9. The ARCH Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the relevant packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.graphics.tsaplots as sgt\n",
    "import statsmodels.tsa.stattools as sts\n",
    "from statsmodels.tsa.arima_model import ARIMA\n",
    "from scipy.stats.distributions import chi2 \n",
    "from math import sqrt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the Data and Pre-processing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_csv_data = pd.read_csv(\"Index2018.csv\") \n",
    "df_comp=raw_csv_data.copy()\n",
    "df_comp.date = pd.to_datetime(df_comp.date, dayfirst = True)\n",
    "df_comp.set_index(\"date\", inplace=True)\n",
    "df_comp=df_comp.asfreq('b')\n",
    "df_comp=df_comp.fillna(method='ffill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_comp['market_value']=df_comp.ftse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "del df_comp['spx']\n",
    "del df_comp['dax']\n",
    "del df_comp['ftse']\n",
    "del df_comp['nikkei']\n",
    "size = int(len(df_comp)*0.8)\n",
    "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The LLR Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LLR_test(mod_1, mod_2, DF = 1):\n",
    "    L1 = mod_1.fit(start_ar_lags = 11).llf\n",
    "    L2 = mod_2.fit(start_ar_lags = 11).llf\n",
    "    LR = (2*(L2-L1))    \n",
    "    p = chi2.sf(LR, DF).round(3)\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df['returns'] = df.market_value.pct_change(1)*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Squared Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['sq_returns'] = df.returns.mul(df.returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Returns vs Squared Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cI6IMMXhERERERERERESWGDwiIiIiIiKaBzhojYjSxeARERERERFRAfOpo9aY8oiI0sXgERERERER0Tw3PDaNXSfaoDDCREQCDB4RERFRwRqfCOa6CEREOedzkC977Y5z2HGiDT3Dk9kvEBHlHQaPiIiIqCA1XRzFLU+cQEXjQK6LQkQ0Jyg2WY+CoWhsmSh7HhFRMgaPiIiIqCB19PsBAPLF0RyXhIgot3xw0PXIwSJENH8xeEREREQFSbsPYv4OIiKVzenQl3oRIprHGDwiIiKiguRTk3zwRoiI5j1HvYrUcyYD7kQkwOARERERFTbeBxERAeDpkIjSx+ARERERFSRtdiHeLBHRfOdkGG/8nMmTJhEJMHhEREREBSk+SoN3QkQ03zFfNhFliMEjIiIiKkjMeUREFMPZ1ogoUwweERERUWGKD8Fg+IiICAC6hyYsX9MCTApD7kQkwOARERERFaREjo+cFoOIaM44Vd9v/SJzHhGRDQaPiIiIqCBx2BoRUYyPQ9KIKEMMHhEREVFhY/SIiCgl9tYkIjvFmbxZkqQjAN4BIKQ+9T1Zlst1r38VwCoASwC8JsvynZlsj4iIiMip+LTTjB4REaXEc6Y3hsamcNtTZfjRNz6Fz350ea6LQ+SZtINHkiT5AHwMwAdkWQ4LXl8CYD2APwNwEcAeSZL+Rpblveluk4iIiArL4bNd+P0PXosbrr3c83XHZxfifRARzXPOhq1xbJsX2nv9AICT5/oYPKKCksmwNUn9d78kSTWSJP3Q9PofAWiWZblNDS5tAvDNDLZHREREc9jjW2uw/8xFx8srioJN+5vwmxcrslIeH2NHRESq1IGheICJJ00iEshk2No1AA4B+BGAhQCOSpIky7J8QH393QB6dcv3Anivmw1cd93SDIpHc8ny5ctyXQTyEI9nYeHxLCy5PJ41LcOoaRnGv3zt9x0tH43G7lAmZ8JZKfeVV44AABYvLs7b73m+lpvEeDwLS74cz+XLl+GKyxcJn9dbuHABAODqqy93/dlGxqehALj2ysvSLmeueXU8r1R7Hi3K42tPIeC+917awSNZlssAlGmPJUlaB+BrALTgURGMcWsfgKibbQwPB+IVS8pfy5cvw+CgP9fFII/weBYWHs/CMleOp9My6K/x2Si33z8NAJieDs2J/eLWXDme5A0ez8KST8dzcNCPicmg8Hm9cCgCABgZmcTgFQtdbWPFysMAgPW3fyXNUuaWl8fTPz4FAJiZCefNd6TQ5NPvMxeKinxpddRJe9iaJEl/KknSX+qe8iGROBsAugC8S/f4BgA96W6PiIiIyA2fOgaDMwcRUTadbuhHW+94rothy03KIybMJiKRTIatXQ3g15Ik/Qliw9b+DcD3da+XA5AkSfoIgDYA30YsgTYRERERJqZDqRfKANN3ENFseHpnPYC53evGScJsbZIBBtyJSCTtnkeyLL8JYA+AKgCVANbLslwmSVK1JEnvlmV5GsC/A9gG4DyARgCvZ15kIiIimsuC6tCHVNZsr8tuQbRWdN4JERGlxsnWiMhGJj2PIMvyXQDuMj33Gd3fhwB8OpNtEBERUX6ZnAljkZp41U7P0ERWy8FWdCIi5xg7IiI7afc8IiKa66KKgo4+PyrlwVwXhYhywBfP30FENL/5BOPWZoLGXqLxob6MuBORAINHRFSw3jjWins3nMGa7edyXRSiecVp6/Ws3aDwRoiI5jnRefkHq45lZVuKomA6GM7KuvMJg3BUaBg8IqKCVSEP5LoIRPOTk8yssyA+21qOy0FElBc8mqFyT1kHblx1HN2DAQ8KRURzBYNHRFSw5sbtK9H80H9p0vV7olmO6sTPAYweERGl5NUMlacbYo13d607neGaiGguyShhNhEREdG51mE8uqXG8fI3rjqGL378Hch2VIc5j4iIVA5a1HyJpEeZbWret97N+x1ABYo9j4iIiOaAqZkwjtf05GWOhO5B46xpqarN08EISmp7s1cgU0nycZ8SEXlpNsMZDJ0QFSYGj4iIiOaAlw80YcPeRjRdHM11UVxLt5U52zEdtn4TEakcnBA9yxPHcy9l6NY1pdhy5EKui0EmDB4RERHNAeMTQQBAMBzNcUncS5oC2uGNQ9aDR7O0HSKiuaSkpgeNHSNpv5+nTMq1Ef8M9pV35roYZMKcR0RERHOBlp8nD2vt6TYyK9m+RYnv0zzcqUREaXphb2PSc67O0xanzL3lHWjtGcdN/+NThufDEWOjh49dj4gKEoNHRFS4OGaF8ojPs3luZl/ST00B/JNBjPhn8P53LrN+Y9aHrXk0BIOIaB6xCuxvPdIifP7+jZXZLA4RzREctkZEREQZMQ9bUwD8ekMF7nnhjO37sh3UYfiYiCjGSXuaL802jI5+v2lF7t5PZGXVlmrMhCK5LgapGDwiIiKaA3x5PGytKKnnkYLh8emU7zN/1jONA+jo84sXTkM+71MiIspP7PjunbrWS5A708/fRd5i8IiIiGgOycs4h6mmLMq3IWb8tE/tqMO9G+x7K7mjDVvLy71KRB4IznKvhf2nO9E1GDA8Nz4ZREltD6qaBvMiB9vcLyHNJwsXMGQxV/BIEFFBCIUjuHvdactpzsfUmayI5qp4+CUPa+3mVtbalmFH78v6bGv5m0aKiDzQ0j2G7z9yzPE5yQuvHr6Ae01Ddte+cQ4vvNWIJ944h/q2S7NWFr2kWTFFy6j/ZnxuNr1fURSEwhx6ROkpLmbIYq7gkSCigtAzNImuwQA2H2gSvv6TJ07gVH3fLJeKyLlEcuf8i3QUpdlH36vg0fGaHqxYeTiph0HiRij/9ikRZa65awwAcL59dgM2kajxnDMSmIn/7Z8KzWpZNO7O0pmdM83XsX2nO/G9h49hfHJ+NeTx0uONYvY8mjN4JIgob0WjCvaVd1p2STdXlJrUSiTRnDaPKpteBcp2lbYBQPKNiXoSqG9nvgSi+Wgu5j3Lh3Q4Xu+vsrp+AMCofybFkoUhH45xPmHwaO7gkSCivHWyrg9bjlzArtL2xJMeXbGjioLoXKpt0qyKRhWcbujPyXcg3751FY0DGAukeUPg8Yf1scpORDqJkauzc2a16uWYN+emeA/YrKx2TgXxsmmefEyahxg8IppnDpy5iOM1Pbkuhie0qTunZsKer/unT5zArWtKPV8v5Ydj1d14emf9rP5W8rFyHY5EsXZHHbaXtKX1/tn6qFqrZXXzEG5dU4pQODpLWyainJrlaa+cnNNydoqfzV1h+pB5EjqjHBsanRLmxrIbet7Z70djB3sXzxYGj4jmmVcONWOD45mQ5rb4zXaK19MxPhnCWCCI6uYhXHIw5TgVFv9kLCfFpfH50cU+XXM+l5Bi/OPlA00Y8c9gNN2eUkSUn2brVGVZIZml7WfIq4kb5viVIev0h7ulewwrVh5G10DAcvn5aDQwg9ueOoludWbCcCSK254uw7O7zrtazz0vnMGDr1Rlo4gkwOAREeUt/cU5W13SV2+rxX0bK7Kybpq7FiyIfbsi0dnpoTI8No2q5iH1Uf5Uu6NzpKhaDMsqYKyYgkiz3BmBiHKktSeW63D2Ykdz5KSYoUw/x1xvV5hNZxoHAAB1OZplb66SO0cxNDaNbcdaASSSzJ9rTZ4Zkd+nuYPBIyLKf7qrSmd/AIOjU56ufiwwv2YHIWBBUezyGInMTo3lIV2r2dGq7lnZpheicyV6ZMFcOq24eZN/hIjS1ndpEqcbBmZ1m1Y3uT6Lv2eTq/NeBqd2uVMwhGgen3K170SRYB8cre6et73bl16+EEAiBYXdd65QgrKFgMEjIspfuu4D+grbfS+ypxBlpljteRSOZL/nUSQaxYAu4FnfPoKaC0Ooah7M+rYzNeeHranMxWTPI6LCF5gKJR5keKqamglb5korPdeb2crnElM6AP9kEL967hR6hyccr+J3m6vQNSgeojUfgwDaxBs+04XHPxnExn0yVm2pyUWxci6ezF7dP/HvhuD6rCixxqoVKw/jzZPt8efnegNWIWLwiIjynvnSYagwEqVBS7AcnoWeR40do0nPPf56LZ7Ydi7r286Um3pb12AgazdZqYJY8cppngS7iMhb+qDFxHQIK1YeRkWj815JNz16HPe/JG6YEg2zAfL7fKMVvap5CL3Dk9hb3pnR+rReT3m8S9KmBY+KTF2PtH3hn5yfvdvNMaJU342Q2pi3Wxc8au5Krj9RdjF4RJSnLo1Ppz89doFItFpkeTuz0EuhazAwZ5Ip7ihptawkzxcLilLnPPKsq3me9YIJR