J7/crLS1Ndrtd3/zmN7VmzRqNGzdOUv9Q3Jtvvlnf+ta3dM4550TrcjAIwtVnLr74YtXV1emXv/ylent71draGnpsjHvMyHEy/WXu3LlKSEjQD3/4Q3V1damzs1N33XWXAoFAaB/uMWeHcPUX7i8jUzAY1B133KF58+ZpypQpkvrnN4qJiTnm+W2Xy6W6urrQPh/9oPlB+wdtklReXq4f/ehHeuyxx2S1WiN8JRgMkewvCxcu1B//+Edt27ZNhmHo3Xff1R//+Ef5/X41NTVF+MoQCafbX05Gc3Ozbr75Zq1evVoOhyOcZQ8wJMMJm82mZ555Rvv371dqaqri4+P12muvadGiRQP+BeED3d3devzxxweMmpCkyy67TL/85S/1rW99S3a7XePHj9cVV1whScc9Doank+0vd999t9ra2vTqq6/q3Xff1fLly3X99ddr586dkqTf/e53am9v14oVK6J1KRgk4eozkydP1qOPPqpf/epXio+PV1ZWlgoKCuRyubjHjCAn018yMjL09NNP6/nnn1diYqKcTqfa2to0a9as0D7cY84O4eov3F9Gpttuu027du3Sk08+GdbjBgIBfeELX9DKlSs1fvz4sB4b0ROp/iL1v8dZtGiR5s6dK5vNpmuvvVbLli2TxOek4SqS/eXrX/+6vvCFL+gzn/lM2I89QNgfFDkN+tjzmh/V1tZmNDQ0GIZhGOedd57x7W9/+5h9/vznPxs2my2038cFg0Gjurra6OrqMvbs2WNIMt55552w1Y/BdTr9paKi4phngA3DMC655BLjm9/8pmEYhnHttdcaZrPZsFgsoS9JhsViMb7yla9E7oIQcZHqMx9VV1dntLe3Gx0dHYbZbDaeeuqp8F4EBs2Z/k1qbGw0WltbDcMwDJfLZdx3332GYXCPGaki1V8+ivvLyHDbbbcZubm5xsGDBwdsX7dunSEp1A8+kJ+fb/z61782DMMw7r777mOeAz948KAhyXjvvfeM1tbW0P3kgy+TyRTatm7dukheGiIgkv3lo3p7e42jR48afX19xgMPPGAkJSUNmOsGw8OZ9JePOtGcE06nc8D9xWw2h+4vDz/8cNiuY8jHYk6nUxkZGSovL9e7776ra6+99ph9Hn74YV1zzTXKyMg47jFMJpPcbrfi4uL0xBNPKC8vT7NmzYp06YiCE/WXrq4uSccmwRaLJTQz+v3336/t27ertLRUpaWlevHFFyVJf/vb33TvvfcO4lVgMJ1Jn/kol8ulxMRE/e1vf1NsbKwuvfTSyBePQXcyf5PS09OVnJys9evXq6GhQddcc40k7jFnozPpLx/F/WV4MwxDt99+u9asWaP169eroKBgQPvs2bNls9m0bt260LaysjJVVlaquLhYklRcXKydO3eqoaEhtM8rr7wih8OhSZMmyeFwaOfOnaH7S2lpqb71rW9pwoQJKi0t1Zw5cwbnYnHGBqO/fJTNZlNubq4sFouefPJJXXXVVYycGEbC0V9OxqZNmwbcX376058qKSlJpaWluu6668J2PVEbOdHe3m6UlJQYJSUlhiTj17/+tVFSUmIcOXLEMAzDeOqpp4zXXnvNOHDggPHss88ao0aNMpYsWXLMccrLyw2TyWS89NJLxz3PfffdZ+zYscPYtWuX8dOf/tSw2Wwn/BcODF1n2l96e3uNcePGGRdccIGxZcsWo6Kiwvi///f/GiaTyXjhhReOe85Dhw4xk/4wNlh95ne/+52xbds2o6yszPjv//5vIy4uzvjtb3876NeLMxOOv0l/+tOfjE2bNhkVFRXGX/7yFyM1NdVYvnz5Cc/JPWb4Gqz+wv1lZLj11lsNp9NpbNiwwaitrQ19dXV1hfb51re+ZeTn5xvr16833n33XaO4uNgoLi4Otff19RlTpkwxLrvsMqO0tNRYu3atkZGRYaxYseKE52W1juFpsPpLWVmZ8Ze//MXYv3+/sWXLFuOGG24wUlNTjUOHDg3m5eIMhaO/GEb/Z+qSkhLjm9/8pjF+/PjQ37iPrwb0gUit1hG1cOK1114zJB3ztWzZMsMwDOO3v/2tkZuba9hsNiM/P9/48Y9/fNxfzooVK4y8vLwTDj+66KKLDKfTacTGxhpz5swxXnzxxUheFiIkHP1l//79xpIlS4zMzEwjPj7emDZt2jHLRH4UHxyGt8HqM1/+8peN1NRUIyYm5lP7FIaucPSXH/7wh4bL5TJsNptRWFho/OpXvzKCweAJz8k9ZvgarP7C/WVkOF5fkWQ88sgjoX26u7uNb3/720ZKSooRHx9vXHfddUZtbe2A4xw+fNhYtGiRERcXZ6Snpxt33nmn4ff7T3hewonhabD6y549e4wZM2YYcXFxhsPhMK699lpj3759g3WZCJNw9ZfPfvazxz3OicKqSIUTpvcvCgAAAAAAICp4oAgAAAAAAEQV4QQAAAAAAIgqwgkAAAAAABBVhBMAAAAAACCqCCcAAAAAAEBUEU4AAAAAAICoIpwAAAAAAABRRTgBAAAAAACiinACAACExc033yyTySSTySSbzSaXy6VLL71Uf/rTnxQMBo/Zf+HChbJYLNq6dask6fDhw6HXn+hr9erV2rBhwwnb6+rqBvuyAQBAGBBOAACAsLn88stVW1urw4cP66WXXtJFF12kf//3f9dVV12lvr6+0H6VlZV6++23dfvtt+tPf/qTJCkvL0+1tbWhrzvvvFOTJ08esO2GG24IHaOsrGxAW21trTIzMwf9mgEAwJmzRrsAAAAwctjtdmVlZUmScnJyNGvWLM2dO1eXXHKJVq9erX/7t3+TJD3yyCO66qqrdOutt2ru3Ln69a9/rbi4uNBrJSkxMVFWq3XAto/KzMxUcnJyxK8JAABEHiMnAABARF188cWaPn26nnnmGUmSYRh65JFH9KUvfUlFRUUaN26c/v73v0e5SgAAEE2EEwAAIOKKiop0+PBhSdKrr76qrq4uLVy4UJL0pS99SQ8//PApHzM3N1eJiYmhr8mTJ4ezZAAAMIh4rAMAAEScYRgymUySpD/96U+64YYbZLX2vw256aab9P3vf18HDhzQ2LFjT/qYb7zxhpKSkkI/22y28BYNAAAGDeEEAACIuL1796qgoEAtLS1as2aN/H6/HnzwwVB7IBDQn/70J917770nfcyCggLmnAAAYITgsQ4AABBR69ev186dO7V06VL99a9/VW5urrZv367S0tLQ169+9SutXr1agUAg2uUCAIAoYOQEAAAIG5/Pp7q6OgUCAdXX12vt2rVatWqVrrrqKn3lK1/R7Nmz9bnPfU5TpkwZ8Lq8vDytWLFCa9eu1ZVXXnlS52poaFBPT8+AbWlpaTzeAQDAMEQ4AQAAwmbt2rXKzs6W1WpVSkqKpk+frvvvv1/Lli1TSUmJtm/froceeuiY1zmdTl1yySV6+OGHTzqcmDBhwjHbNm3apLlz557xdQAAgMFlMgzDiHYRAAAAAADg7MWcEwAAAAAAIKoIJwAAAAAAQFQRTgAAAAAAgKginAAAAAAAAFFFOAEAAAAAAKKKcAIAAAAAAEQV4QQAAAAAAIgqwgkAAAAAABBVhBMAAAAAACCqCCcAAAAAAEBUEU4AAAAAAICoIpwAAAAAAABR9f8D5AitVcA+6d4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n",
    "usphci.plot(figsize=(13,3));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:05.244509Z",
