180210_TEST_GARCH_MSG.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting arch\n",
      "  Downloading arch-4.3.1-cp36-cp36m-win_amd64.whl (502kB)\n",
      "Requirement already satisfied: pandas>=0.18 in c:\\programdata\\anaconda3\\lib\\site-packages (from arch)\n",
      "Requirement already satisfied: matplotlib>=1.5 in c:\\programdata\\anaconda3\\lib\\site-packages (from arch)\n",
      "Requirement already satisfied: scipy>=0.16 in c:\\programdata\\anaconda3\\lib\\site-packages (from arch)\n",
      "Requirement already satisfied: statsmodels>=0.8 in c:\\programdata\\anaconda3\\lib\\site-packages (from arch)\n",
      "Requirement already satisfied: Cython>=0.24 in c:\\programdata\\anaconda3\\lib\\site-packages (from arch)\n",
      "Requirement already satisfied: python-dateutil>=2 in c:\\programdata\\anaconda3\\lib\\site-packages (from pandas>=0.18->arch)\n",
      "Requirement already satisfied: pytz>=2011k in c:\\programdata\\anaconda3\\lib\\site-packages (from pandas>=0.18->arch)\n",
      "Requirement already satisfied: numpy>=1.7.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from pandas>=0.18->arch)\n",
      "Requirement already satisfied: six>=1.10 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib>=1.5->arch)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib>=1.5->arch)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=1.5.6 in c:\\programdata\\anaconda3\\lib\\site-packages (from matplotlib>=1.5->arch)\n",
      "Installing collected packages: arch\n",
      "Successfully installed arch-4.3.1\n"
     ]
    }
   ],
   "source": [
    "!pip install arch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GARCH\n",
    "* [GARCH Website](http://www.blackarbs.com/blog/time-series-analysis-in-python-linear-models-to-garch/11/1/2016)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.tsa.api as smt\n",
    "import statsmodels.api as sm\n",
    "import scipy.stats as scs\n",
    "from arch import arch_model\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from pandas import DataFrame as df\n",
    "from MSM_util import *\n",
    "from lmfit import minimize, Minimizer, Parameters, Parameter, report_fit\n",
    "import sys, scipy, numpy\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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WPzecu89sg6+vPsK6GdS4djXGXti52Pt/7of1Ppff979VnP2fBT7XWWzVUx97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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b7994f828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hyper parameters\n",
    "\n",
    "# How much period taken into calculation and prediction\n",
    "m = 20\n",
    "# number of days prediction\n",
    "RV = 22\n",
    "# kbar\n",
    "kbar = 8\n",
    "\n",
    "xls_data = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = xls_data.iloc[:,3]\n",
    "GLD = xls_data.loc[:,'GLD']\n",
    "\n",
    "GLD2 = GLD.shift(1)\n",
    "GLD2[0] = GLD[0]\n",
    "GLD_r = np.log(GLD/GLD2)\n",
    "\n",
    "GLD_d = GLD_r - np.mean(GLD_r)\n",
    "plt.plot(date_GLD,GLD)\n",
    "plt.title('de-mean data')\n",
    "plt.plot(date_GLD,200*GLD_r)\n",
    "\n",
    "data = GLD_d[::-1]\n",
    "\n",
    "\n",
    "startingvals = []#[1.2, 1.2, 0.5 , 1.2 ]\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 5]\n",
    "op_methods = 'slsqp'\n",
    "\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tsplot(y, lags=None, figsize=(10, 8), style='bmh'):\n",
    "    if not isinstance(y, pd.Series):\n",
    "        y = pd.Series(y)\n",
    "    with plt.style.context(style):    \n",
    "        fig = plt.figure(figsize=figsize)\n",
    "        #mpl.rcParams['font.family'] = 'Ubuntu Mono'\n",
    "        layout = (3, 2)\n",
    "        ts_ax = plt.subplot2grid(layout, (0, 0), colspan=2)\n",
    "        acf_ax = plt.subplot2grid(layout, (1, 0))\n",
    "        pacf_ax = plt.subplot2grid(layout, (1, 1))\n",
    "        qq_ax = plt.subplot2grid(layout, (2, 0))\n",
    "        pp_ax = plt.subplot2grid(layout, (2, 1))\n",
    "        \n",
    "        y.plot(ax=ts_ax)\n",
    "        ts_ax.set_title('Time Series Analysis Plots')\n",
    "        smt.graphics.plot_acf(y, lags=lags, ax=acf_ax, alpha=0.5)\n",
    "        smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax, alpha=0.5)\n",
    "        sm.qqplot(y, line='s', ax=qq_ax)\n",
    "        qq_ax.set_title('QQ Plot')        \n",
    "        scs.probplot(y, sparams=(y.mean(), y.std()), plot=pp_ax)\n",
    "\n",
    "        plt.tight_layout()\n",
    "    return "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model1 TEST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SoYmJiawjSIbUf9jUf9jUfzIqDY1n3fnwLb1s/Wl9Xr6SZP8NNzjWu1XDpnku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\n5NgwDMMwDMMwHJYcG4ZhGIZhGIbj/wPBqSG8N6eYiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b79c52cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "a0 = 0.1\n",
    "a1 = 0.5\n",
    "b1 = 0.3\n",
    "\n",
    "w = GLD_d/np.std(GLD_d)\n",
    "eps = np.zeros_like(w)\n",
    "sigsq = np.zeros_like(w)\n",
    "\n",
    "for i in range(1, len(GLD_d)):\n",
    "    sigsq[i] = a0 + a1*(eps[i-1]**2) + b1*sigsq[i-1]\n",
    "    eps[i] = w[i] * np.sqrt(sigsq[i])\n",
    "\n",
    "_ = tsplot(eps, lags=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     38,   Neg. LLF: 28699.466988245593\n",
      "Iteration:     10,   Func. Count:     68,   Neg. LLF: 28699.28530979977\n",
      "Iteration:     15,   Func. Count:     98,   Neg. LLF: 28691.783263773377\n",
      "Iteration:     20,   Func. Count:    128,   Neg. LLF: 28611.505030022636\n",
      "Iteration:     25,   Func. Count:    162,   Neg. LLF: 28553.901587193508\n",
      "Iteration:     30,   Func. Count:    193,   Neg. LLF: 28552.9274090419\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 28552.927409903044\n",
      "            Iterations: 30\n",
      "            Function evaluations: 193\n",
      "            Gradient evaluations: 30\n",
      "                     Constant Mean - GARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                      -0.001\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -28552.9\n",
      "Distribution:                  Normal   AIC:                           57113.9\n",
      "Method:            Maximum Likelihood   BIC:                           57137.2\n",
      "                                        No. Observations:                 2533\n",
      "Date:                Mon, Feb 12 2018   Df Residuals:                     2529\n",
      "Time:                        15:35:56   Df Model:                            4\n",
      "                                 Mean Model                                \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "mu           -80.1705     52.041     -1.541      0.123 [-1.822e+02, 21.828]\n",
      "                               Volatility Model                              \n",
      "=============================================================================\n",
      "                 coef    std err          t      P>|t|       95.0% Conf. Int.\n",
      "-----------------------------------------------------------------------------\n",
      "omega      8.2859e+08  2.728e+06    303.682      0.000  [8.232e+08,8.339e+08]\n",
      "alpha[1]       0.9926      0.184      5.395  6.855e-08      [  0.632,  1.353]\n",
      "beta[1]    7.4354e-03  4.181e-03      1.779  7.531e-02 [-7.582e-04,1.563e-02]\n",
      "=============================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "# Fit a GARCH(1, 1) model to our simulated EPS series\n",
    "# We use the arch_model function from the ARCH package\n",
    "\n",
    "am = arch_model(eps)\n",
    "res = am.fit(update_freq=5)\n",
    "print(res.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model2 + Forecast\n",
    "[forecast GARCH](http://arch.readthedocs.io/en/latest/univariate/forecasting.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "returns = GLD_r*100\n",