6J4emcd+i5Numr1u3vdaazb05DWNofHpnHjqmPoGRK3fo+qQ0vNLbvauUErpfaveTkiKjzGvIgJ2nnk7TPOAiLn22O5ajr7xddon0Uv6LdPX9Qv5Ghbc4fHFat8+/gesszJ53CG1ermIfSPTHperrlCUWI9+w5WXLRdRjOPv0pzQkbBI0mS/lOSpHr1/wctXu+QJKla/f+mTLZHRAk/W3sSP3nS+6nkS8/1umqNyym3V5A0o0xFs1Dpu3vdady9/nTWt+PErtJ2tHSP57oYOaXdDFh9Zaqbh/CztSdR2zIkXsCFfGvFae0Zx+mGAax/qyHeomrH3PqeTmt8pTyA6WAEx6p7XL/XuO3Yv3l3H0dkY+eJNnRbBFZJpTvtaEFvp9f2h1+tTmtDp873CZfYfLAZk9Pp95BWFAVvnerAiN/7BkTLHkLzsMdQRnRfLcVi2Jro27enrD2ph+7qbbW445lTHhcw9/SNOq8easb2kjYA4txc+noDv4q5lXadVZKkrwL4awCfBfAZAJ+XJOl/mBb7AoBvybL8GfX/NekXlYhmw7o9DVi7o87x8qcb+l0tnx3ZvZQsEGU5pIKWqOyJX2/rHVf/9We8Lae9YELhqOXwiFwpqxffHOmZb0Ky2VNQURRTcMo4VEXbOH/RVCimZsLYeaINv3v5bK6LMvekmH3RybnXbbDbcE2weGtgKhS/UU5Hz/AkXj/agqfUutfkdDj+WigcSXu9evFemp6sLb31tPaMY9uxFo9KkBuKouiCldbLaLYda027h26+SUyCqiBokU/MsKzg9zQfh0HmWiYNnr0AbpVlOSjLcghAA4D3m5b5AoBfSpJUK0nSk5IkXZbB9ogoS8KRKIKh9CocT++sz5+eSmnyCa74FY0DGPJ4Vrf5oObCEFZtqZ7zuSD0w5u6BgKGhNax59XlPPgcTnvBbD1yAY9uqUGLOvV0rnX2+7H1SOqKvTlBajoJU52+42drT+LwWfFsdb969lTS8DWifKedguyG2M43iqJgb3kH/BOJ3j2K6XXA+mbesC6X216pC+LZjeqNZJDoVyv/5EwYbb3j+OFjx3GmcQAVjQP43sPHcNGDIfBz4Rr9m40V2FPWketiZCye88jc84hdYAHEfmOXLVqQeMIn+P4pusTjpvfS7CpO942yLNdrf0uS9FEA/wTgS7rnlgKoAvBzABcAbABwF4BfOd3GddctTbd4NMcsX74s10UoWOnuW/37vvvAQfQOT2D3I193tF7Ra9k+xsNjUyjy+XDNlYkY9LKlsb8vu2wRrr768qTyFBcvMDx32ZJF8XKO+mewaV8DvvsPn8KihcblzIqLfEmfb+3Kw1h2+SJsvu9v0v5MIm7348RUCIsXLYgnePZym9deewUWOFxvS9coIlEF77z2cigKcPWyxYhEFWx+uxH/8GcfxrLLFwEAHl95GABw/fXLkpJHZtP2oxfw8Q9ci0986FpHyy9duhgAcPmSRfHhhPrfx9IrYq8vuXxRxt/9wYB1sswdpe0IR6L4wTc+jUsTseWKFy10/fv00oA/Vo5gyNnN6vXXLzN8P6+7Tly+HbokmObPED8eDvb3GXkA3/zrj2PvyTZcd1XifDE+GcKVVyxSy7AU116ZH+1ZvH4WFq+P54Q6QYTPl3ydmq+aOkew9UgLlqlTgQPAZZfFzptTM2F0X4o1BixeXJxyn5mDPOblly9fhssWL4RIcXFRfHltBk9zedIxrZ56i4p8uKQGyFr7/PHZQbVrhbmcV6jXLdFrmsWLY7eGVy5bgiuWXYYX9jYKy7vsyiW4bLGz28jly5ehWK1nXX315a4/92x+r73a1lUvXxz4AAAgAElEQVRqfqzFixdisfr9uPLKJYb1L9Lylgp+u7moZ8+2q9TfYXHxAlx95ZL480W+WL3BsOzVSxJxAd3+6h1L5J6cD/tsLkg7eKSRJOmTAPYA+Lksy83a87IsBwB8TbfcIwDWw0XwaHg4wCn4CsDy5cswOJj50A4SS3ff6t+nTcGqf85qvVbHM9vHeIUadFh/+1fizwUCsYvG1FQQo6PGZIKDg36ETd23p6eC8XJu2NuI4zU9eNc1S/DlT78bQGwo0q4TbfjhNz6VtH3959NaRPyTQc8/t2h9HX1+vPv6y7GwODnItWLlYXz2o9fjR9/4w7S2Z/f7/IfbduPuf/8CPnjDlSnXc8ujxwyP19/+FZw634ctB5vQ0+/Hir/9hOH1wUH/rAaP1u+uj5fLiXE1Gfa0Li+Ffj9NqrOjTExk/h0YG7PuwbarpBUA8I9f/j2EghF1+UkMDvpR2zKEyxYV42Pvuzq+/Gycb82/tVQGB/2GFler8u063mpYpqJxAL/37itx7ZWXIaBWsqemUu/vUCiKXUeasf6tBnzwBmPFMaLeXA0NBRCZmfuzMvL6WViycTy1IUvRqMLvimpwKHbjrh/OpZ07Vr9ei+oLsVx14VAk5T4z9+jSL68dzxmLc0konFh/xDRz59RUED999CgWFRfh1m991uEnixkZidXZQqGIoR6kBbrG/cmTOQwO+jExIc6RpP9MwWBsn42OT+JCe2KY9NS08dz7zBs1+PZXP+aovIODfkTU+tilkQkMLnF3+zkwMO5pL53WnnFUygP45l98xPC8l7/PsfHYdX1mJoQFvthxCQSmDesfV4N8ot9uLurZs210LFaXCIUiiIQTv1VFSf6sIyOTuLw4kWFce31U1yvc/J5sXz9feltG12AAd/yvz2dtGwBQfr4fz+0+j7U//XLKxm43iop8aXXUyTRh9pcAHAJwuyzLL5pee78kSSt0T/kAzP2aGhHFNXaMYGAOz/BgNcMJAOxLMa3sArUVcIPaqgYAz+6qR03LMAZHjRUvc86j2ezNPRaYwb0bzuB7Dx+LB9DMqpozT9pspfli+kOknt11HoC4e346Q5ecemxrDTYfbMpoHaJhDQ3qjDuAfqjZ7A1bM3tsa61hiMRscVveUDhqOt7Okmyv3VGH326qdLcxAIOjU5hSb4ACU6x2EM1XonNV54Bf97qTnEdONmT1Zvv1NneNob59xMEGjLSGF/2EBanK2XRxFOXn+51vRLHP9zg94zbVQWxdm/bHrs1Hq7od5/BzU+caGp3Cq4eabSdz+M3GCuwt75y1oXlaFcjcYDYbKaDzoROGAiUpSXbScHdFEX8PLI7h6YZ+/N2tOzGYxfQSR6q60dyV/TQC2461IKooGBX0KMyFTBJmvw/ADgDflmX5VcEiUwAelCTpQ5Ik+QDcBGB7utsjb2zc14hnd9WnXpAIwIOvVOH2PJjhQXTp2HLkgjDfQP/IJAZGp7CoOPn0F0+iaXrefMHPJFeBWzOmXFSHKrtwy+qSWdv+xcEAdpS0xnNiTc2EsfXoBYRSJDfUW7AguQLqZZ0tMBXCjx47jtaeWBLr2pZhHKzoymidoindH3q1Ov65U83GZrbzRBtWrDwcH1ag53Y2vzmQisKVzQeaDGV2kppFW3x43P1sQoGpEE7Vx26Skmd6g/B5onyV72lTbn68BJv2y56uM/H7tm5gApKv7eJ1ZVAO3d/Jxyn9FWvXjGjUed6clS+fRUe/uBfG1Ew46TkFzvaPWx19fjy7qx4b35bx6JYa4TKBqRDGJxM3yk5m9dQ8s6se+89cREdf6h4ns3UVSDRG+cwvZHW7jR0j+M6DR3BhFgIcabFIQujziXeNYlVJF9DqAF0e5P/KREPHCFasPIxL48m9AV0T7JTe4Qncva48NiHILMmk59HPAFwGYJUkSdXq/9+XJOktSZK+IMvyIIDvAdgNQEbsUD+SeZEpE0ere3DKTcsDUR6bEpxM73jmFG5/ugwLRcEjiGfYMlegZrMlx1zZePlAE8YnxReJC11j+PWGM57NtgIAJ2p7sau0HTtPxGaG2X2yHXtPdaKk1vmU6cWCCqiXdSa5cxQT02HsKWv3bJ1WU7qbZ2FzWql9+3SsJ5woT5DTm798vUnsGpwwBo8c7LNMgzvajYP5p8qQEdHcEpgKWSa5z5TxnJmcbNfZKTXzxNbi14zL7ShpdX2Daeh55Lp0Cc+/eT7+t7ZPFEWxbdg4ca4XI35nwf3HttbEZygFkPI+5ObHS3DL6hPxx24uB+GI84Wz2Yig70kTtahPaM9nqxh1bbHe0o2d7nu32ekfmcT3Hj6K/gxHJuhjR/p9MzUTSWoAVJT8azgDYj3sACT1UNpR0or2vnHRW5LEJ2gRvLa7tB1dgxOobZm9mXgzSZj9YwA/Frz0tG6ZbQC2pbsNIiJH0rigmLvIAroLk+kKr69A3fV8Ob70qXep68g+q5Y/RVGSWhw37ZfRORBAReMg/vgPbvC0HMNqpVbreWPO32BHnHTbu1pAYuYzz1apm9VDvP99dldz4fLaX8lvsNqG3kzQu4DgbIsFZROf20nPPa+OZXLPIyXl+gNTIUxOh/COay63XohIFVUUhMJRLPYwF4Ub2nd5Wj1HjE8E8cyuenzv7z8ZTxCvCUyFsHSJOLlzoUv85hPnW8+GraXxXv1LXYMT2FXajvq2S/jVv34h9Xrj61cMwZ509QwnBwGSVidYfXXzIP7ic+9NuX67G9tgKIJQJIorLrP+Xrr5bFaNgOL1Ol5tRpSoRc8j1XQwgrHADK5aKk5onvZ2XewLN8rq+hAKR3Gqvh9f/9MPZbw+0XHYcuSCaRklve94jhvdElVFY9l3lbZjV2m7ozycTuqIsymjnEeFrGsg4MlUl0SFIhyJ4umddbho0e05F8NA4pUm9T8zuxIJex5pXYsFy2/Y24AX9zWie2giflGbzYTPZsLdrRbnOV0rohPTwTCqU+RNSupt5eKji/ImZPp18U8GcV7NQWRXMers91vmirJl1fNI/TdRYXe6Qp/h/XpOvkdP7axLKoNIz1DAVRf/dKRTkdF/fZz03PMueGR8rN1gW+Xc6ujz4+bHS/JiuO5cU31hCENZzC8xV20+0IQfPHIsKbFyLgyMTuFQZRcaOkZwsPIiVqw8jDfURPR1bcO4+fESx3lmCoFoeLX+nO7VsLU0Uh4Z6kzaOdHpcHDtvVHFZuMuKLpzsj6glupaEnLRiGTl3g1n8KPH7Ifim4uxu7Qt5XX91xsqcOp8X9Lztz11Urfe2cp5JA7i6Lf/n+qsrmZuyrh2Rx0eeCmRJzDRg9q44bbe8Tlxvkp8NAd1AgB9l5z3dBLtt2AoIhyiOStMPQ0zXYer1zzG4JGFu9eftvwhE80HowFjd+T2Pj9ONwzg8deqAMRyuHTqAkk56U2qvx4Kx0cbHx+tTgy1ul6dwvud1ySmB7VKaujzAcdrenGsusf0vHG5Ef8MJj0cd3yyrhd+iyFqokqdVStqVFFsEwe/8FYjVm+rjc+6J1IhD8aGquk2GwxFLC+C+uezkfPooVeq8fCr1YhGE4kWRfvEnCC0rL4PXYOpGwYSlT1zsnTjmHu3ib9Fn9tJq6B8cTTlMr3DE/jebw9hlzrEcE7RfW5nPY+sl2npGXM8vt9yPerTUUXBidreeC6qlh5vc0MMjU5hxcrDaOmeozknPLT69VrcNQ/rTcdrYteF3CWmTWx3VDeMSAtEHKy4CABo7Y4NkZiz+U+yTNje4qR3Sga1m/5Lk/FcfI4K5MDEdCg+/HliKoQX3mrMaH0AMCMY6h61SlCsExHk8HOrV9DrSVSW4bHp+Hl6e0lb/Pkkuqe2HW1NenlIN7V7VAEmp0M4UdvrstTO6UuYXJ9I/D0+GcJ//C45IObmsFY0DuCC/lpjrK4AiDWQ3PdiRTwVQS5pw/kVJXUvQAXA7zbH7j988CEUjsA/GUy5f/SNXXc8ewo3PXo8ZbnGJ4O2gdNzrcNJ+Ugtt+9Lbjh0Xf+16+iegzZsBo881j0YyHlyLiIv3PPCGfELSqySvPNEG36zsdLwvJfK6vow4LAVu/RcH3qGrAMfItrJe/GiBbrnxB/CqqdFkekMeuuaUsseC6OBmXhPGSeGxqbw/JsNWLP9nPB1URdeq2vInpPtuPnxkqSAoGZgRJ1SNsXFMF5JBTA9E8b3HzmGJ984h/8QtAC