     "iopub.status.busy": "2022-11-02T17:12:05.243163Z",
     "iopub.status.idle": "2022-11-02T17:12:05.252603Z",
     "shell.execute_reply": "2022-11-02T17:12:05.251798Z"
    }
   },
   "outputs": [],
   "source": [
    "dusphci = usphci.diff()[1:].values\n",
    "def compute_coincident_index(mod, res):\n",
    "    # Estimate W(1)\n",
    "    spec = res.specification\n",
    "    design = mod.ssm['design']\n",
    "    transition = mod.ssm['transition']\n",
    "    ss_kalman_gain = res.filter_results.kalman_gain[:,:,-1]\n",
    "    k_states = ss_kalman_gain.shape[0]\n",
    "\n",
    "    W1 = np.linalg.inv(np.eye(k_states) - np.dot(\n",
    "        np.eye(k_states) - np.dot(ss_kalman_gain, design),\n",
    "        transition\n",
    "    )).dot(ss_kalman_gain)[0]\n",
    "\n",
    "    # Compute the factor mean vector\n",
    "    factor_mean = np.dot(W1, dta.loc['1972-02-01':, 'dln_indprod':'dln_emp'].mean())\n",
    "    \n",
    "    # Normalize the factors\n",
    "    factor = res.factors.filtered[0]\n",
    "    factor *= np.std(usphci.diff()[1:]) / np.std(factor)\n",
    "\n",
    "    # Compute the coincident index\n",
    "    coincident_index = np.zeros(mod.nobs+1)\n",
    "    # The initial value is arbitrary; here it is set to\n",
    "    # facilitate comparison\n",
    "    coincident_index[0] = usphci.iloc[0] * factor_mean / dusphci.mean()\n",
    "    for t in range(0, mod.nobs):\n",
    "        coincident_index[t+1] = coincident_index[t] + factor[t] + factor_mean\n",
    "    \n",
    "    # Attach dates\n",
    "    coincident_index = pd.Series(coincident_index, index=dta.index).iloc[1:]\n",
    "    \n",
    "    # Normalize to use the same base year as USPHCI\n",
    "    coincident_index *= (usphci.loc['1992-07-01'] / coincident_index.loc['1992-07-01'])\n",
    "    \n",
    "    return coincident_index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the calculated coincident index along with the US recessions and the comparison coincident index USPHCI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:05.256336Z",
     "iopub.status.busy": "2022-11-02T17:12:05.255960Z",
     "iopub.status.idle": "2022-11-02T17:12:05.455398Z",
     "shell.execute_reply": "2022-11-02T17:12:05.454560Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "coincident_index = compute_coincident_index(mod, res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, label='Coincident index')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(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,
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    "execution": {
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   "source": [
    "from statsmodels.tsa.statespace import tools\n",
    "class ExtendedDFM(sm.tsa.DynamicFactor):\n",
    "    def __init__(self, endog, **kwargs):\n",
    "            # Setup the model as if we had a factor order of 4\n",
    "            super(ExtendedDFM, self).__init__(\n",
    "                endog, k_factors=1, factor_order=4, error_order=2,\n",
    "                **kwargs)\n",
    "\n",
    "            # Note: `self.parameters` is an ordered dict with the\n",
    "            # keys corresponding to parameter types, and the values\n",
    "            # the number of parameters of that type.\n",
    "            # Add the new parameters\n",
    "            self.parameters['new_loadings'] = 3\n",
    "\n",
    "            # Cache a slice for the location of the 4 factor AR\n",
    "            # parameters (a_1, ..., a_4) in the full parameter vector\n",
    "            offset = (self.parameters['factor_loadings'] +\n",
    "                      self.parameters['exog'] +\n",
    "                      self.parameters['error_cov'])\n",
    "            self._params_factor_ar = np.s_[offset:offset+2]\n",