    "am = arch_model(returns, vol='Garch', p=1, o=0, q=1, dist='Normal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 3825.014770625835\n",
      "Iteration:      2,   Func. Count:     15,   Neg. LLF: 3824.592333966819\n",
      "Iteration:      3,   Func. Count:     24,   Neg. LLF: 3824.2189992718763\n",
      "Iteration:      4,   Func. Count:     33,   Neg. LLF: 3823.440878972009\n",
      "Iteration:      5,   Func. Count:     40,   Neg. LLF: 3819.3183763082434\n",
      "Iteration:      6,   Func. Count:     47,   Neg. LLF: 3818.695194042147\n",
      "Iteration:      7,   Func. Count:     54,   Neg. LLF: 3817.596365949996\n",
      "Iteration:      8,   Func. Count:     61,   Neg. LLF: 3817.4264754409646\n",
      "Iteration:      9,   Func. Count:     67,   Neg. LLF: 3817.336455265128\n",
      "Iteration:     10,   Func. Count:     73,   Neg. LLF: 3817.1868171101105\n",
      "Iteration:     11,   Func. Count:     79,   Neg. LLF: 3817.180821399338\n",
      "Iteration:     12,   Func. Count:     85,   Neg. LLF: 3817.1806886428117\n",
      "Iteration:     13,   Func. Count:     91,   Neg. LLF: 3817.18068721023\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 3817.1806872091593\n",
      "            Iterations: 13\n",
      "            Function evaluations: 91\n",
      "            Gradient evaluations: 13\n",
      "                     Constant Mean - GARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:                    GLD   R-squared:                      -0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                 -0.000\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -3817.18\n",
      "Distribution:                  Normal   AIC:                           7642.36\n",
      "Method:            Maximum Likelihood   BIC:                           7665.71\n",
      "                                        No. Observations:                 2533\n",
      "Date:                Mon, Feb 12 2018   Df Residuals:                     2529\n",
      "Time:                        15:35:56   Df Model:                            4\n",
      "                                  Mean Model                                  \n",
      "==============================================================================\n",
      "                  coef    std err          t      P>|t|       95.0% Conf. Int.\n",
      "------------------------------------------------------------------------------\n",
      "mu         -8.3351e-03  2.037e-02     -0.409      0.682 [-4.827e-02,3.160e-02]\n",
      "                              Volatility Model                              \n",
      "============================================================================\n",
      "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
      "----------------------------------------------------------------------------\n",
      "omega          0.0124  5.821e-03      2.131  3.310e-02 [9.947e-04,2.381e-02]\n",
      "alpha[1]       0.0489  1.005e-02      4.871  1.111e-06 [2.925e-02,6.864e-02]\n",
      "beta[1]        0.9435  1.249e-02     75.525      0.000     [  0.919,  0.968]\n",
      "============================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "# split_date = dt.datetime(2010,1,1)\n",
    "res = am.fit()#last_obs = split_date)\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18b79d32710>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1Zra2rKysNWWJiEiEQm4GZpYAPA/c5pyr8LoQ59x859xo59zoPn36eL17ERFfRBJhDfDQ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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b7a8afba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forecasts = res.forecast(horizon=22) #, start=split_date)\n",
    "forecasts.variance.plot()\n",
    "\n",
    "# forecasts.variance[split_date:].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>h.01</th>\n",
       "      <th>h.02</th>\n",
       "      <th>h.03</th>\n",
       "      <th>h.04</th>\n",
       "      <th>h.05</th>\n",
       "      <th>h.06</th>\n",
       "      <th>h.07</th>\n",
       "      <th>h.08</th>\n",
       "      <th>h.09</th>\n",
       "      <th>h.10</th>\n",
       "      <th>...</th>\n",
       "      <th>h.13</th>\n",
       "      <th>h.14</th>\n",
       "      <th>h.15</th>\n",
       "      <th>h.16</th>\n",
       "      <th>h.17</th>\n",
       "      <th>h.18</th>\n",
       "      <th>h.19</th>\n",
       "      <th>h.20</th>\n",
       "      <th>h.21</th>\n",
       "      <th>h.22</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2532</th>\n",
       "      <td>2.030156</td>\n",
       "      <td>2.027219</td>\n",
       "      <td>2.024304</td>\n",
       "      <td>2.021412</td>\n",
       "      <td>2.018541</td>\n",
       "      <td>2.015692</td>\n",
       "      <td>2.012864</td>\n",
       "      <td>2.010058</td>\n",
       "      <td>2.007273</td>\n",
       "      <td>2.004509</td>\n",
       "      <td>...</td>\n",
       "      <td>1.996342</td>\n",
       "      <td>1.99366</td>\n",
       "      <td>1.990999</td>\n",
       "      <td>1.988358</td>\n",
       "      <td>1.985737</td>\n",
       "      <td>1.983136</td>\n",
       "      <td>1.980554</td>\n",
       "      <td>1.977992</td>\n",
       "      <td>1.97545</td>\n",
       "      <td>1.972926</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          h.01      h.02      h.03      h.04      h.05      h.06      h.07  \\\n",
       "2532  2.030156  2.027219  2.024304  2.021412  2.018541  2.015692  2.012864   \n",
       "\n",
       "          h.08      h.09      h.10    ...         h.13     h.14      h.15  \\\n",
       "2532  2.010058  2.007273  2.004509    ...     1.996342  1.99366  1.990999   \n",
       "\n",
       "          h.16      h.17      h.18      h.19      h.20     h.21      h.22  \n",
       "2532  1.988358  1.985737  1.983136  1.980554  1.977992  1.97545  1.972926  \n",
       "\n",
       "[1 rows x 22 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecasts.residual_variance[-1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>h.01</th>\n",
       "      <th>h.02</th>\n",
       "      <th>h.03</th>\n",
       "      <th>h.04</th>\n",
       "      <th>h.05</th>\n",
       "      <th>h.06</th>\n",
       "      <th>h.07</th>\n",
       "      <th>h.08</th>\n",
       "      <th>h.09</th>\n",
       "      <th>h.10</th>\n",
       "      <th>...</th>\n",
       "      <th>h.13</th>\n",
       "      <th>h.14</th>\n",
       "      <th>h.15</th>\n",
       "      <th>h.16</th>\n",
       "      <th>h.17</th>\n",
       "      <th>h.18</th>\n",
       "      <th>h.19</th>\n",
       "      <th>h.20</th>\n",
       "      <th>h.21</th>\n",
       "      <th>h.22</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2532</th>\n",
       "      <td>2.030156</td>\n",
       "      <td>2.027219</td>\n",
       "      <td>2.024304</td>\n",
       "      <td>2.021412</td>\n",
       "      <td>2.018541</td>\n",
       "      <td>2.015692</td>\n",
       "      <td>2.012864</td>\n",
       "      <td>2.010058</td>\n",
       "      <td>2.007273</td>\n",
       "      <td>2.004509</td>\n",
       "      <td>...</td>\n",
       "      <td>1.996342</td>\n",
       "      <td>1.99366</td>\n",
       "      <td>1.990999</td>\n",
       "      <td>1.988358</td>\n",
       "      <td>1.985737</td>\n",
       "      <td>1.983136</td>\n",
       "      <td>1.980554</td>\n",
       "      <td>1.977992</td>\n",
       "      <td>1.97545</td>\n",
       "      <td>1.972926</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          h.01      h.02      h.03      h.04      h.05      h.06      h.07  \\\n",
       "2532  2.030156  2.027219  2.024304  2.021412  2.018541  2.015692  2.012864   \n",
       "\n",
       "          h.08      h.09      h.10    ...         h.13     h.14      h.15  \\\n",
       "2532  2.010058  2.007273  2.004509    ...     1.996342  1.99366  1.990999   \n",
       "\n",
       "          h.16      h.17      h.18      h.19      h.20     h.21      h.22  \n",