+crA5/vcC845C6gr5/RsrcPvTZZavawEgBYqri+dzu8/j7nX2N7g3rjqG1w7HepeJ8lseOHMRp88PxB87oa1GdIPp1bVfyz+R9dk/0iiwcVYgdz2P/JPGGUbu31iJh1+pdrhdi/Ujdix+/HgJ1r/VgLdOdThan1v16m9eCzAUunweXpku7buaq9iRfrPiXH4qdyNt85roFKMFCPTndO+GrVmv5zcbKxxvy4kfPVYSb9zWB+INxXR5kMcCiXNsfJ1K6tWIJoDIBv9UCD9/6iRePdRseF50PbX6HR6t7k6qAymKgnV7GrD+rQZDY6gnBIfb/F1KnlFM9J70f7GJYWuJwoxNxPZBu4OE4tnW0BHLxeTkE7aZgrAPvVqNH+vyYjmh1ZHsGlOHx6Zxy+oT2HuqA4GpUFJer67BAB7dUuM4yb8oY4Hb3uFeDE31EoNHHrtr3WncPQ9b3qjwjJumhNQPEdMqDPqKg9dDZZ578zx+82KF7TL6oM4LexuTXrdNVmkzzM3pZ4lGlaSEd1YXpfs3VuDhV53d8GrrBoytZMbXjRWNcCRqqBTrk0dXNg0CSO5Nlg5tthatR1RV85Dwwn+wMpHsMJ2E2S09446Ch4oC+yFkadTXp3U3wOYcBYoCvHKoOb4fHAePXCbYTnq/oRBprcK17sEAfr3hTObdvE3lddJDY/+Zzvjfz+1ODMPUdl9Hv99Rclmrc8Avni7DzhNtmJiOfTbz+c5KS8+Yq6l/47MizZFKH2VPrir2+s0uLC7S5cMxLpf4HRf+d9HuE+rrDalGrU1Mh1I2NqQrnaOw7ViL9fo8OqzasEYFxu+0aPXasDWniX/TFVDrG3WtxgY48bUk8dzw+DT8k0GM+GewcZ+Mx1+vNS6pAGPquT/oYgZZR4THIyl6lHo1pmUudI85viaLezq7iyLvPdWBezfEGpOrm4c8nZAlzkEboDb8FgDgy6wH5V6bxiItv2dNyzB+8sQJ3Lqm1PD6pFpn0BpdAaCqeRCHz1rM8Cvope6+55H13tHfm82WeRc86rs0iTufL09qySRyorPfj+au1MNHZpPVGOC6tmGMTwZx65pS/HqDRS8iN3TnLtFsFtrJcOeJNtsTs8Y/GbScSlW70bJrHTATJSK0TVYpbOHR/jC9YHHeDkcU/HpDheWMI/phbNqU405vUlPlYogqxjxP333oKNp6E/tz27FWzAQjsX0Y77pskXxbXSAcVlJWSrQu0W5uhn1Znm0t3i04RRf29NZtXp25pdB+Ay/vb0JF40D8saiy67SITuNgXt3EbjvWivY+f7x10G054uUxlSnioHzasAQg1uqcWFfivRccDAWz25S+t5FpNKKl+zdW4hc2PeLMtN9xNtJL9AxNuO5xSdkzB1KIIBpV8ObJdgDJ3/23T18UPj+f2c0mBgCvHmqO30xmyryldM7Te8rs6la69XmRB8nFsLVfb7Bv6POiLACSPtdUMIIVKw/jYMVF9KlDBLsGjefEobHpeDnNdU59wnEosWGA2ZCooxifd3LK0H9PpmbCeOClSjy1o87mHfr3atvXlUWw3hmbXEBbj7ago8+P1p5xrN5Wi1cOXRAul4lsBD68WKNoiH1ixt3ETn1i2zls2t8kXIeocVO/7xscjEiwz7Ep/m5l07wLHu091YGeoQmcVVvi88XEdMjVjTRlxz0vnMFvN53NdTEM+gTjxaNRBateq8FDm6sw4p/JuHvq/RsrcLE/MRwzLKglTwfD+MXTJ7HzRBu2Ho21jg2NTeF7Dx9Ft+AG53ebq+KtGWZOKlXTwbChBcS2u75wG9bbNX+6VPWw6aD4onvrmtKkG81bnjhhG0DqHZ7A8ZqelJVaJxW7/3zhNG5+3D4RpX8yiE712P52U6Wj8eCAu/weViErL8RmnfNyjUbmoXzJ3c7tHTrbhbU76uIVjXR7oEwHI7hkMy3yha4xR7mE3PBqFruLAwFDq67b3DCG5V2WxW5/FwtnAXRmNDDj6HNowaNUQdnxyaDjYbqaO58vx53Pl7t6D2VPrnqX6a+X59tHkp+fj8Eim2NhHLZmvxott1A2eH1YFMsH6a8vVV1M1JCYDdpvS9/bA4jVMQFg88Fm/PLZU/EhgmZWpYwqiSBA11AA37rzLe/yH4mGrSU9kXr/6S8zITUI5rROLxq2ppVLv96frSlNWffTGkIHR5wnrdakvF4qSDvgmXIPitbrYFtWi2gfo8lBHkqrNenL/JCDEQlez5aXqXkXPNIqcqLfa9PFUZyqT87MPxf86LGSlDeBlHuT02EXJxR3WnrGcEBNfGkgOKloF1p90Kaz34+SNPNutPSMY295rMVLUcTTtHf2BzA4mmihW7HyMDbukxEKR3HyXPLFWGsxN3eB3X+6E6teq4k/rm0ZRn1bcmT+xlXH8ZIu0i8KHtldVkSVokTPI3cVojeOJSdl1AJK2rAYPbtkv796rhwb9jbGc+5YiSqpi6lVtOwW27S3If63m0/d6SK3m+jC51WVUz9sLRtNL4fPdpu2577buZ7cKTg/OFyHNgOouZVu76kOPLCpEluPJH9nBken0O0gQbi9zPervvHDbZArapXXw4aTwJd+FsD4Yrovq92N00+fLMX2kuTfvZkWBK6+YD2b4UwwgltWn7DN8eWUoigoPdfreNYm8k4mwaNMjpdi+DvxSCuPk7wqhcbqI474Z7IS8Eh1c3fkbFdyI5rLYsz6sEgHdYyGDud5HJ0oPdeLu9YlB8SthgqHHAb3rINHiQpE90Ds+NQKZiOMKgrOtQ5nfAzM77dbm9ZwZbfNEf8M7nvxTHzoXfL2Yv/qv56i3FuieurKTZWGIeOTagOI2z0wPhHET58sxYv7klNLaCLqxBXZsPlAk6uh9ymPsdt8RYK6SLrfo7ly6s7L4NHAyCS2HrmQ1s63a/1d+fJZPLvb3RTXuXCosivltNpOrd1Rh0derXK07GhgBrtOtDF3g43HX6/BypfPIugwC7+V6uah2MxWOvdvrDQkIdaI6iyiQ3TPC2cMeYGiimI53ErkqqWL43+LkiSKvhd1atBnJhTBvRvOCKdxNl+0Xj18wTBM5rGtNXjktdSReWHPoxQNHcnLK+L3pagZVgp6MuoDYGaiqevNzuiGOonEbqid/Ra1oIPoY6RbkbacQUZAVFnx6jSi6FoObXr0eqbmgrFiGXV4DLTKy7o9DWjrHUf30ASGxqY8ucnXevqZu+sDsdw+d5lydrT1jjuacc6qq32m3PY8CmfQ88iunlCsnwVQFExOse5zLamnPHcyFfgPVh1LuYxTVc1DWLenwbOZdIKhCJ7bfT5lvrS5ksjTjfa+cWw9ml5dUkRJs+dfQ/slfO/ho+k3PFls1moYdrZzY5Se68V3HzoSrycMjE55OgtpJm5dU2oahmb8fda3XcKKlYfRn6J3hdtegi8JhrS4PQopl9cv4NmwNV3gXlAA0TUnE+v2NKBbsM7n32wQLJ3oiZPKiMXQQ0Pjk/5JkyNnu/Holhqs2lKDFSsPux69YjXsyO7U84NHjqFSHrRc5mzTIG5dU4q2Xj9O1Fo0DGvv1X1Iraac6rzX1DWGMl2Hiqd31qcss1lD+6V4b7DTNnXa7sEJy/yeIm5yQA6NTacY7ulgGzp237jVr9eirddYNxblJEr7kiN4Yy56JeVl8Gj1tnPYW96Z1H3RCa0e57Ty2js8gdufKbMdZtLZ78e6PecdzTrw9unOjBPLvXygCau31aZe0ER08a5oHEB9+4hgafF2d5xog9zhbPn5SJvlyEmALRKNJp1kNKu31RpmtrKjIDGOW1EUNLRfshxGpfeLp07i1jWlhtkBnUw9eaFrVDh9vN1v6mzTIDr6/Hj7THLPKVGLRzpEARm7oxAft6y7RGhlMR8/t+fm4zU9hnwstS3GYK+TG8pUFEVxPbtPS/eYYTakmx8vwf7y7MwypXe8ugcrVh42tI55dsOmy7SY6Sq7hyaw1mJ2O836t0yVWIttBkMRw77Wf6fue7ECdz1fjtueKsP6txpmvTXpvhcrHCWBtfyWpvH11fKwAO57aESj0bSPrd1vZIFu2NrR6h5MzYTx0tu6GVRM7+0dNt3UqPvh5QNN8VmAXnpbxj26STM8+Km7ouXs0GbUMTt8tgu1DoJemjONAyir78PWI9aJeoG50yLqxv0bK7H3VKdnwz23CXqgOnFerVPJaQaPFIsHlr+zLB+s1w5fQDiixHsq3P50WXx2ML1wJOqqAcvseE3suiKqtzj/iLElNx9owoqVh+MNQebEzHrn2y/h9qfLMh6p4PYamGp5/fHW9wJPl4K530vN6bBCbYp3s9iwd63xSeupl0zr+aT1gneacyhpey5zJq7Zfs4wRE1/OXnyDeu6ythEEC/tl3FITeJcJBirabfpDYIJaPScfi/WbK9zFRRKh9U+VJycC23eN21xP2R3zKovDOE+3UQ/ped6UVqnnidseh6NTwRx5/PlhqD0dDCMHz12HHWtw/YNpA7VtQ0b6zcZyIvg0ab9smG4jdarY3h8GitWHk7ZWjPiT4y1NLekRqMKXtzXaJl0cp8apKpqto4y3/PCGZSe6zNUjoOhCG569HhSdPq1wxdcJ5bzqsXGTYVRRLs5H3WY8FevsWMEK1YedtVbIRMXuscQyWH2yvHJUMreR7tOtOO+FyssA0hWzCedPSfbce+GM+jo86OzP4CHXq3GywfEidv0tATO/bogrN0FUd9ysvr15F41dsGjxQsXGB4bkud6NNWr8ALloOdRR78f4UgUY7qW9WPVxlYcq6TkVswX3vo2ccC1onEALT3pzRjhouNR3Ev7m7BuT6J35WzlUdMuiFp+AiCzi+DRqsRQMn3Lofm38bJFAkO9nqGJ+H54emcdKmR3LYpWFYmfP3XS0KPEqr5Rfr4fR6q6xS9abtTd4nquzose5pI63aBPGu7uvdFooifeqfPubtjsKnrmILu5t4G5wvmr54zDKXzwoaFjBIcqu7BfDYwfqeo2DOlMlbssW8YnQkld9d843opN+5vw2NZY67kTWmAlVW/JudTzaCww46g8PpeNiSKtPePxfXRCMDzbzqXxacN3zotvSo2unmd5U5ViHdGogh+sOoaj1cnnpWAo4njSB/2GhsdncKjSOBvRpv1NSTMZuXFA/c31667PfZcmY8Ekl4dUmx30qisWAbAOvgKI5wj0cqpzJze3bn5i+vuRdCmKsVxlczCtRzDDmb/EPY9Svy8SVRzN9pm8Qfdv0Z/Hnb794VercOSsuF6R6Alj7bhNigvzeSUciWLdm+eFIwtmg+j03T0YSPpN6eufVpPHAIn90qnL81pW14fv/O5IrKe4i2O4bo+4x5y5zOXn+9EzNBE/pwFA7/AkJqbD2Has1ZDUPV2rXqtxX9e0MKeDR68casZMKILDZ7sNw22070OL2rJv3hnjE8H4j21sIjbb1Otqt37zdMk9QxM4Vt2D1a+Le/LEe/w5qACO63pjtPSMY2ombMhBkW7lqibDoI8m09a1K5YsBJCYptANLXBlN82oV9r7xvHAS5XYftybbvsinf1+rFh52LIX2e1PlwlbOsYCM/ETrDZsxO0FyDzMqEUNyI1PBuM3Q3b5Ncz0X+3zNln/9b+AcVHPI5vv9yIteKQY/kn5vkzZdc/Xb/bNk+3xVlIA8RtBV9uy+RxXLCkWbnvtjjrcv7HS9baAWAU/nX2nvyDONv0F+xm1C3QqTRdHDTmvpmbC2KhrPRFW/lSHrKZO1bnz+fL4bISXxt23gludVkW986wc9eiC7kQasSPPrXIwDFUvqijxILvbnop2P5GpGeONh7lCmTJHgQ946BX7Yd/6mQb1OR1G/DO4cdWx+JBSt1Jdh8+1DuOOZ08ZnkvnhlI7xxSlqC3OldhR10AAP3my1NFvSgvsZVI3skzQqygpewD/bO1J3PHMKdtlHNHtfH1jalRwvRU/YRSJRjETjOClfcmt1A+9UoVbnjhh+36r6rK5UaumJbP0C1ct1QI9sWCWoij45bOnbHtkpKI1dM0EYydK0WdJ/CYyO0PqfzN2w9T9k