    "            self._params_factor_zero = np.s_[offset+2:offset+4]\n",
    "\n",
    "    @property\n",
    "    def start_params(self):\n",
    "        # Add three new loading parameters to the end of the parameter\n",
    "        # vector, initialized to zeros (for simplicity; they could\n",
    "        # be initialized any way you like)\n",
    "        return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0]\n",
    "    \n",
    "    @property\n",
    "    def param_names(self):\n",
    "        # Add the corresponding names for the new loading parameters\n",
    "        #  (the name can be anything you like)\n",
    "        return super(ExtendedDFM, self).param_names + [\n",
    "            'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1,4)]\n",
    "\n",
    "    def transform_params(self, unconstrained):\n",
    "            # Perform the typical DFM transformation (w/o the new parameters)\n",
    "            constrained = super(ExtendedDFM, self).transform_params(\n",
    "            unconstrained[:-3])\n",
    "\n",
    "            # Redo the factor AR constraint, since we only want an AR(2),\n",
    "            # and the previous constraint was for an AR(4)\n",
    "            ar_params = unconstrained[self._params_factor_ar]\n",
    "            constrained[self._params_factor_ar] = (\n",
    "                tools.constrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[constrained, unconstrained[-3:]]\n",
    "\n",
    "    def untransform_params(self, constrained):\n",
    "            # Perform the typical DFM untransformation (w/o the new parameters)\n",
    "            unconstrained = super(ExtendedDFM, self).untransform_params(\n",
    "                constrained[:-3])\n",
    "\n",
    "            # Redo the factor AR unconstrained, since we only want an AR(2),\n",
    "            # and the previous unconstrained was for an AR(4)\n",
    "            ar_params = constrained[self._params_factor_ar]\n",
    "            unconstrained[self._params_factor_ar] = (\n",
    "                tools.unconstrain_stationary_univariate(ar_params))\n",
    "\n",
    "            # Return all the parameters\n",
    "            return np.r_[unconstrained, constrained[-3:]]\n",
    "\n",
    "    def update(self, params, transformed=True, **kwargs):\n",
    "        # Peform the transformation, if required\n",
    "        if not transformed:\n",
    "            params = self.transform_params(params)\n",
    "        params[self._params_factor_zero] = 0\n",
    "        \n",
    "        # Now perform the usual DFM update, but exclude our new parameters\n",
    "        super(ExtendedDFM, self).update(params[:-3], transformed=True, **kwargs)\n",
    "\n",
    "        # Finally, set our new parameters in the design matrix\n",
    "        self.ssm['design', 3, 1:4] = params[-3:]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what did we just do?\n",
    "\n",
    "**`__init__`**\n",
    "\n",
    "The important step here was specifying the base dynamic factor model which we were operating with. In particular, as described above, we initialize with `factor_order=4`, even though we will only end up with an AR(2) model for the factor. We also performed some general setup-related tasks.\n",
    "\n",
    "**`start_params`**\n",
    "\n",
    "`start_params` are used as initial values in the optimizer. Since we are adding three new parameters, we need to pass those in. If we had not done this, the optimizer would use the default starting values, which would be three elements short.\n",
    "\n",
    "**`param_names`**\n",
    "\n",
    "`param_names` are used in a variety of places, but especially in the results class. Below we get a full result summary, which is only possible when all the parameters have associated names.\n",