       "2532  1.988358  1.985737  1.983136  1.980554  1.977992  1.97545  1.972926  \n",
       "\n",
       "[1 rows x 22 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecasts.variance[-1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MSGARCH\n",
    "\n",
    "\n",
    "* [web site](https://github.com/ChadFulton/statsmodels/blob/master/examples/notebooks/markov_autoregression.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TEST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18b79c0dd68>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GuLz0f3vsNFulqkH8KZViqWLZRp0BxCRIO3rq5BTmg1FolDLY2aS0mmNhcMdC+gTA7BPL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b79e5d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the RGNP data to replicate Hamilton\n",
    "dta = pd.read_stata('http://www.stata-press.com/data/r14/rgnp.dta').iloc[1:]\n",
    "dta.index = pd.DatetimeIndex(dta.date, freq='QS')\n",
    "dta_hamilton = dta.rgnp\n",
    "\n",
    "# Plot the data\n",
    "dta_hamilton.plot(title='Growth rate of Real GNP', figsize=(12,3))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>rgnp</td>         <th>  No. Observations:  </th>    <td>131</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovAutoregression</td> <th>  Log Likelihood     </th> <td>-181.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Mon, 12 Feb 2018</td>   <th>  AIC                </th>  <td>380.527</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>15:47:56</td>       <th>  BIC                </th>  <td>406.404</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>               <td>04-01-1952</td>      <th>  HQIC               </th>  <td>391.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                     <td>- 10-01-1984</td>     <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>approx</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.3588</td> <td>    0.265</td> <td>   -1.356</td> <td> 0.175</td> <td>   -0.877</td> <td>    0.160</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    1.1635</td> <td>    0.075</td> <td>   15.614</td> <td> 0.000</td> <td>    1.017</td> <td>    1.310</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.5914</td> <td>    0.103</td> <td>    5.761</td> <td> 0.000</td> <td>    0.390</td> <td>    0.793</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>  <td>    0.0135</td> <td>    0.120</td> <td>    0.112</td> <td> 0.911</td> <td>   -0.222</td> <td>    0.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L2</th>  <td>   -0.0575</td> <td>    0.138</td> <td>   -0.418</td> <td> 0.676</td> <td>   -0.327</td> <td>    0.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L3</th>  <td>   -0.2470</td> <td>    0.107</td> <td>   -2.310</td> <td> 0.021</td> <td>   -0.457</td> <td>   -0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L4</th>  <td>   -0.2129</td> <td>    0.111</td> <td>   -1.926</td> <td> 0.054</td> <td>   -0.430</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.7547</td> <td>    0.097</td> <td>    7.819</td> <td> 0.000</td> <td>    0.565</td> <td>    0.944</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0959</td> <td>    0.038</td> <td>    2.542</td> <td> 0.011</td> <td>    0.022</td> <td>    0.170</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                         Markov Switching Model Results                         \n",
       "================================================================================\n",
       "Dep. Variable:                     rgnp   No. Observations:                  131\n",
       "Model:             MarkovAutoregression   Log Likelihood                -181.263\n",
       "Date:                  Mon, 12 Feb 2018   AIC                            380.527\n",
       "Time:                          15:47:56   BIC                            406.404\n",
       "Sample:                      04-01-1952   HQIC                           391.042\n",
       "                           - 10-01-1984                                         \n",
       "Covariance Type:                 approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.3588      0.265     -1.356      0.175      -0.877       0.160\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.1635      0.075     15.614      0.000       1.017       1.310\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.5914      0.103      5.761      0.000       0.390       0.793\n",
       "ar.L1          0.0135      0.120      0.112      0.911      -0.222       0.249\n",
       "ar.L2         -0.0575      0.138     -0.418      0.676      -0.327       0.212\n",
       "ar.L3         -0.2470      0.107     -2.310      0.021      -0.457      -0.037\n",
       "ar.L4         -0.2129      0.111     -1.926      0.054      -0.430       0.004\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.7547      0.097      7.819      0.000       0.565       0.944\n",
       "p[1->0]        0.0959      0.038      2.542      0.011       0.022       0.170\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model\n",
    "mod_hamilton = sm.tsa.MarkovAutoregression(dta_hamilton, k_regimes=2, order=4, switching_ar=False)\n",
    "res_hamilton = mod_hamilton.fit()\n",
    "res_hamilton.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: certifi in c:\\programdata\\anaconda3\\lib\\site-packages\n"
     ]
    }
   ],
   "source": [
    "!pip install certifi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LlMT8wWUMey0bBwYycCmhD4PDAJH6TpOBty2GitYJeasVFXutfhVzp2VjpaLiNXccxYnV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nCvADeD2GpymNA7G4wvodB0hHJyZCgwy3wOcNaSJnweYW0a8zlUtqby7hNG1axLVrfN2acLVSxM\nJrII8DXthgA/Mjy7JnpcqZkodBcJNCsDphgfOBgdydy0YJkPxqejTIVjHBsOEE+6FyOmBt5c66PG\n5ynIB27VQU/XNrQYrFzwIQfngrtXgIeNm5pLA0+kkjlUC59JIZvdLafG7+Vr77uA337T2rTvs8xE\nlZj4rBVpuvgDXet5YTIRisyJQLeorzKCSftS0jknQzGsx8RNC74ZH3jxJvSFroH3jhpBjaFonIHJ\nUGL7yFSYap9Q7fMULsDNe2q1bC0VKxd82MF+cPcK8IhRbi+Xv8NKJet3aDGX3hGj3WL3orm53rec\nt5T1XXMj0CEpiK0CE182X1Mlr0tTOawgtkwsbqyaI8CHkzQbN2mkCQ1cB7EVzYnRGWvMseGZDIWR\nQIQmM66m2u8p0gdujwndEuBODmRzrwAPx3NGoMOMBp46eTiFw2ki0POhkgUhwuZnphPgulDFwiSb\nCR2MhXRqPYbkACFXmtBL8IE7oZNgJTk+MiO0jw7N/H80EJ4R4F5PQT5wS4DbZ0K3GppoE7rtTEei\nOSPQYSaf0Kka+JGUHPB8sXzglTBVR7OsdP0eXet5IWIEsaU3oYMRTJqaDWLlgDfXeN2lgZdqQtca\nOMdHp6nyefBIqgYepqnaEEs1/uJM6HZFobfW+RCcXU7VvQI8HMtLgFf5PLTW+hyrgR8dCtBQ7WNR\nQ1Xug5PwVzBYLJsJXQexLTyCkRjhWDyHBl7FRCjGVFKv52EzAr2zocpVAjxkauDFFgzxeWXB/z5O\njAZZ3lLLkuZajplWSIDRQISmGmNer/F5CEbyv092p5H5PEJLrc/R5VRdK8AD4VheJnQwzHdO7Uh2\neHCK7kV1GXuaZ6KSfYWzrXStABI3Tcia0rAamaR2IkvGKsyRbEYfDkTwCLTV+Vz1vARLLOTi98qC\nt1D1jk6zrLWWVe11szTw4WQTuq8wE7rdaWRgpJJpDXwemI7kp4EDdDRUObYe+rGkJiaFUMlCLuFo\nFhO6bpe44MhUBz2ZxVZfgiRL2EggSkutD7/X46rnZcYHXqwJ3bPgNfDjI9Msba5lZduMAI/FFWPT\nSRq4X4pLI7NJAwejnOqgg8upulaAByMFaOANfsfWQx+bjtBal3niy0Qlfc3ReByfR9IXmNFR6AsO\nSwPPFoXelQgmnfkdDgeitNX58HncVZksVGoU+gLXwIORGIOTIZa11rKyvY7ByTBToSjj0xGUYsYH\n7is0Ct1MI7NVgDtbA8/8i3M4gXCMxU35Cb6mGh+T4VhFe2dnYioUpT5LT/NMWObryvjAM7fsm4lC\nX9hRtguJmV7gmZ/j9no/XoFTszTwCK21fnxed7lcQiVqegs9iO3kmJFCtqyllmq/cQ97RgKJ+9lY\nneQDL0QDj9tvQm+v8zM8HSHuQNkBLhbghZjQKxnwlY1YXBGKxvMeRzK+Cpqqw9F4xh+JjkJfeEyG\ncpvQvR4xXFnJAnw6yrKWarziLg28VBO6EcS2cBe4J0aNkrpLW2oTVpujQwEWNRg9H5prZvLAC0oj\ni9obxAbGwjMWh7HpKIXbSeefvEYqIjeKyF4ROSAif5Jmf7OIPCQir4nILhH5iP2XOptgAUFsCb+s\nw34zVjnYojTwCpqqo/F4bg3cRROypjTG89DAwcwFz2BCd5NGGozE8chMKmehLPQgtuMjhgBf3mr4\nwAF6hgOMmJ3JmpI08HBM5a39Ws+QXXng4PxyqjlHKiJe4OvATcDZwPtF5OyUwz4N7FZKnQ9cA/yz\niBSWF1UggUgsZxlVC8s047RJIhDKr6NaOvwVNFVHoplN6B4RvOIuk6imNGai0LPrKF2NM8Gk05EY\nwWjcNKG7SwMPRWNUedPHgOSD37Ow08h6R6cRga6mGprr/DTV+Dg6FEjUQU8W4JB/S1G708jAiEIH\n51Zjy2eklwAHlFKHlFJh4D7g1pRjFNAoxhPdAAwD87pkmQ7HqMlT8Dm1OljA7Gme70IkmUQhlwrl\ngfuzmA8XepDOQsOKQq+vzv4cLzY7A8biKlFG1dLA3dRONBiJU1WCn9Xn9ThuLionJ0an6WqsSWjK\nq9rrOTYcYNTMt26qmQlig/xbis5HGlmbGWDs1Lai+QjwZUBP0utec1sy/w6cBZwAdgCfVUrNuesi\n8gkR2SIiWwYGBoq85CTfcZ4m9CqHmnWnEg1Zigliq2Qp1cwmdNBpMguNiWCUuipvzujfrsYqYnFj\nMkwV4G4SaMFIrCQzrd9lUfd2c3zEyAG3WNlWZ5jQA2F8HqHODGyzAtyC0XxN6PankZ0OGng+vBV4\nFVgKXAD8u4g0pR6klPqmUmqTUmpTR0dH0R9mBZHkq7n6HWpCn7ZBA6/EmKIxhT9Lxx+f7ra0oMjW\nCzwZq7HQqYlIou9za53fdWlkwWic6hK0vIXejezE2DRLW5IEeHsdPSMBhibDtNT5E66J6kJN6OZx\ndqaR1fg91Fd5GHJoLng+Iz0OrEh6vdzclsxHgB8rgwPAYeBMey5xLlbwV95BbBUUdtkoxYQuIhWb\n+HKZ0P0ebUJfSGRrJZpMohrbRDhRRrWt1mc291COTPNMRygSK82E7nHXeO0kHlecHA2yrGW2Bh6J\nKV4/NU5r3UzoVMKEnqcAt+ZCO03oYKSSOTUXPB8BvhlYLyKrzcC09wEPphxzDHgzgIh0AWcAh+y8\n0GQszbWm4Ch0Z/1gAiWY0KFybQlzmdAXeprMQiNXJzKLxUmdAa1GJq11PrzmAtthP8+MBKOl+cCd\nOh+Vg4HJEOFYfJYJfZUZif76yVQBbtynwn3g9tYna6/3O7Yees5fnVIqKiKfAR4FvMB3lFK7ROQO\nc/9dwN8A3xWRHYAAn1dKDc7XRU8nTOj5Cb6q0zCIDUxTXKU08Cwm9IXu41tojAejNNfm1sDrq700\nVHkTueCN1V78Xs+MO8glz0wwEiu6ChtUNn6l0hw3c8CXtdQktq0wBXgkpmhJqkpZ40/WwHPf70jU\n3m5kydcx4lYBDqCUehh4OGXbXUn/PwHcYO+lZcYSfLVV+X1RvgpWLctGQoDniN7NhM8jFWonqhIB\nJunQUegLi4lghOVJJtFsdDX6OTURocortJo5tpYAd0skeqhEDTw5g8S1tayLxMoBX9ZSl9i2tKU2\n4VZI1sBn+8DzEOCxOF6PJCw6dlHl4JgFVz4/hZrQnauBl2ZCr6gGnjUK3bkPvMZ+8g1iA6sveJiR\n6Shtptbu1EJLmSjVB+7UoNpycDxRhW1GA/d6hOWmSb2lPkkDLzCNzJiX7BXe4OygQ1cK8GCBJnSn\nllJNWBLyXIik4qtQsFg4Sy100P2OFxr5+sDByAXvmwwzHIjM0cDd4nYxTOglCHCXuQzs5MToNE01\nvjlBjyvNjoxtJQSxhXO49orF7zEqwjkRVwrwQgWfk6PQa/yeok0+VvRuuYnmWOn6Pe5qD6kpnkgs\nznQkllcUOhga+HgwxqmJMG2uFeDxknKNK9nHoNIYOeB1c7avbDM08FlBbP7CBLiRHTMPAtwrRB0a\nlOtKAT5dZB640yaIQDhatPkcKmfayWlC1xr4gmEyzzroFlYueCiqaK01BbjLorKtUqrF4nfZgsVO\njo9Oz0ohs7BqoicHsRWaBx6NqXkxoVd5RWvgdmIJcPf7wPOv554OX4UqnmVrJwqVS2/TlJ+ZVqL5\naeCLG2c0LKtM5UwQm80XN08EI/GSTOgLueWuIcBr5mxfvagBgEWN1YltVV5BMBZ7+ZArvbVYnFyY\nyp0CPFxYExDH1kIPlSbAK9XVKJ88cLdEFGtKY9ysg261hcxFV5IAT/WBO+33mQ6lFMForCQTulNj\ncuab8WCEiWB0Vg64xbVndHDnbRfyhhUtiW0iQo3fU0AQm7K1jKpFlYNr17tUgBtfaP610B2aRhaJ\nUVuKCb1Cmm5uH7hzV6wae5kMWZ3I8nuO2+v9WI9Oqg885oLKZOFYHKWK7wUOSSb0BfYbSe4DnorP\n6+Hmc5fM6fBW7fPk7wOPzo8GbsUa5dvWtJy4UoAHIlGqfPkHfzm1cEIgFKW+FBN6hSqe5TSh60ps\nC4ZCTeg+j7CowTi21Uwjc5MP3PLHluJr9S3QNLKZHPD8agaAEYleSDvRbCWei8XJCy5XCvBgOFZQ\n6pVTTVal+sArVXM8ZzcyXchlwWC1Es03iA1m/OBzotBd8MxYKawlNTNZoGlkR4cCwEzltXyo9klB\npVR985FG5lALLrhUgE9HChN8HhG8HudNENMlmtArlW+dlwndgQ+7xn4mCoxCB8MPXu0Tas00oZk0\nMvuvz25CpjCxo5Sq0+aj+ebw4BRNNT7a66tyH2xSU4gJPVZael8mnBoEDXmWUnUagQI1cDADERwm\nVKZKNaFXQAOPxRVxlb3esI5CXzhYGnhDAQL81za2s35RbcLf6abmHqGooYGXVErVoRbB+ebI0BSr\nOxrm+LmzUePPX4DnKvFcLE7+vlwpwIORWN4R6BZOFCrT4cLHkUwl8q0jeXT80VHoC4eJkBGPUu3L\n/zm+cHkjFy5vTLx2UyEXy5xrRx74QksjOzQwxcXdrQW9p9rnYSoUy+vYSCxe0EIyX6oSFhPbT10y\nrjWhF66BO8usq5RiKhylvqQo9PKnN8y07Mteic1piyXN/DARjOYdgZ4JdwlwUwMvJQrdRRYHuwhG\nYpwYm07ke+dLISb0XCWei0X7wG0mUITm6ndYLl8oGieu8s9lT4evAqVULZN9PpXYlAPTLjT2YtRB\nzy8CPROWidINCqmlgVeXUkrVs/Ci0I8OBVAKVnfUF/S+Qkzo8+UDd2oWE7hUgE8X4QN3WkeZ6RJ7\ngUNlor3zNaGDOyZkTWlMBCMFBbClw00auB0+8IUYxHZ4cBKANYsKE+DVhaaRzVM3MtAauG1MF+ED\nr1Tjj0xMmdXkSjOhlz/fOpxHHuxMmoyW4Kc7hXQiy4SbBHjCB667kRXEocEpALoLFOA1Pg/BSH73\nKRKNJ3Ls7aTKwXn77hTgRUWhO8sHbmngJZvQK6SBV2VJo3FTaUxNaUwGo3mXUc2EuwR46XngTi3t\nPJ8cHpiis7G64GeloEIu8fnxgTt5PnOnAC8qCt1ZPV2nTAFeX11aIZeYoqwR39Ykm61ggpsqa2lK\nwzChl+YDnwnqsuOK5hdLmJSSB+6mBYtdHBmaYnWB2jcYPvBIXOU1xxk+8PnpRgbO/L7cKcCL1MCd\nNEEErIYs/tIKuUB5H6xCTOgLyce3ULHDhO51kUCzNPBSfK1ej+CRhZVGdniwOAFu1ZwP5TGXzFct\ndGuedZICaOE6AR6JxYnGlQ5iw0jXgvIKykQQWxYNxMlBHxr7iMcVk2EbotDdJMCjpZvQwaxL4YLx\n2sHYdITByXBxGngBPcEjMZV1XioWpzbDAhcKcKsXeDFBbE4S4LaY0CsgKK1JNlu6xkJt1rDQmAxH\nUSr/TmSZmOkH7vznxY5CLrCw+gUcMQPYijWhAwRz9ARXSs1bP3AnZw24T4AXGfzl93octcKf6Wle\nggm9AsEVEXMl7MvSCc7vIo1KUzzF1EFPh2VSdpKLKxOhaIwqn6egcqDpWEjFjg6bAnxNgTngMJNv\nn0sDn1Es5q8bmdbAbaBY07PTNPCANY4CXQHJzPjAyzfzhQsxoTvofmvsZ9IU4A3VpZnQwazr78AJ\nMpVQJJ4w65ZCpRoRVYJDg1N4pLAuZBaWBh7KoYFbrr35SCNz8nzmOgFuCb5ifOBhB/1gEgK8xCh0\nKLMGHsttQp8JSnKBSqUpmmJaiWbCLQI8GIlRU8Ki22IhmdAPD06xvLWuoHr5FtV5+sAjeVSILBbt\nA7cRywde6I+oymGlVAPhKF6PlFT6ryI+8MRKV0ehL3TsMqGDexrghKJxewR4BYowVYojRUagw0wQ\nWy4feKI+xTyY0J2ct+86AW6lcdQV6Dt2XCW2kNHTvBRfmq8CgjKcRylVHYW+MBhPaOD2mNDd8LwE\nI7GScsAtKlGEqRIopYpOIYMkE3qOlLt8SjwXizah20gpJnQnfQHT4VhJKWRQmdVQfc4AACAASURB\nVK5G+ZjQnbxi1diHpYGXGoUOhgB3Q1q0bSZ0B7Y3ng8GJkNMhqIla+A5feDR+TOhe0Qc6+JxnQCf\nSSMr7NKtH4xTOmQFIrGCrQip+CuQrpXPSldHoS8MJkOWCX3hBLEFI/GEVlgKCyWI7fBA8SlkMOMD\nz2VCzye4thScpgBa5DVaEblRRPaKyAER+ZMMx1wjIq+KyC4R+ZW9lzlDMJFGVqgJ3YPCObmmgVC0\nZA28EgUw8vKB6zzwBcFEMILXI7YJNDcI8FA0VlQwVip+j2dBmNAPl5ADDlDjNyux5QxiMwV4lvTW\nUvA7dMGVUwqKiBf4OnA90AtsFpEHlVK7k45pAe4EblRKHRORzvm64JkSpIWXUgVjpTYfqQaFErDR\nhG48vKVPKvkQziPa08nF/zX2YZVRLTUnGtylgbfVlz5/+L2Sd59rN3N4cIoqn4elLbVFvd8yoecq\nYzqfPnAwm2E5cD7LZ7SXAAeUUoeUUmHgPuDWlGM+APxYKXUMQCnVb+9lzjBtVkIqVIAn6tk65EcT\nCEdLNqFXpJBLItozn37gznvgNfbRNx5kUUO1Lefye5zVqyATwWiMaht84D6HCgS7OTQ4RXd7XSK1\ntFB8HsEr5FzsJNLI5smE7vN4HKmB5zPaZUBP0utec1syG4BWEXlKRLaKyIfSnUhEPiEiW0Rky8DA\nQFEXbFUwK9RsZwmcsEMiZezUwCthQs+vH7jzHniNffQMT7OitTjNKhUjiM35z4tRyMWeILaFUCfh\n2FCAVe3Fmc8BRIRqnyfvQi6lNJnJhps18HzwARcBbwPeCnxBRDakHqSU+qZSapNSalNHR0dRHzQd\nMTqRFWq28ztOAy+8JWoqlUhvsExZ2VbUs037mtOVnpFAUdW10uGWoK5QNEa1DT5/pwZF2c3YdITW\nutKCHGv8uXuC52MZLAWnpSFb5GPDPQ6sSHq93NyWTC8wpJSaAqZE5GngfGCfLVeZxHSkOM3V0gqd\nI8Cj1NtlQi9rGlmcKm/2WtBu6i6lKY6xQISJYJQVrTYJcI8Qijj/eQnapIH7Fkga2VQoSn11afNc\nYRq4jkJPZTOwXkRWi0gV8D7gwZRjfgpcKSI+EakDLgVet/dSDQLh4vIwnZaMb4cJ3VeJdqLReE4z\nldPutcZ+ekYCAKxos8+E7pC1dVaMPHB7NPDTfYGrlGLKBkWlxuchmGMuCc9jHrh1XifOZznvrFIq\nKiKfAR7FCHX+jlJql4jcYe6/Syn1uog8AmwH4sC3lFI75+OCg5HiTM8JH7gDZolYXBGKxu0zoZe5\nnWiuKH4dhX760zNsCPDlNmrgThdo0VicaFyZCkRp1+pUgWAnwUicuMImDTzfSmzzl0YWdqCFKK87\nq5R6GHg4ZdtdKa//Cfgn+y4tPcVWMEtEocdidl9SwVipcKWuTGeamZS3G1muVa6I4PVoE/rpzIwG\nbp8P3OnPiyVEjOIipc0jbliwlMqUNc+V0LAJDA08FM1+v+fdhO4Rphy44Kp8QnSBFGtCT+SB5/Cl\nlINie5qnkmgnWmYTej4NA/weZ/Vf19hLz/A0TTU+mmtLr8IG7hBowSIbKaXDqT5VO5kK2aOo1Pgl\ndz/weU4j83vdm0bmKIJmFHqh+B2URjZlCvBSV6aVCmLL50eyECaohYydEejgjlroVi6yLZXnFkA3\nsqmQPfNcjc+TfynVeUwjc4D3dQ6uE+DFBn85KY1spppcaStTr1nkoKzNTOIqsXDIhhs0Kk3x9AwH\nbItAB3ekkYVMDdyWUqpeY8ESd0hvhvlgxoRePh/4fKWRObXwjusE+HTRGrhzcpMtE3qpUehQ/raE\nRhR6vhp45e+1xn6UUvSOTNsWgQ6Gj9HphVyCEfs08IXQ8McyoZdacbLG7yGkS6mmxXUCPBiJUVNU\nFLpzNHC7TOhg+JrLngeehwl9oeS5LkQGJkKEonHbTehOF2ZBM5DKrlKqgCPNsnZhmdAbStTAa/LK\nAy9DGpkDn0/XCfBAOEZdET8gK2faCQJ82iYTOpTftBONq7x+JG6IKtYURyIC3UYTutdTXktSMYQs\nDdwWE3r5aziUG7ui0PMxoVvz+nymkTlRIXGVAFdKGSb0UjRwB5h17QruALOmcjlLqUbjefnA/S7Q\nqDTF0TM8DdhXxAXMBZ/DH5cZDdw+E7oTtTq7sC8K3UNMZXd/RmLGvGRHZ7x0OLWdqKsEeCgaR6ni\n0q8cFcQWsSeNDKwHq3xjyteE7tQVq6Z07C7iAu7wgVtBbLaUUq1AI6JyE0i4Cks3oYMR/5SJfC2D\nxVLlNfq3K4cFHbpKgCfyp0sIYnOCBm6Z0EsN7oDy+5ojsTxN6J7Tv9LUQqVnJEBHY7Ut+dAWPo8Q\nV85uQTsvQWyn8W9kMhTF75W8FvzZsAR4MJxZgIfzKPFcCj6PoHDegstdAjxSigA3hhpxgAZumdCL\nGUcq5fY1W6aqXCyEWs8LFTvbiFr4KlBVsFBCNgaxVaIMcrmxo5EJQLXPuFfZNPB8LYPF4qQg6GRc\nJcADJVQw83kEjzhEAzcbIhTb5D4Zf9k18PwKuego9NMXu4u4gDtMygkN3AZBsRA69k2FYiX7v8Eq\nXZtbgM+nCd1JacjJuEqAB0vQwMH40ThhBTUVitpiPofyR6FHYiqvYgmGZaDy91pjL9FYnJNjQVsj\n0CFJoDlsgkzG7lKqAFlkkusxNPDS71Wt6bIIZDGhR2IqsQicD/wOaoaVjKsE+HSJwV9+rzhDA7eh\nlahFuWuOGytdHYW+UDk5FiQWV7ZGoMOMAHfC7zMTlgZebYMGnkgjO41/I1NhexQVa8E0nc0HXiYN\nPFc6W7lxlQAPlFjBzO8QDdyOXuAW5Y72Nla6Ogp9oWJFoNutgbshLzoUjeHzSF7Pfy4Whgk9WnIR\nF4A6UwO30tLSEY3F562MKsz4wLUJvQSsFVixJiyf1xkC3K6VKVQmiC0vE7r2gZ+WWEVc7EwhA7CU\nWicL8GAkblvk/YwJ3bnjLRW7FJV8TejzqYE71ULkKgFeqg+8yuOM+tz2mtDL62vO24Suo9BPS3qG\np/EILGmpsfW8XodOkMkEozFbUshgYWjgkzZp4NZ8b1V2S0e+81KxVGkfeOnMmNCLeyic4gOfcrEJ\nPZrnStfv1XngpyM9IwGWNNfaru3MCLTK/z4zEYrEbelEBjMa+OkswAPhGHU2BLFZJvRAKFceuI5C\ndzSl5IGDc6LQp+00oZfRVK2UIhyL5+UD9OogttOSnuGA7QFs4A4feDAas6WMKiyMPPBJm/LALatH\nLg18PvPAdRCbDSSagJQQhf7/t3feYZJVdcJ+T8XOYaZ7enqmJ8MwwWEIwxBWQZToouiKCCiimFh1\nVxc/Ub9dfdg1o9/qqgiii4iKGFERHHJygMmByfRMhwmdc1V1V7rn++PWra7pru6ucFPV3Pd5+unq\nm+qerlvnd37ZDh+A3kFsZglK7X18ThT6KcvRgVHdA9hg3AduNw0nlXA0rksZVRhvrmTnBUs+ROMK\nkZiiSx642yXwu8XMaWQ61NWYCieNTAdGo3FcIveOM3bpUa0KcH00cDNN1dn03HWi0IuPsWicnpGw\n7kVcILUSm32fGTWITW8NXJfL2Y5QWJ866BolXhehGX3gZkSh2+v5LCgBHoqolX1y7TjjcVm/gpJS\nEorEdNPAzeyjrD28mZjQtfuyW/F/h9zpC0YAaKjy635tT9KEbl+JFo7F9fOBF3kQm2burtDBBw5Q\n4hHT+sAzrRCZK1qRGKvlx0QKS4CHc2slquGzQRBbOKag5NhRLR1m+sA1DTwjE/opEKRzqpFsD6mT\nVpVKUgO38fOipwaeLB1rM41OL7RnRS9LY6nXNYMPPLMKkbky3o7aXqXzCkuAR+N5TR5elyBqcdPh\nZIs9PaPQTYrczdaErp5TnBPUqYhe/Z3TkRTgNtNwUhmLxvXLAy+ABUs+BMKaBq6TAPe4ZvCBG5tG\nNt4My16fV2EJ8HAsrw5edkgjC+nYShTUiS+ugGKCqVrTFjIR4O4iNxGeiuRbCXE6xi029hXg4Zh+\nhVwKoXlLPuj9rJR4xbSV2AxvZpKYz8I2c/EUlgCPxPMqjm+HNLJ8Oqqlw0xTtbb4yaRpgLcAgpIc\nsiNghgndxs/LWDSuSx10AJcQuF3Fa0LX+1mZSQM3Kw/cavkxkQIT4DFK89Bc7aGBa9GZegtwXS43\nLeM+8MwKuUDxahinIpr1yEgBbmcNXE8TOqiNiIrVhK73s5KJD9yMSmx2yGJKpcAEeDwv37HXBrXQ\ntQe71KufCR3MWclr/p9MVrqFoFE5ZEcwrG/8RirupA/cns/Lwc4RRsIxZpX7dLumWsNBt8vZikBY\nX0Wl1OuathuZ0SZ0JwpdB0KR/KLQ7dCNLKTzg22mpqsFy2WSruFEoRcfRkahj+dF22uCBDX180t/\n2kN1qZf3X7BIt+uamQJqNiGdAx5LPCK5gJyIlJKYYnwzE5coUAEuhLhKCHFQCNEshPjCNMedJ4SI\nCSGu0+8WxwlFYnk9EF4bNDMJRfUN7jAzn1SLEPZmUPHIrrWDHXInGMmvlPF0mGlJypY/bj/O5tZ+\nvnDVCt018GK1UAXDMYTQ71kp8bgYjcaJp5nntP+hkaVUwR7yYyIzjlgI4QbuBq4GVgE3CiFWTXHc\nt4An9b5JjXxLkGplRxULV73ayjQfX34qHrd56SjaFyUTDbwQ8nodsiMUVgsQuQwoWTnucrHXBDkU\nivL1x/dz9sIarl+3QNdrF7MGHozEKfPq96xoLUW1fhipjKe3GucDB3WutUMp7lQyWbKsB5qllEek\nlBHgYeDaNMf9C/AHoFvH+0sSVyThmJJX+pUderq294fwuASzyvRZyXvN9IFnkQduZ43KITeCEX2a\nU6TDrnUDvv3kAQZCEb76zjfovnAp5pa7QZ0amWiUetX/fShNKlk281I+eF3WB0FPJJMRzweOpvx9\nLLEtiRBiPvAu4J7pLiSE+JgQYqsQYmtPT09WNzqeP52fBg7WCvDNLf28YX61fpXYLIhCz6RpgOMD\nLz6C4fyCSKcjWTfARhPka8eG+NWmdm65aDGr51Xrfv2iNqFH8iu6NZESj9aRbLIGHjFLgLuF7QoN\n6TXi7wGfl1JOOzop5X1SynVSynX19fVZvUGyMEAewV9W5/KNRePsPjbE+Utm6XZNM9sSZuNrsqtG\n5ZA7IR3b4E5Es37ayeWyYW8HLiG4/fLlhlzf43IV7QJX1cD1W+xpJvR0xVySrj2DTeh21MAz+TYe\nB1KdP02JbamsAx5ONBmpA94mhIhJKf+ky12iT2UfzdxslQDfeXSQSFxhvY4C3NQ0sqxM6E4eeLER\nCMd0K405ESEEHpe9fOD9wSg1pV4qS7yGXN/MMshmEwznF3A8kVLPND7wmHkauN2i0DP5D28BThdC\nLEEV3DcAN6UeIKVcor0WQjwA/FVP4Q36FMe3OjJ6c0s/QsC6RTpq4CYGi2UTLOJo4MVHKBLXNQp7\nIh6XsJUJfTAUoabMGOENWlSzYZe3lGAkxpzKEt2up/nA02ngWvEfU0zoNno+IQMTupQyBnwKeALY\nD/xWSrlXCHGbEOI2o29QY1SH9CurNfDNLf2c0VBJtY6TgsfMPPAsaqE7UejFh95a1UTM7KyXCQOh\nCLU6BZumw+MWRRvkGQzr7ANPmNDTlVONZFFgKh88LvtFoWf0H5ZSPg48PmHbvVMc+8H8b2syemjg\nWsCXFR9CNK6wrW2A69c16XpdM4PFcotCt9cD75A76qRsTBAbqIFsdtJwBkNRmmrLDLu+1yWKdoGr\nLvb0e1aSQWzTRKH7PAb7wG1oQi+YSmyjOvrArZgk9p4YZjQaZ/2S2bpe18ymIbmY0G32vDvkQdDA\nIDZQn2U7aaSDoSi1RprQnTSyjClNCOd0GriZaWR2WmBCAQnwYLKPdv4+cCtWUZtb+gA4b0mtrtc1\nsy1hNiZ0q+MNHPRFSpl3N8CZcLvsVUp1IBSh1kiff5Ga0BVFEorqm3KYjEJP09Ak2SXRZbQP3NoU\n5HQUjAAf1ZqA6OEDt+BD2NzSz9K6cl0DOyC1lKqul01LLib0YjURnmqEYwpxRRpWyAXs5QMfjcQJ\nxxSDg9iKsxvZaDSOlPrWzPe51VrkoTT10MfTW01II7OZSbFgBHhQhzacVmmFiiLZ0jqga/qYhtk+\ncJcYL7oxHcn7ssmE7JAfQZ2bU6TDTlHoA6EIgPFBbEUowDUtuUxHAS6EoNznSauBm5lGZpcFpkbB\nCHDN91HiKbxCLoe6RxgajXLeYv0FuJl54JEsWvZ5E+asYtQwTkX0qMMwE3bSwMcFuLFpZDZT6HRB\n6xpWobO7pczvTttS1Kw0Mo+jgeeOHo0UNGFndhT65pZ+AIM0cPMEZSyeecs+7TBHAy8OAgkN3KhC\nLgAe1/hkbDWDoSgANQZq4HbU6PRAj4yhdKgaeLpSquakkXkLtJmJLQhF8+tEBtYVF9nU0s+86hKa\nakt1v7bZJvRMyxWqlbWKc4I6FQkZYBadiJ3SyBwTeu4EDVrslfnd6ZuZJISqzynkYl9UDTy/B8Jn\nkQl9a2s/5y2ZRaLUrK6YGSwWzcKEDsWdJnOqoZlFjWpmAlqajj2el4GEBm68Cd0e49UTo9wtZd4p\nfOBacK0TxGZf8u0FDintRGPm1S8ci8bpGg6zvKHSkOu7XQIBmDGkaBYmdEj4NItwgjoV0TRwI6PQ\n3TYKYhsMqhq4sSZ0F4pUWyUXE0a5W8r87mnzwA1PI7NhM5NTSoBbYULvHBoDYG6VvuljqZil6WZj\nQofEfdnsgXfIjUA4/zoMM6E2M7GHMBsIRSn3uTPqvJcrHgsLSxmJUYu9cp8nbSU2zQduhgk9rkhb\nLbgKSIDnb0K3Ig/8xNAoAI3VxglwszTdrE3ojgZeNIz7wI2OQreHMFMbmRinfUNKVoxNxqwXRi32\nynzpNfCYSSZ0Oy64CkiAx/Mq4gLqCh/MjULXNPDGGv0D2DS8JlV0isSyNKEXaZTtqch4apDBeeA2\nWfCpVdiM839DShlkm/lV8yUZha7zYq/c77G2lKqFvTSmoqAEeL4BNEIIfG6XqYEIHUVkQo8pCt4s\nTIoem9W2dsidYDiGS4DfQJOynXzgA6GooRHoAO4ibbkbjMTweVy6C1RVA5/ahO7JI8U4E+xYHrqA\nBHiMUh1MMj6Py9QPoHNojJoyb97Wg+nwmFSSMRpXklpDJjhR6MVDMKK2EjUik0LD67aPMDPFhG5D\nk6weBMMxQyw15X4P0bicpIBF4wo+t8vQZxOsb0edjgIS4PoUxze7JVzH0Kih2jeYZ0KPZmtCL9Ja\nz6ciIZ37O6fDLezjAx8wuBMZFK8PPBTOP+A4Hdo1J2rh0Vh2wbW5YmUzrKkoCAGuKFKXKHRQNXCz\nTejzDPR/Q8JUbYKcjMSzM6GbtbBwMJ5AJGZoABvYxwceVyTDY1HDNXA7BkXpQcAgDVyb/ydWY4vG\nFTwG+7/BnhaTghDgY4kkZz2qQFlhQp9rYAQ6mCcoY0qWJnQbFeZwyI9QOGZoChkkotBtoN0MjUaR\n0tgiLpBSBtmM1beJ6KVsTUTLQppYjS2SZX2KXPE4QWy5oUXA6vFQeN0uwiYJ8LFonL5ghEajTegm\naS5Zm9Ddwlb9nR1yJ2hwL3Cwz/NiRhlVsLa9sZEEwjFD3C3a8zdRA4/FlWSVTSOx4+dVEAJ8NFma\nTwcN3MQo9K7hRAS6wRq4OvGZFMTmRKGfkgTN0MCFPZrfDCYEeLXBGrjHhlHNehCKGPOsJDXwiT7w\nLOelXElGoTsaeHYk+8vqoIH7TTShaylkRvvATQtiU3KoxGYDn6ZD/oQicUMbmUAijUyRSGntMzMQ\n1Oqgm1PIpdgEeNCggMfypAl9og/cHBO6o4HniJ7F8c0MYkuWUTVaAzfThJ5FvWGnFnrxoKYGGWtC\nt6pb4ETM6AUO9gyK0oNgJGaIu6UsaUKf6APPrkJkrjhR6DmSLOOog1nGa6IJ3YwiLmByHngW5Qqd\nKPTiIahDN8CZcLu01rjWTpBm9AKHcRN6pMiC2IJG+cCTJvTJUehmpJHZMWugQAS4vhq4eSb0UapK\nPIbnz6qmakPfAsh+pet1uSzXphzyR1Ekoag+dRimQ3NjWv3MDIQiuF2CqhKDv7c2FAj5EokpROPS\nmDQyTQMPp/GBm6iBO1HoWTKqpwB3u0z7ADqGxmisNtb/DSamkcVlVh1/zAquczCWsVgcKY1tJQr2\n0XAGQlFqSr3GV/bS0siKSIAn66AbkUbm1Qq5TNDAY9Ip5GJngjq2p/N6XKYFIXQOjdFYY6z5HMzt\nRubJ4oviRKEXB4FkcwpzBLjVz8zQaIQag/3fUJxR6NqzYsRiz+N24fO4JvnA1eBaMwu52GdOKwgB\nrmngetQT97vNjUI3so2ohhnR3ooiiSnZRXt6bZLX65A5gXCM8772NM/s70puCyXbQxpfiQ2sF2gD\nQeMbmUBqVLN9BEK+aNqxUSmH5T53Uh5oaLXQjWZcA5/cEc0qCkKAJwu5eAsnCj0ci9MbCDO3ygQT\nugmariaIs6uF7qSRFRpHegL0jITZ3j6Q3BbUMYh0OtxJH7jVJnTjG5mAPfOK82VcAzdmsVfm8yTl\ngUa2BaZyxY616wtCgIeians6PerdmhWF3j0cBjBFAzfD16wtELLNA48roFic1+uQOW19IQCOD4wm\nt5nRCxzGNVKrF32DJjQyAftYHPQkpKO7Mx3l/sktRc0q5GKXIMtUMhq1EOIqIcRBIUSzEOILafa/\nTwixWwjxmhDiZSHEWj1vMhTWLwJWjUI3/gPQUsjM8IF7XS6MngO0SSa7KHR7+DQdMqe9XxXgJwbH\nktuSGrjBeeBumwi0gVCE2nITNfAiEuBaCl5ViTELoDKfZ1Ip1UiWbY5zRXuPgopCF0K4gbuBq4FV\nwI1CiFUTDmsBLpFSrgG+Atyn502qxfH1WdGZZULvGFI1GLN84FGDK1hFchDgySAdx4xeMLRrGvjg\nuAY+7gMv/iC20UiccEwxJ4itCH3gyfLRBtW+KPe7JzUzMSuNTAhhainuTMhk1OuBZinlESllBHgY\nuDb1ACnly1JKzWn2KtCk502GIjHd0hK8bjUK3ehyjckiLiakkWmC0kjTozapZhMson2pHA28cGjr\nDwLQOTxGLLFoCxrs19Tw2MAHblYjE1AFgsdVXBp490gYv8dFVakxi710Gng0LrMqMJUPXrd9etZD\nZgJ8PnA05e9jiW1T8WHgb+l2CCE+JoTYKoTY2tPTk/FN6tmezu/Rci+NFSqdQ2NU+j2G+w3BnIIQ\n2rWzTSMDRwMvJNr7Qnhcgrgi6UxoU8k0TpM0cCt9jGaVUdXwe1yTNMpCRmufbFQOfZlvCh+4CRo4\nmFuKOxN0HbUQ4lJUAf75dPullPdJKddJKdfV19dnfF1VA9fJhJ74oI2OJOwYGjXF/w0ppmoDSzLm\n5QN3BHhBEI7F6RgeY+2CGmA8kC1ZCdFwDdz6UqpmlVHVmF3mSS6UioGu4TEaKo2b98p8nrSlVM1I\nI4PCFODHgQUpfzcltp2EEOJM4KfAtVLKPn1uT0VPDdysajrqStR48zmMC8oxA/MTtXrNufjAHRN6\nYXBsYBQp4aJls4FxP3gwHMPrFvg9xR/EZqYJHaC+3JN0txUD3SNh5lT5Dbt+uS+dD9ycNDJQ579C\nM6FvAU4XQiwRQviAG4C/pB4ghFgI/BG4WUp5SO+b1LOVoS8xCRn9IZwYGqPR4CYmGpq5rzcQNuw9\nNK3Il00zExtMyA6Zo0WgX7A0IcAHxgW40TngYI9KVwMhrZWoOSb0+nLPSRH/hYyUks6hMRoMnPfK\n/B5C0ThKwqoXVyTxLAtM5YPP4yJso/lsxlFLKWPAp4AngP3Ab6WUe4UQtwkhbksc9mVgNvAjIcRO\nIcRWPW8yFInpUsQF1A8AjNXAIzFFLeJiQgQ6QH25Otl0GWiKS/rAs2kn6kShFxRaBPrpDRXUVfjG\nNfCI8Y1MYLyQi5UWm8GgqoGbZUKvL/fQGwgTtlF1r1wZCccYjcYN7b5Y7nMj5bi1MZfYnHywWxR6\nRstqKeXjwOMTtt2b8vojwEf0vbVxQuG4bv43MzrKdI+MISXMM8kHXlehCvDOIeM08FxM6F7HhF5Q\ntPWFKPW6qa/wM7+mNCnAQxFj2kNOxA4+8IFQlHKfO7nQN5r6cvX/2j0cZsGsMlPe0yi6EwqEkSZ0\nzRIbDKupxZoAN9MHbieLou0rsUmptjLUPwrduA+h08QUMoC6Mi8CYzXwXEzoThR6YdHeH2LhrDKE\nEMyvLU2a0ANh/VxY05HMi7ZQwxk0qYyqhibAT6Tk3RcqXYnqk0aa0DVLkBaJHs2hQmQ+2E0Dt70A\nD8cU4orUtZALGDtJJKuwmWRC97gFNaVuU0zoTiW24qW9P8jC2aoWqGngUkpC4ZgpJnSPDbIW1Cps\n5vi/Ydz9VQyBbJriYqgP3Kf1BFdN6FqtAjNKqUJhRqFbip69wGFcABmRRial5JEdx/jqY/so9bqZ\nV2OOBg5qOoqRAlwzoWfnA09YOxwN3PZIKWnvD7Fo1rgAD8cUegMR1QduggY+7gO31oRuVgQ6pGjg\nQ0WggY9oAtxAE3pCkdM08FwqROaD3aLQjf9W5oneRSQ0X4neHYD2nhjiy3/ey7a2AdY2VXPv+1eb\nUsRFQ80nNc4HnvQ1ZROF7vjAC4aekTBjUWVcA69Vf58YHCVokgZuh/aag6GIqb7oUq+LqhIPHUUQ\nid49HKayxGNoxoJWDVDLBY/mUCEyH3wel61qodtegOvZCxzGTeh6pgJIKbnl/i2A5K7rzuS6c5pw\nmVBcP5W6MjevHzPeB56LCd3RwO1PWyKFbGFCeGkBmMcHR9UsEFM0cG3BZ7UGbp4JHWBeTWmyd0Ih\n0zVsbAoZTNbATY9C97icdqLZoNW91asOc9KEruMqqnN4jN5AmE9ftpzrMxZ7WQAAH7hJREFU1y0w\nXXiDqoH3ByOGpaNoVd6yaenqKcJuS8WK1kZUE+BNNerv4wOjBMNxU6xJVvvAw7E4w2NRZpnQiSyV\nxuqS4vCBD48Zaj6HcUus5gPX5nHT8sBtZkK3vQDXVlqlXn0mECOi0F/vCgBw+pwK3a6ZLbNT0lGM\nYNzXlH0UulNK1f6094dwCWhKmM6rStU6/kcHQozqmAUyHVocklVBQloluoUmp3PNrS61hQD/wP2b\nuWvDgZzP7x4OG6+B+ydGoZucRuZEoWdHspWhThq4EVHozd2qAD/NQgFeV6YKcKMC2XL5otihspZD\nZrT3BWmsLk1+P4QQzK8p5VDXCGB8IxPtPT0uYVkeuFbIZtFscwX4vOoS+oMRxqLWFXOJK5JXD/fx\nwqHMm0yloiiS7hHjTehJDTxhmX3uoHq/ZgUMO1HoWRKKGhSFruOH8Hp3gNoyL7NNNr2lMjspwI3R\nwGPxPGqhOxq47WlL5ICnMr+2NGldMiMKHdRnxqqgx7Y+tZXqwlnlpr5vY0L4WKmFnxgcJRJXeL0r\nkFMMwkAoQjQuaag01oRe4nUhBITCMTqGRrnvxcNcc2YjZ8ytNPR9NdQodPvMZ/YX4InC9brngeto\nQj/cHeC0ORWGtdDLBE0DN6qzUSSHYBEnCr1wONofmqR5zq8ppS9RWtToXuAaXpd1E2Rbf4gyn5u6\nCnMX4vMS9SI6LCzmcqRXXbxE4krydTZo847RGrgQgjKvm2AkzrefOIiiwOevWmHoe6biaOBZEtI5\nD9wQE3pPgNPmmLMCnIpKvwufx5UsZ6g3yUIuWeSBa8c6Uej2JhCO0RuYnD41v3bcLGlGMxNQC3JY\nFSTU1jdeic5M7KCBt/QEkq/3dwxnfb4We9NgQvGqMr+Hra39/HH7cT70xsWmpv1pUehS2mNOKwAB\nrrMGnjAB65XL1xcI0x+MWOr/BnVl2lDlN0wDj8UlHpfIKsJ+PArdHg+7Q3qm8v3OT/ErmqWBW+kD\nb+sLmu7/BpLNP6xMJWvpDVLuc+N1Cw50jmR9fpdJGjio5VR3HRtiVrmPT156muHvl4rPZnNaAQjw\nOB6X0K25gN/joq7Cz