    "\n",
    "**`transform_params`** and **`untransform_params`**\n",
    "\n",
    "The optimizer selects possibly parameter values in an unconstrained way. That's not usually desired (since variances cannot be negative, for example), and `transform_params` is used to transform the unconstrained values used by the optimizer to constrained values appropriate to the model. Variances terms are typically squared (to force them to be positive), and AR lag coefficients are often constrained to lead to a stationary model. `untransform_params` is used for the reverse operation (and is important because starting parameters are usually specified in terms of values appropriate to the model, and we need to convert them to parameters appropriate to the optimizer before we can begin the optimization routine).\n",
    "\n",
    "Even though we do not need to transform or untransform our new parameters (the loadings can in theory take on any values), we still need to modify this function for two reasons:\n",
    "\n",
    "1. The version in the `DynamicFactor` class is expecting 3 fewer parameters than we have now. At a minimum, we need to handle the three new parameters.\n",
    "2. The version in the `DynamicFactor` class constrains the factor lag coefficients to be stationary as though it was an AR(4) model. Since we actually have an AR(2) model, we need to re-do the constraint. We also set the last two autoregressive coefficients to be zero here.\n",
    "\n",
    "**`update`**\n",
    "\n",
    "The most important reason we need to specify a new `update` method is because we have three new parameters that we need to place into the state space formulation. In particular we let the parent `DynamicFactor.update` class handle placing all the parameters except the three new ones in to the state space representation, and then we put the last three in manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 4.685876\n",
      "         Iterations: 290\n",
      "         Function evaluations: 488\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               -2019.612\n",
      "                                                          + AR(2) errors   AIC                           4085.225\n",
      "Date:                                                   Wed, 02 Nov 2022   BIC                           4178.745\n",
      "Time:                                                           17:12:09   HQIC                          4122.150\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              -0.7047      0.036    -19.635      0.000      -0.775      -0.634\n",
      "loading.f1.std_income               -0.2593      0.039     -6.701      0.000      -0.335      -0.183\n",
      "loading.f1.std_sales                -0.4496      0.023    -19.232      0.000      -0.495      -0.404\n",
      "loading.f1.std_emp                  -0.4083      0.038    -10.620      0.000      -0.484      -0.333\n",
      "sigma2.std_indprod                   0.2351      0.045      5.198      0.000       0.146       0.324\n",
      "sigma2.std_income                    0.8709      0.030     29.035      0.000       0.812       0.930\n",
      "sigma2.std_sales                     0.5222      0.035     15.087      0.000       0.454       0.590\n",
      "sigma2.std_emp                       0.2618      0.023     11.373      0.000       0.217       0.307\n",
      "L1.f1.f1                             0.2834      0.054      5.253      0.000       0.178       0.389\n",
      "L2.f1.f1                             0.3923      0.058      6.718      0.000       0.278       0.507\n",
      "L3.f1.f1                                  0   1.15e-10          0      1.000   -2.26e-10    2.26e-10\n",