5Ge7M1E6dAC2KyMQNeYW1WSLGeoN9G4knWqhmZtd3zg5qMokgdfaWVoNDrj\nsVob0UUTfL+pGrgZQWxgnY9RUSRHB0ZZNNtc/zeoNS5qy7ycsFADP9IbZNmcCpbVV+SkgWuxN/UV\nxvrAYVyZ+7fLTqeqxNycfSNcsPlQEAJcryIuoGqqZy2oZtexQV2u97oNItA15lSV0D1iXBpZtsUS\nhBB4XcJWeZOnCtvaB/jyn/fyy1fbZjy2vV8L3jpZ+2yyQAP3uq15XjqHx4jEFNNTyDQaq0ut9YH3\nBFlSV86qxioOdGSvgXcOjzG73GdKF7c5VX5On1PBjesXGv5eE/EZEASdDwUgwGO6r/7XNtVwuCfA\n8NjM2slMNHcHKPe5TWtcMh2aBm6EfyYaV3LKtfS6haOBW8CW1n4Ant7fNeOxrX0hqku9VE+oQFZX\n4U9+5uZFobssCXrUCtkstkADB7XynVU+8LFonBNDoyypK2dFYyWdw2MMJIIXM6XbhCpsGt+9/ix+\nd9uFWRWV0guvCd0ss8H2AjwY0b+IxNoFNUgJrx0byvtazTaIQNeYW1XCaDTO8Fgsp/Pvef4wzx3s\nTrsvFpc5VTuyMi3oVGZLiyrAdx4dpDcwvVVm19FBVs+rmrTd5RLJkqpmBbF5LLLYaFYIK3zgkNDA\nLRLgbX0hpEQV4HPV52B/Z3Zm9K4R46uwadSW+0xt+ZqKo4FnyWgknqy+oxdrm2oAdXLLl+buAMts\nYD4H1bQE5BSJHgzH+M6TB/n2hoNp9+diQge1mIsThW4uiiLZmmiqIyU8dyD9ogxgZCzK/o5h1i2e\nlXa/5gc3o5kJqD5wKyw2bX0hPC5hmSVtbnUJQ6PRZNCumbT0qm7ApXUVrGxUBXi2ZvQuE6qw2YFk\nLw0DBfiTezszPtb2AjwUiVGmUxlVjeoyL0vrytmVpwAfHovSOTzG6RankGlo0ay5RKJvbx8grkj2\ndQxzOCWlRCMalzmZ0D1uYWhQkpSSra39tknrsAMHu0YYGYtx84WLmVtVwjP7pxbgO9oHUSSct7g2\n7f75NWp1NrPMlVb5wNv6QjTVllpiloXx5jEnLOhKpuV9L64ro77ST12FL6tAtmhcoTcQZs6pIMDd\nxprQFUVy1xPplah0FIAA118DB9WMvvPoYF4T/2EbBbCBuoqH3KqxbW7pxyVACPjrro5J+6Ox7KPQ\nQc0FN1Kj+tueTq679xWez7EEZKGxra2fn750hMHQ1D7KrQn/9/lLZvGWlXN46fWeKZvcbG1VP/ez\nF6YX4Dedv4g7rjwj/xvPEI9FzSLa+oMstMj/DaoJHaxJJWvpCVJf6acyEdG9srEqq1Sy3kAYKccV\niGLGiDoiqTx7oDuZ2ZQJhSHADTDfrW2qpnsknFfetJ1SyGA8BzOXeuibjvSzZn415y2exaO7T0xa\n2MQUBW8WvcA1VJ+mcQL88dfUxUY2ZqdCJRJT+PTDO/nqY/u56JvP8l+P7uN4msjlza0DNFT5aaot\n5bKVcwhG4mw60p/2mltaB1g1r2rKbmNnLajhI29aqus4psObRczEoa4RXSZSKSVtfSEWWRSBDjBP\nE+AWaOAtvUGW1o0vXlbMreRQ10jGJVU1hcEsH7iVGJ1G9uMXD59Uf2Em7C/AwzFDAmjWLlD94PmY\n0Zu7A/g8LlMrAU1HiddNdak361zwsWicnUcHWb9kFm8/s5Hm7gAHu05egUfiEk8WVdg0jIxCD8fi\nPJ9oZvD0/m6UIve1/2brUY4NjHLn21dx1eq5PPhKK2/+9nO8crgveYyUki0t/Zy3eBZCCC5aVkeJ\n18UzaaLRo3GFHUcHWLcovf/bCrwZaOBSSn70fDNXfPdFvv/M63m/52AoyshYzLIANoCGalX4WRHI\n1tIbZGl9qgCvIhxTaO3LrFaGmUVcrEazQkYN0MC3tfWzpXWAj75pScbn2F+AG9TKcNW8Krxuwc6j\nuUeiN3cHWFpXjtuC/t9T0VDlz1oD33V0kEhcYf2S2Vy9phFXGjN6NJZbGpmRUegvN/cRCMe49qx5\n9IyE2alTbr/Z9AcjfPiBLWljDzTGonF++OzrrFtUyy0XLea/33sWL9xxKXUVfr779KHkcccGRukc\nHuO8RFBaidfNG0+r45kD3ZOsKntPDDMWVZLH2gHPDLXQFUXylb/u564NBynxunhkx/G8F25tWiEb\nC03ofo+bugq/6Sb0oVCUvmCEJSkauBbItj/DQDZtvplzCmngYQM08HtfOEJtmZfrz1uQ8Tm2FuBx\nRRIMx3Qt5KLh97hZ1VjFzqMDOV/j9UQKmZ1oqCrJWoBvbulHCFi/eBZ1FX4uWlY3yYyeqwm9vtzL\nwZ6QIT6jJ/d1Uu5z8+//uBK3S/DUvplznu3Irze388yBbr771KEpj/nlq210DYf5P1eekUxZnF9T\nykfftJTNLf1sa1NN5Fr+d6pQfuvKBo4NjHKo6+QFguYrXzdFAJsVqBab8Wdla2s/LxzqYefRQVp6\ng9z+253cv7GFD/3DYr76zjUcHxxle3vu32EY70JmpQYO0FhdYno1tpbE2JfUjc9jy+aU43EJDmSY\nStY1PIbbJagrL34BXl2qxgm05dDwZTqauwM8ta+LD1y4OCuLs2UCPJMJ/bHXOojGJWcvMGaCWbug\nhteODRHPYQU/Fo1zdCBkOwE+t6oka7/+5tZ+zmioTBbyePvaRtr6Quw5Pv4FjuSYB37d2nr6QzGe\nas6+utN0xBXJU/u6ePOKOcypLOH8JbMKUoDHFcmvN7fjdgkee62DI2m08GA4xj3PH+aNp9VxwdLZ\nJ+27Yf0Casu8/Oi5w4Dq0670e05qr/iWFXOAyUVdtrT2s3BWma1Mn96UQi472ge47t5XuOX+zbzz\n7o1c+p3n+dPOE3zuyjP48jWruOoNc/F7XPxl14m83lOrBW9VFTaNxuoS06uxaSlkqRq43+NOlFTN\nVAMPM6fSn1WfhEJlaV05a+ZX86tN7bpmvvzkxSOUeF184MJFWZ1nmQA/3BOY1lwkpeRHzzWzrL6c\nK1Y1GHIPa5tqCEbi05oup+JwTwApsU0KmUZDVQk9I+GMFyXRuMK2tgHOXzKusV25ei4el+DR3erE\nOBqJExiL5uQDP7epgpUNZfxuz0BOC6Wp2N4+QG8gwpWr5wJw+aoGmrsDtGS4Mo7EFJ7e12V5RaUX\nX+/h2MAoX75mFX6Pi3uePzzpmAdebqUvGOH2K5ZP2lfm8/Chf1jCMwe6OdA5zJbWfs5dXHuSW6eh\nqoQ186t5Ym9nctJR0+8GbKV9g+py0bo9feNvB6ir8PGbj13A/R9cx39fv5aHPno+n7z0NIQQVPg9\nXLaygcd2d+TUw1qjtS9EQ5WfEq85ue5TMa9GLeZiZkrkkZ4gLjF58bKysZIDGaaSdQ2PnRIpZKCW\nh77losW83h3g5ZTYk3w42h/ikR3HuX7dAmZnWUveMgGuSPjYg9sYjaRPb3lmfzcHOkf4xJtPM2xl\nd9bC3Au6NNsshUyjoboERTJj9S2NvSeGCUXirF8yrtnVlPm4eHk9f9x+jJv/dxNr/+tJDvcEc/Jx\nCSF4/7kNnBiOsmGPfpHiT+zpxOd2cekZ9YAqwAGe2pfZe3ztsX185MGt05qtzeBXr7ZTV+HjxvUL\nueG8hTyy4zjHBkLJ/ccGQvz4hcO8dcUczpki1euWCxdT7nPzjccP0NwdSOvTvnH9QnYfG+L+ja2A\nGrjUF4zYyv8NibTDuOT5gz1sbunnX996Oucvnc1bVjTwT+c0cdGyupOOf8dZ8+gLRtiYx2Ta3h+c\n1MjFCpY3VBIIx/j4L7bllEmSC0d6gyyYVTaphvmKxipODE1fUjUWV/jZxha2tQ3QVJt55HShc82Z\njcwq9/Hzl1vzvpaiSD73+134PC5uu2RZ1udbJsAXzCplz4kh7vjD7kkrTiklP3yumabaUt5x1jzD\n7mHJ7HIqSzxZC/DXjg3xtcf2U1vmZXGdPSLQNeZmmUq2uUWd+M5bcrJweM+5TfQGInQMjXHzBYt4\n8Nb13Pn21Tnd08VLq2mq8nLPC826aBdSSp7Y18lFp81O5q421ZaxqrEqIzP646918PNX2phT6efe\nFw6zI08faq50DI3y7IEurl+3AJ/HxccvWYoQcN+LRwA42DnCu+95GQl8/uoVU16nuszL+y5YxAuJ\nXPj0AnwBl69q4Jt/28/uY4NsbR1IHGs/DTwci/OtDQdYNLuMG86bvmHFm8+op7LEw593Hp/ymIc2\ntXPrA1vom2JR29YXYqHF/m+A69c18cWrV/DCoR4u++8X+O2Wo4Zr4y2JJiYT0Vw1X3t8f9p7eLm5\nl7d9/yX+89F9nLuoli9cNfXzWWyUeN3ccN4Cnt7fddJiOxd+9nIrrx7p58tvX8W8LNLHNDIS4EKI\nq4QQB4UQzUKIL6TZL4QQ30/s3y2EOGema1aVeLnjyhU8uusEdz/XfNK+Vw73sfPoIB+/ZFlOftdM\ncbkEa5tq0qaSSSl5bHcHd/5lLy+93pM0/z65t5Prf/wKXreLX3/sAvwea81uE9FyMTNNJdvc0s/S\nunLmVJ5sArt6TSOv3XkFT99+CV+6ZhUXL6/PudOQ2yV4z5pa9hwfZmNz/man/R0jHO0fTZrPNS5f\n1cDWtoFprQ9tfUE+//vdrF1Qw4bPXMzcqhI++7tdjEXTW4KM5OHNR5GQ7KrUWF3Ku89p4uEtR9mw\np4P33PsyUsLvbruQ5Q3Tu2o+/MYl+NwufG4XZzZVT9ovhODb151JfYWfTz20g+cOdlNT5mVpnb0s\nSF63i4FQlAOdI3z2ijNmfOb8HjdXv2EuT+7tSvsZPrCxhf/7yGs8e6Cbm36yadKzMRqJ0z0StjQH\nXMPjdvHxS5ax4TMXs7Kxijv+sJsP/mwL3SMnf5cPdY1w009e5e0/+Duf/e0u7nvxMBube6cs1jMV\nUkpaetML8LMW1PCvbzmN3287xi83tSe3x+IK//noXm766SZCkTg/vvlcHrx1vW1Sac3i/Reovupf\nZNDtbyqau0e4a8MBLls5h/ec25TTNWackYUQbuBu4GpgFXCjEGLVhMOuBk5P/HwMuCeTN7/tkqW8\n6+z5fOfJQ9z5l70cSuQe//C5ZuZU+nMeVDasW1zL3hPD3PaLbew5rqaUHRsI8eGfb+WTD23nF6+2\ncfP/bubCbzzDv/x6Bx//5TaWN1TwyCcvShb+txPTaeA9I2Ee293BxuZeonEFRZFsbuln/ZL0ZtRK\nHXvtvvW0SuZU+vnR8805+yulVLMS/rzzOELAZStPjo24fFUDUsKzU5QOHYvG+cSvtiME3H3T2cwq\n93HXdWs50hPk2xmULxwMRdjY3MuvNrXR3J1fUF4srvDwlnYuWV5/0uR32yXLiMUVbvvlduoq/Pzh\nnzN7zhqqSvjEpct497lNU/pya8p8/OCmszk+OMrf9nSyblGt7QKPvIl6+2+YX8U1axozOucda+cT\nCMcm1Xz/2cYW7nx0H1eubuDnt66nrT/Ijfe9Sk9Ky12tF7odNHCNJXXlPPzRC/jKtavZ1NLHVd97\niaf3dRFXJD9+4TDXfP/vHOgcobrUy4uv9/D1xw/wvp9u4tyvPM0nH9rOn3ceZ8/xIfYcH2LviSGa\nuwNp40+6hsOMRuMsrU+/iPvMZcu59Ix6/uvRvWxr62coFOVDD2zhZxtb+eBFi3n69ku4cvVcWzRy\nMpt5NaVcsWouv9lyNKfFfzSucPtvd1Hmc/P1f1qT8/8wk3j19UCzlPIIgBDiYeBaYF/KMdcCD0rV\n1vKqEKJGCNEopZxckzMFIQTf+Kc1COBXm9p44OVWVs+rYu+JYf79bStNCSr5+MXLUBTJz15uZcPe\nTi5YOovdx4aQEv7jH1dy0/kLeeFgD4/sOM4Tezt525pGvnPdWkNS2/RgdoUft0vw6K6OZDT6YCjK\nppb+k0r01ZR5OX/JLIbHYpy/1Hg/qM/t4iNvWsLXHz/AGV/awNyqEubVlDCvpjT5U1Pq5XBPgP0d\nw+zvGGFoNIrXLfC4XAgBA6EIY1FV+K9fPIv6ypN98qvnVTG/ppRv/G0/f9p5nMbqUuoqfYxG4gyP\nRmnpDbL3xDA/+cA6mmrVCfuNp9fx/gsWcv/GFpbWlyOlmkvdMTRKKBJnLBonHFM4PjA6qerZmvnV\nvPPs+Zy1oIah0Qj9wSiDoQjhmEI4piRbsNZX+plT6U8GqERiCruPDdI1HOar7zw56nRxXTm3XLSY\nAx0j/PCms7MKavnMZZOD3CZy7qJZ3H75cr79xMEpG5hYiaZxf+GqlRkvLi5cNpu6Cj8PbW6nutRL\nMBJn97FBfvBsM1etnssPbjobr9vFzz64nlsf2MKNP3mV2y9fTpnPnYy0tqqN6FS4XIKbL1zMhctm\n8+mHd/KRB7eycFYZ7f0hrlo9l6++6w3UJZ6N/mCEHe0DPL2/i6f2dfPY7snTbqXfw9mLajlvUS3z\nakrxuEWyherSNBq4dg/fe+/ZvOPuv/PPv9xOhd/D0YEQ33r3Gt47g2vjVOCWixazYW8nP3y2mcV1\n5ZwYHKVnJIzbJSjxuvF7XFSWeJhd4WN2uZ/KEg/HBkZ5vTvA1tZ+dh8b4p73nTPJ+pkNYiYfixDi\nOuAqKeVHEn/fDJwvpfxUyjF/Bb4ppfx74u9ngM9LKbdOdd1169bJrVvHd/cFwjyy4zi/3txOMBzn\nmc9eknEP4kOHDlFRMbMpMBAIsHx5+klueCzKL15p46FN7ayYW8md71g9ySykKNIyjWWmMaaO7b0/\nfoWtbaqPU6D6bM5ZVMuFS2dzwdJZdI+E2bCnk6f3q2bHF++4NFmLWe/7Sr2/Zaedzl92HedITzAp\nEE8MjdIxOJas1iaEGpuwsrGKugofUUUSiysoEmrLvNRVqILwwmWz05YcfHJvJ3/eeYKOoVE6hsbo\nC0Qo87upKvFSWeLhXWfPn1QaNBiOcfX/vJTUxrxuQWN1KeV+D36PC7/HxZyqElbPq0ouEp472MOf\ndhznteNTFwLyuV1EFYWpvmLza0p54XNvNr2BhqJIHtlxnMtWNSTzWo0g02dDIxAI4K6dxyuH+5Im\nykz5yl/38b9/bzlp29VvmMv3bzz7JDfcpiN93PrAFoIpwbNul2D7f1w+qR/6dGQ7tqmYbk7SiMQU\n/t9TB3l05wnuuGoF1541b0qNTVEku44N0jMSRnvsRsZi7GgfYGvrwKQKix6X4OUvvmVaIXKwc4R3\n3r2RUp+be99/7pQWO71I97/N5P+U7TWzZeI9SCm5+n9eOqlufE2Zl7giCUeVKcutuoRaNOgda+fx\nb5enH5MQYpuUct1M92SqABdCfAzVxM7ChQvPbWub7D+QUqJIsqpu1tbWRjg8c9S13+9n0aLsJga7\nMNMYcxlbJKbQH4wkm6AYcV8a091fXJH0BsL0ByMsml1mWu/pVLqGx2jrC7FgVikNlSUZL9SauwMc\n7Q9RW+5jVpmPmnIvJR43XrdACLWzVl8gQs9ImN5gGJcQeN0Cn9vFotnlk6wIxUSmz4ZGPt/PYDjG\nltZ+SrxuKvweKvweFs0uSyvoBkMRTgyOMRqNEYrEqSn1sSZN3MB0ZDu2qTB7ThoajTIUihJVFOKK\npMLvySh46khPgIoST17aYqak+9/m+3/S4/NKdw8dQ6O09AaZV13K3OqSk6zGcUUSGIvRF1TntqHR\nKPNqSllSVz6jdVlPAX4hcKeU8srE318EkFJ+I+WYHwPPSyl/nfj7IPDm6UzoEzVwBwcHBwcHh8wF\neCa2uy3A6UKIJUIIH3AD8JcJx/wF+EAiGv0CYGgm/7eDg4ODg4ND7sxoq5RSxoQQnwKeANzA/VLK\nvUKI2xL77wUeB94GNAMh4EPG3bKDg4ODg4NDRs5GKeXjqEI6ddu9Ka8l8El9b83BwcHBwcFhKmzd\njczBwcHBwcEhPY4Ad3BwcHBwKEAcAe7g4ODg4FCAOALcwcHBwcGhAJkxD9ywNxaiB8i9Eryx1AG9\nVt+EgTjjK2yc8RU2zvgKH6PHuEhKWT/TQZYJcDsjhNiaSRJ9oeKMr7BxxlfYOOMrfOwyRseE7uDg\n4ODgUIA4AtzBwcHBwaEAcQR4eu6z+gYMxhlfYeOMr7Bxxlf42GKMjg/cwcHBwcGhAHE0cAcHBwcH\nhwLEEeAODg4ODg4FyCkhwIUQ9wshuoUQe1K2rRVCvCKEeE0I8agQoiqxfbEQYlQIsTPxc2/KOc8L\nIQ6m7JtjxXgmouP43iuE2C2E2CuE+JYVY0lHNuNL7DszsW9vYn9JYvsGIcSuxPZ7hRBuK8YzET3G\nJ4SoTPlMdwoheoUQ37NmRJPJ8hl934SxKEKIsxL7viaEOCqECFg1lnToOL5imGOmG1/BzzFCCK8Q\n4ueJ7fuFEF9MOcfcOUZKWfQ/wMXAOcCelG1bgEsSr28FvpJ4vTj1uAnXeR5YZ/V4jBgfMBtoB+oT\nf/8ceKvVY8thfB5gN7A2ZVzuxOuqxG8B/AG4weqx6Tm+CdfcBlxs9dhyGeOE89YAh1P+vgBoBAJW\nj8mg8RX8HDPV+IpojrkJeDjxugxoBRYn/jZ1jjklNHAp5YtA/4TNy4EXE6+fAt5t6k3piE7jWwq8\nLqXsSfz9dAbnmEKW47sC2C2l3JU4t09KGU+8Hk4c4wF8gC0iOPUan4YQYjkwB3jJsJvOkjye0RuB\nh1Ou86qUssOQm8wDvcZnV3QaX7HMMRIoF0J4gFIgAgwnrmPqHHNKCPAp2Atcm3j9HmBByr4lCdPP\nC0KIN0047+eJfV8SQghT7jQ3sh1fM3CGUE3sHuCdE86xG1ONbzkghRBPCCG2CyHuSD1JCPEE0A2M\nAL8362ZzIKfxJbgB+I1MqAI2ZrpnVOO9wK9NuyN9yXV8xTDHaKSOr1jmmN8DQaAD1aLwHSllUvib\nOcecygL8VuATQohtQCXqKgrUD2WhlPIs4HbgoRT/4/uklKuBNyV+bjb5nrMhq/FJKQeAfwZ+g6q5\ntQLxSVe1D1ONzwO8EXhf4ve7hBBv1U6SUl6JaoL1A28x9Y6zI6fxJbiBwhB6U40RACHE+UBISrkn\n3ckFQC7jK4Y5Bpg8viKaY9aj3vc8YAnwWSHEUu0kM+eYU1aASykPSCmvkFKeizrZHU5sD0sp+xKv\ntyW2L0/8fTzxewR4CPWDtCU5ju9RKeX5UsoLgYPAIWvufmamGh9wDHhRStkrpQwBj6P6tlLPHQP+\nzPjq2nbkOj4hxFrAk/hsbc00Y9QolIVIWnIZXzHMMSmkG18xzDE3ARuklFEpZTewEVg34VxT5phT\nVoBr0Z1CCBfwH8C9ib/rtcjBxKrqdOCIEMIjhKhLbPcC1wC21QyyHd+Ec2qBTwA/Nf/OM2Oq8QFP\nAGuEEGUJM90lwD4hRIUQojFxjgf4R+CA+XeeGdmOL+XUGykQoTfNGLVt11MA/uGpyHZ8xTLHpGyb\n9PkVyRzTTkKzFkKUowZWHrBkjjEyQs4uP6gTWgcQRdVgPgx8GnX1dwj4JuNV6d6N6vvYCWwH3p7Y\nXo4a2bs7sf9/SBP9W6jjS7nOvsSPLSK0sx1f4vj3J8a4B7grsa0BNap0d2L7D1A11aIYX8q+I8AK\nq8ekwxjfDLya5jp3Jc5XEr/vtHpseo2vWOaYGT6/gp9jgArgd4nPaB/wucR20+cYp5Sqg4ODg4ND\nAXLKmtAdHBwcHBwKGUeAOzg4ODg4FCCOAHdwcHBwcChAHAHu4ODg4OBQgDgC3MHBwcHBoQBxBLiD\ng4ODg0MB4ghwBwcHBweHAuT/A+68jYnlgjnZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b79d9ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBER recessions\n",
    "from pandas_datareader.data import DataReader\n",
    "from datetime import datetime\n",
    "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))\n",
    "\n",
    "fig, axes = plt.subplots(2, figsize=(7,7))\n",
    "ax = axes[0]\n",
    "ax.plot(res_hamilton.filtered_marginal_probabilities[0])\n",
    "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n",
    "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n",
    "ax.set(title='Filtered probability of recession')\n",
    "\n",
    "ax = axes[1]\n",
    "ax.plot(res_hamilton.smoothed_marginal_probabilities[0])\n",
    "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n",
    "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n",
    "ax.set(title='Smoothed probability of recession')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       0.000166\n",
       "1       0.000251\n",
       "2       0.013413\n",
       "3       0.002246\n",
       "4       0.007288\n",
       "5       0.003544\n",
       "6      -0.003872\n",
       "7       0.007899\n",
       "8       0.006456\n",
       "9       0.000329\n",
       "10     -0.003994\n",
       "11      0.002697\n",
       "12     -0.009009\n",
       "13     -0.001481\n",
       "14      0.012863\n",
       "15     -0.011788\n",
       "16      0.000249\n",
       "17      0.001401\n",
       "18     -0.001892\n",
       "19     -0.001319\n",
       "20      0.008388\n",
       "21     -0.003936\n",
       "22     -0.003293\n",
       "23      0.003790\n",
       "24     -0.008337\n",
       "25      0.004881\n",
       "26     -0.000494\n",
       "27     -0.003473\n",
       "28      0.003971\n",
       "29     -0.001734\n",
       "          ...   \n",
       "2503   -0.028523\n",
       "2504    0.006694\n",
       "2505   -0.017335\n",
       "2506   -0.000324\n",
       "2507   -0.016907\n",
       "2508   -0.000333\n",
       "2509   -0.017848\n",
       "2510    0.007386\n",
       "2511    0.000292\n",
       "2512   -0.014067\n",
       "2513    0.005146\n",
       "2514   -0.000088\n",
       "2515    0.025201\n",
       "2516   -0.020546\n",
       "2517    0.014772\n",
       "2518   -0.017489\n",
       "2519    0.009915\n",
       "2520   -0.009201\n",
       "2521    0.009911\n",
       "2522   -0.014040\n",
       "2523   -0.012173\n",
       "2524    0.012506\n",
       "2525    0.016511\n",
       "2526    0.006805\n",
       "2527    0.015036\n",
       "2528   -0.000449\n",
       "2529   -0.023370\n",
       "2530    0.001551\n",
       "2531   -0.028296\n",
       "2532    0.006747\n",
       "Name: GLD, Length: 2533, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GLD_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2017-12-08    0.000166\n",
       "2017-12-07    0.000251\n",
       "2017-12-06    0.013413\n",
       "2017-12-05    0.002246\n",
       "2017-12-04    0.007288\n",
       "2017-12-01    0.003544\n",
       "2017-11-30   -0.003872\n",
       "2017-11-29    0.007899\n",
       "2017-11-28    0.006456\n",
       "2017-11-27    0.000329\n",
       "2017-11-24   -0.003994\n",
       "2017-11-22    0.002697\n",
       "2017-11-21   -0.009009\n",
       "2017-11-20   -0.001481\n",
       "2017-11-17    0.012863\n",
       "2017-11-16   -0.011788\n",
       "2017-11-15    0.000249\n",
       "2017-11-14    0.001401\n",
       "2017-11-13   -0.001892\n",
       "2017-11-10   -0.001319\n",
       "2017-11-09    0.008388\n",
       "2017-11-08   -0.003936\n",
       "2017-11-07   -0.003293\n",
       "2017-11-06    0.003790\n",
       "2017-11-03   -0.008337\n",
       "2017-11-02    0.004881\n",
       "2017-11-01   -0.000494\n",
       "2017-10-31   -0.003473\n",
       "2017-10-30    0.003971\n",
       "2017-10-27   -0.001734\n",
       "                ...   \n",
       "2007-12-31   -0.028523\n",
       "2007-12-28    0.006694\n",
       "2007-12-27   -0.017335\n",
       "2007-12-26   -0.000324\n",
       "2007-12-24   -0.016907\n",
       "2007-12-21   -0.000333\n",
       "2007-12-20   -0.017848\n",
       "2007-12-19    0.007386\n",
       "2007-12-18    0.000292\n",
       "2007-12-17   -0.014067\n",
       "2007-12-14    0.005146\n",
       "2007-12-13   -0.000088\n",
       "2007-12-12    0.025201\n",
       "2007-12-11   -0.020546\n",
       "2007-12-10    0.014772\n",
       "2007-12-07   -0.017489\n",
       "2007-12-06    0.009915\n",
       "2007-12-05   -0.009201\n",
       "2007-12-04    0.009911\n",
       "2007-12-03   -0.014040\n",
       "2007-11-30   -0.012173\n",
       "2007-11-29    0.012506\n",
       "2007-11-28    0.016511\n",
       "2007-11-27    0.006805\n",
       "2007-11-26    0.015036\n",
       "2007-11-23   -0.000449\n",
       "2007-11-21   -0.023370\n",
       "2007-11-20    0.001551\n",
       "2007-11-19   -0.028296\n",
       "2007-11-16    0.006747\n",
       "Name: GLD, Length: 2533, dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "date_GLD.rename(\"date\")\n",
    "GLD_ddate = GLD_d.rename(date_GLD)\n",