      "L4.f1.f1                                  0   1.15e-10          0      1.000   -2.26e-10    2.26e-10\n",
      "L1.e(std_indprod).e(std_indprod)    -0.2123      0.121     -1.762      0.078      -0.449       0.024\n",
      "L2.e(std_indprod).e(std_indprod)    -0.1923      0.094     -2.035      0.042      -0.377      -0.007\n",
      "L1.e(std_income).e(std_income)      -0.1928      0.023     -8.459      0.000      -0.238      -0.148\n",
      "L2.e(std_income).e(std_income)      -0.0926      0.048     -1.916      0.055      -0.187       0.002\n",
      "L1.e(std_sales).e(std_sales)        -0.4850      0.047    -10.241      0.000      -0.578      -0.392\n",
      "L2.e(std_sales).e(std_sales)        -0.2287      0.050     -4.548      0.000      -0.327      -0.130\n",
      "L1.e(std_emp).e(std_emp)             0.2289      0.041      5.639      0.000       0.149       0.308\n",
      "L2.e(std_emp).e(std_emp)             0.4899      0.048     10.170      0.000       0.395       0.584\n",
      "loading.L1.f1.std_emp               -0.0855      0.037     -2.341      0.019      -0.157      -0.014\n",
      "loading.L2.f1.std_emp               -0.0066      0.036     -0.186      0.853      -0.076       0.063\n",
      "loading.L3.f1.std_emp               -0.1723      0.028     -6.074      0.000      -0.228      -0.117\n",
      "====================================================================================================\n",
      "Ljung-Box (L1) (Q):     0.14, 0.01, 1.04, 4.33   Jarque-Bera (JB):   275.13, 9978.10, 26.07, 3786.11\n",
      "Prob(Q):                0.70, 0.94, 0.31, 0.04   Prob(JB):                    0.00, 0.00, 0.00, 0.00\n",
      "Heteroskedasticity (H): 0.75, 4.81, 0.44, 0.43   Skew:                       0.26, -0.97, 0.26, 0.79\n",
      "Prob(H) (two-sided):    0.08, 0.00, 0.00, 0.00   Kurtosis:                  6.88, 26.49, 4.09, 17.43\n",
      "====================================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 1.2e+18. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "# Create the model\n",
    "extended_mod = ExtendedDFM(endog)\n",
    "initial_extended_res = extended_mod.fit(maxiter=1000, disp=False)\n",
    "extended_res = extended_mod.fit(initial_extended_res.params, method='nm', maxiter=1000)\n",
    "print(extended_res.summary(separate_params=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this model increases the likelihood, it is not preferred by the AIC and BIC measures which penalize the additional three parameters.\n",
    "\n",
    "Furthermore, the qualitative results are unchanged, as we can see from the updated $R^2$ chart and the new coincident index, both of which are practically identical to the previous results."
   ]
  },
  {
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    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "extended_res.plot_coefficients_of_determination(figsize=(8,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:12:10.033131Z",
     "iopub.status.busy": "2022-11-02T17:12:10.032467Z",
     "iopub.status.idle": "2022-11-02T17:12:10.267401Z",
     "shell.execute_reply": "2022-11-02T17:12:10.266562Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "# Compute the index\n",
    "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n",
    "\n",
    "# Plot the factor\n",
    "dates = endog.index._mpl_repr()\n",
    "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n",
    "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n",
    "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set(title='Coincident indices, comparison')\n",
    "\n",
    "# Retrieve and also plot the NBER recession indicators\n",
    "ylim = ax.get_ylim()\n",
    "ax.fill_between(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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}