    "GLD_ddate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>GLD</td>         <th>  No. Observations:  </th>    <td>2532</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovAutoregression</td> <th>  Log Likelihood     </th>  <td>7608.896</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Sun, 11 Feb 2018</td>   <th>  AIC                </th> <td>-15203.793</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>14:28:02</td>       <th>  BIC                </th> <td>-15162.935</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>               <td>12-07-2017</td>      <th>  HQIC               </th> <td>-15188.969</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                     <td>- 11-16-2007</td>     <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>approx</td>        <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.0010</td> <td>    0.002</td> <td>    0.471</td> <td> 0.637</td> <td>   -0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th> <td>    0.7162</td> <td>    0.096</td> <td>    7.499</td> <td> 0.000</td> <td>    0.529</td> <td>    0.903</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.0002</td> <td>    0.000</td> <td>   -0.718</td> <td> 0.473</td> <td>   -0.001</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th> <td>   -0.1217</td> <td>    0.027</td> <td>   -4.520</td> <td> 0.000</td> <td>   -0.174</td> <td>   -0.069</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Non-switching parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0001</td> <td> 4.06e-06</td> <td>   33.279</td> <td> 0.000</td> <td>    0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.1512</td> <td>    0.079</td> <td>    1.914</td> <td> 0.056</td> <td>   -0.004</td> <td>    0.306</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0956</td> <td>    0.035</td> <td>    2.697</td> <td> 0.007</td> <td>    0.026</td> <td>    0.165</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                         Markov Switching Model Results                         \n",
       "================================================================================\n",
       "Dep. Variable:                      GLD   No. Observations:                 2532\n",
       "Model:             MarkovAutoregression   Log Likelihood                7608.896\n",
       "Date:                  Sun, 11 Feb 2018   AIC                         -15203.793\n",
       "Time:                          14:28:02   BIC                         -15162.935\n",
       "Sample:                      12-07-2017   HQIC                        -15188.969\n",
       "                           - 11-16-2007                                         \n",
       "Covariance Type:                 approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0010      0.002      0.471      0.637      -0.003       0.005\n",
       "ar.L1          0.7162      0.096      7.499      0.000       0.529       0.903\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0002      0.000     -0.718      0.473      -0.001       0.000\n",
       "ar.L1         -0.1217      0.027     -4.520      0.000      -0.174      -0.069\n",
       "                           Non-switching parameters                           \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "sigma2         0.0001   4.06e-06     33.279      0.000       0.000       0.000\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.1512      0.079      1.914      0.056      -0.004       0.306\n",
       "p[1->0]        0.0956      0.035      2.697      0.007       0.026       0.165\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model\n",
    "mod_hamilton = sm.tsa.MarkovAutoregression(GLD_ddate, k_regimes=2, order=1, switching_ar=True)\n",
    "res_hamilton = mod_hamilton.fit()\n",
    "\n",
    "res_hamilton.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Markov Switching Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>GLD</td>         <th>  No. Observations:  </th>    <td>2532</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>MarkovAutoregression</td> <th>  Log Likelihood     </th>  <td>7845.763</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>              <td>Mon, 12 Feb 2018</td>   <th>  AIC                </th> <td>-15675.526</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                  <td>15:49:05</td>       <th>  BIC                </th> <td>-15628.831</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>               <td>12-07-2017</td>      <th>  HQIC               </th> <td>-15658.584</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                     <td>- 11-16-2007</td>     <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>approx</td>        <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 0 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>   -0.0002</td> <td>    0.000</td> <td>   -0.863</td> <td> 0.388</td> <td>   -0.001</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td> 7.039e-05</td> <td> 3.75e-06</td> <td>   18.759</td> <td> 0.000</td> <td>  6.3e-05</td> <td> 7.77e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>  <td>   -0.0077</td> <td>    0.026</td> <td>   -0.299</td> <td> 0.765</td> <td>   -0.058</td> <td>    0.043</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime 1 parameters</caption>\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.0004</td> <td>    0.001</td> <td>    0.624</td> <td> 0.533</td> <td>   -0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0003</td> <td> 2.17e-05</td> <td>   14.866</td> <td> 0.000</td> <td>    0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>  <td>   -0.0102</td> <td>    0.037</td> <td>   -0.277</td> <td> 0.782</td> <td>   -0.083</td> <td>    0.062</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Regime transition parameters</caption>\n",
       "<tr>\n",
       "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[0->0]</th> <td>    0.9896</td> <td>    0.004</td> <td>  273.472</td> <td> 0.000</td> <td>    0.982</td> <td>    0.997</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>p[1->0]</th> <td>    0.0234</td> <td>    0.008</td> <td>    2.963</td> <td> 0.003</td> <td>    0.008</td> <td>    0.039</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                         Markov Switching Model Results                         \n",
       "================================================================================\n",
       "Dep. Variable:                      GLD   No. Observations:                 2532\n",
       "Model:             MarkovAutoregression   Log Likelihood                7845.763\n",
       "Date:                  Mon, 12 Feb 2018   AIC                         -15675.526\n",
       "Time:                          15:49:05   BIC                         -15628.831\n",
       "Sample:                      12-07-2017   HQIC                        -15658.584\n",
       "                           - 11-16-2007                                         \n",
       "Covariance Type:                 approx                                         \n",
       "                             Regime 0 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0002      0.000     -0.863      0.388      -0.001       0.000\n",
       "sigma2      7.039e-05   3.75e-06     18.759      0.000     6.3e-05    7.77e-05\n",
       "ar.L1         -0.0077      0.026     -0.299      0.765      -0.058       0.043\n",
       "                             Regime 1 parameters                              \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0004      0.001      0.624      0.533      -0.001       0.002\n",
       "sigma2         0.0003   2.17e-05     14.866      0.000       0.000       0.000\n",
       "ar.L1         -0.0102      0.037     -0.277      0.782      -0.083       0.062\n",
       "                         Regime transition parameters                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "p[0->0]        0.9896      0.004    273.472      0.000       0.982       0.997\n",
       "p[1->0]        0.0234      0.008      2.963      0.003       0.008       0.039\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using numerical differentiation.\n",
       "\"\"\""
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model\n",
    "mod_hamilton = sm.tsa.MarkovAutoregression(GLD_ddate, k_regimes=2, order=1, switching_ar=True, switching_variance= True)\n",
    "res_hamilton = mod_hamilton.fit()\n",
    "\n",
    "res_hamilton.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-33-35bc17959f26>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-33-35bc17959f26>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    sm.tsa.MarkovAutoregression(switching_trend=)\u001b[0m\n\u001b[1;37m                                                ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "sm.tsa.MarkovAutoregression(switching_trend=)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
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