0F0DQQcjW7w2mz+rtMJPmSaIkI04YbTj+yqvqBuY2I6bLiWuD31VDkcLtdvavAUJolXFLT0jGXU+8+HWOeA0ro+vCjo1ZKtthP9bjNfmwdGJnHXutNJuVLvfM56comOPn9iaLbgS7/16AVEFQWBqZDrY+akzKLKViJXkuKoIc/tbzUwFcJtT5109ybVnA4eVTUN4pWDyS3H2olbC2aYW9dueeJEfAaSn6gXuXNtseCFVlk43dBvWJfl+GWbgxEKRwxDGBbqusBrFUp90Glveaf1ymxsP57oCq0fBuGW3YVHURS8vL/JMITJrMjiVqJ3eMJxAMQ85bPZI69WCVu73BgLxCoSTnJ6pEsL6FXa9FJo6x1PSgD3kydLcZuaFFWb6cduzLboBsFqLP6CIl+8BdXNDCH6o2rXSp6ytdJmgUULTacafXdSl/WhYCjieIYh25Op7sXRwIxhCEs6rBI6AsCSxcbgkRcBs3SD0bmctUG/7VTnAs3Kl88acl4l3+gptrl59p5Kfd7Veq2ld1xi79lb3gG5Mx+G9CZ/xvGJYLz31bHqbsOQSyD5u2bXaufEpIvklUDqm3u75PeZ9Ih543iisUNUBif3jvpz6vq3GuLniermQUwHIzjiIMApUiGLbzb1pXTcQ8SGlsenyOdDS/eYMCk74H3Po/5Lk2hMY5mbhfIAACAASURBVIi81kv0vIPh+Fpgz+tZCoFYo+aNq44bbojDkSh2Hm9JqotlOqOXVem1YxIKRw3bTHWesww6IdFY5cTByq6snhMTE+DESqp9rvq2S5ajCVJZsED7TsT2lyi4K+qNl84ZUR8wCuty3728vwkPbEo0Kt265iTuXn/akLx4Nsx2ftPb0pgwwMk90WuHknOFaqK6YWsiByou4q1T9kP7R/wzWLHyMOpNja+itb58oAn/8bsjie+ny338oiCgK5IUm9B9xnjuX8SG7t75vAcBbBf6Lk0aegGlQ3/c9Z/1nvWnk3oIa/QzvpoP+b0bzsRnRk51RNJOdq3PH2a5UOz81dgxEq9n6Zd96JUq/J8HjxjeYv6ehcJRDIxMYl+KmEMmx2BOB48A4HhN4uZbq3TFg0eXWfeEGfHPoEbf+0Ld+1pFrq3Xj4GRSeHvVnTC1B+cbcdasHJTJcrPDxiCA8XFyacK/Re0/Hy/4bUn3zhn23V8aiaMlZsqDcNxbl6desa1G1cdEyYYtqsgjQaCOHS2y1FiYrNfPVeOn601Ri8npkO40JW4AXGaoLG+fQQbHZ4crczG5U5LtCqadUwvKT+KYR1FKdfx9M7kYWQvWoxFLl5QlDQzlCP6Fgmbu6FU+9VuOMwCU7O1/jfmtoLSPTThuGJod5LXv3K8pheVKRJUp7LzRLvla+YhH17UyaKmZJaO5TB65MWmzUNMAtPh+Hrli6OOhqp5STsEW4+0WOZV8Fo4xc1uJKpA7hwxNKw8uqUG9244I0yQfssTJ+Kzeb64T8YDL6k3LhYHbLa/QlbDigZGpjATithex938QsxDIN4+neiBKO4haP5dJ2/N/NuPRGO/2zfURiG7c66XxAG21HtH2/VFRT7c/1Il9pZ3Ct8nOkSV8kAs+bDLYb8AcMezp/Bgil5dIvre5W2942jusk5roNUHMxm2ZkXr/dsznPjsByu68PzOuqThJIfVAGK6vyurw6i/JLvp7efV/njzZLvtOdFJgnFFUeCfDArLlAgQx/7Vf95XbAIGom1oinUBxdqWYfQOJ393tRtXJxNfOBXRleHQ2S5D/VkL/FWlmCjH81iPMvsBJLeCDiacaOqyTg0wHYwkpSXQfx9eOdiM14+2WMwYG1tOGwWzo6QVgakQRvwzKXPbah0YnOxdp4dAnwJB1LElEo2is9+vmxgm9q+5B24q5p+i9rC+7VI895+dXz57Crc9lfnMoonyJArUORAQ3+va7EOt80MoHEVHn188mY6zVcX1j0zapqSw6nikQMEjr1XjwVeqDLO0aa8HpkIpGztuevQ4bn/mFLYcuSDszWc5MZALcz54pKftMO2Cc0ztoaLNVtPR5zcM13lcMBTNp/vEoXBUeGLUtwBoJ4fjtT3xFog9ZR1o6hpLCgyIWmP1rY7mCpeWD0nUIygcieKmR48nnfSczMwzHYygvu0SeocnDMvbBSm0i6BWlkg0it9uqkSDLpLuZoaOx7fW4oFNlfH1ZXr9qW+/ZNhPXQMBR/mTai4Mof/SJOpah7GrtM122WhUwZYjFwy5b6wsUI9rXdswKlIEHZ7bXS/8nmkBKP3n6h2ewC91Qw06+5PH1PuKfMKeXh39fuGsX6nov7e2PY9StVbanNDiJyvBd+i1Q83xi6+TiopXFVvzprQZq9KV1LtKx7xXvWiljyqpgwhCOawMZtpjpaFjJKlSZp7e3MlQNSvplM5pA4SXUiXrbO4aw+82V+GmR4/HnzvXOoyOPr/hObMOUw6PdnWoWK7vH6wC028cb8Wa7ec8mz1q5aazlq91CM7FZqIbTfOXyodYQEEbfic65245fAFbDot7+Gj05xAnuR9F30kney2i63mkae/z42DFReNNl2Bla7bHvqd2Q+/HLQIDTk3NhA0zwel7Id73YgV+u+kspmbCST2Rw5FofMhLNnoeaT3RQ7qApDaMbcKUxzLV9meCEaxYeRh7dZMbDI9N48V9jfY9ynUHpbEz8f1I9Xt283uvahq0He6evG59w5HxNVEC6rL6Pvx49Qnc8WwZgqGIISCuDUuJB4/S7hGQ+LtNPQcOj09bNlLFbzYjUax+rSrWazPDOFK6M/XpnWkcQGNHmjP2CSjI/blfZEdJYjRGpkP5Vr9emxi2ZQpGphIPXqqPW7rHcfPjJbh1Takht20wFEn6ekyrAUhn23JWIG3URWy9ydGJnSfacM8LZ+Iz5LV0e5ODVh+g2H/mIla+fNbRfZRXMrl+RBXF0PnB3MlDxEn9/Y5nTiU1OBkCUObe3IKE2FqP1Nh5PPUJRjvf638T+ysuYvvxVkNv8uh8Cx5NzYRR2zIUv+BoF0Nth9274Yxl7iKNvgLUPzIlDh7pgiyJ/Erjwtki9IQ9lnTH26qC8N2HjqKjL5a0dyYUwfhk0DSVqL2omrit9FyvYTajXz1XjpUvn8X3HzmK4bFp2wqK9lo4ouD1oy3YUdKG5q4xPC9I9pVqyl4gEfSwO7GXqDNlpBpve+OqY3jk1Wq8oZvJ5O71py1zDbTpgkqPv16LO58vx6otNdhR0ga5M5a4W3+TVFbXh9qWYTR0jmBfeWfKWQb0ugYnsDbFjVxZfX9S77ipmTCK1anl9d+3Xz1XbqiQLzIlmgaARcVFST29gMTFKBPmIaB6qU40dsPPzG/Vr6ulZxz3v1SJxo4RlNenPnHvdpG3w67MmYzzFllUnHysNOZu0V4EwBRFwdYUN5gi/SNTKKvLTeJLu5b1wFQI1ReGkoZMaU7V9+GhV6rw2FZBo4BHXWHSWY2iKEnnubfTHKLsdrteu1fN/QTEhuRqvV61a+xoYMby+GST3Ueta73k2Q2OaDX3vXjGcqiw+fui/11f6B6LDUsxr9QHwwcSfef2ne7EvtP23yHzakuspmqOl02wjhQ7bnI6HB8ep8/vct+LFdh8sNnQ0GF34941EMCBCmMeuSNnu/D41hrcsvoEtlgMhQOA5q5RdNv0NL13wxn89MlE0mVDngjVE9tqcfe60/FkpHLnCL770NF4vcdNEvnAVCjlNO5A4tqt7xmxwGKYnP4rEAxF8NjWGlQ1Dcbzmzyl9kDeeSLRALb+rQYcq+7Bg69UOZptSO9AxUWcrOtF36XJpEAW4DR5c2yZJ944h4dfTfRqmpgO2eZ70392c7mf3X0+6bugDW8eHJ3GHc+eige/9Q1rWnnTva7qP682mqCu9RL8U+Jhn9ryJTW9OHC6M9YwmeE5yKsGBzf3Dqko6fZuzrJdpe3xv+3SPjihH9mRzieNKgrq2+zz0jZ2jiate/+Zi/j+I0cd7d8dJckN36LJTuyGRRX5fPF7I7vviKNAsKnML5l6ezddHBXmDQ2FooZgulec/HZqW43HaE9ZB47X9IhzD3kYXDe+MfU69J0RtJ63ipKibmrz2sGKLuw+2Z7oTY5EXSCTRrfi1IvMHS+9LYtnN3Dx+fU3GU++cQ7f//onk5ZJN5J9w7WX227P7rr20n7Z0JNmxdc+4WibA6NTOKyb6eW6KxcbXteSjJ5tGrT9XNF48ChqGN+rKArq2oax+vVz+OLHlwOI/ej+55d/L+mGLRyJxodiLVhQBISjtl1KS9WZSQZGJnHNssVJr7f1jqNnaCIeFHEy49VMMBIPLiQqhokdX67O+FPbMoQP3LAMAPDcm7Fx5D//1mcAxLq43r3uNO74X58z5Kqxm3FPURRXF+195Z0oVodyDYxMYd2b57Hs8kWC9Sb+vuKyYkxMh/HJD10rzOegz43lisMb5pTBI7shYuprh8924+Pvvwaf/sh1Scs8+EoVvvWVj6Qsh5tZA+3KnGocu1sjfuvjv9GUSLC9z2/IX5BOIvloVIlP8ezW5oNN+NzHlqf13kzYBXkeebU63rvj0R/9adLrz3qc7+HS+DSuvfIy07Puo0cKknuEpuoF4gXR9NReMoyHV39H/7n+NPyTIdz1b1/I6rbN7H7HPl92W8fbev14dpf4u2f+tui/3lpl7af/9GnDMpPTYUNuwXRnY0vqSZzG+VlRYrPqdA0E8O2/+ljS6w+9WhVvaDHPHCtal6F8uoDMiXO9wDngLz//3vjn1d9wVMqD+NZfflS43t+qvcHW3/4V4esDI8Zu+aIWXFltaHzlUDP+6ovvQ50pkaqoYa2srg/LrliIj77naixcWBQv993ryjEaCFqWR7NIbRzSJ/TV8uolBTl0NyyNnSOobRmOX+fW/eIv4n9rx/zna0/G6xsXbIbk2N2YPv9mrGHwuisX46Ebv2T5PkVRMD4Zis9CpokqSrwHtl6qYcP6eqLoO7mvvBN/+8cfwOYDzfizz7zb8PvQGnzkzhFDI4K2P9O5ppfV9+Mj77lK+NrElLgxLTFcLvZHpj1qAXGOrsBUCI9tTZ7ZdrYoyuykgciEeQa/TLTbzHxsdYyPnO02pFexIsqPGgxFHfV6tAue69ldB8+1DKNe/Y7ZjUJ5+NVq3P4vn7PdTlPXGN7zjqUAgB26gLbe3vJOXLZogaFxPKoo+LmHw9U0TvahqBfhhr2N+JM/uMHwXDSqpGygTjvnke5vczJvjT7wrt2zT0wln38zMe96HvknM0/+aB6i/LRgxh99kMXNztWGIenpr6123VLNQ7BSjZfV3P50mSHCO2yR/f+VQ83WScGRqOiJfoS7S9sRjkTjXR0BcUvP47qLnLYvxgJBrH6tyjDrSFvvOO578QxmTDdc+orE8Ng07nuxwjDNoV0dW5tuW19+US8abay6aJYMrWKndXE3t7A/sS0xg4d5L/mnQrZjeM2VpGA4Et9HByouorSuT9jSPDkTwkv7ZUzNhLH86iUAjInZveC02pMqum87pFL31rU76qxzNMz1mooNN1O8bz7YbJjOe0+Z+0pvJvtqYjqMHz5mPXxptqxYeRhdgwEoimIYFuQ2MOJkCKuZqPdeOhTFeIMYCkexsDj5N/qe668AAHzgncs82a4od5GXinXnGW1LbmaQ85JdZa3I58t667jluc88JE1wkTK/83ebzxpmj7ULHk3NhPHS3gaEI1EMjSZ6Sk/NhJNmriq16E0YjSoIhaOICBqPFCVWgT5Y2YXalqGkHrL6Hrr6FnpzGR96pSppwoBwOHmfhcJR4W/Vq2GHQKKOZzhmpl1svoaKeqw89+Z5rHqtBj9YdczQMDMasK+H/nh1CS6NT8d7ompDD8YmgvFjvbe805AMXF9U8/ehRJdXU1FiicTNDVXWOY9S71etztjZ70dd6zBuevSYoaHuaFU3fvLECXSbhv1Z3YCmSoavr6NZdfi694UzKKvvw8qXz+L96vly8aJEz96ndtQZrhEKYvle0rmOAsk9J+Lls+rRFX899q8XHV+135e+XnCmoT+ta5tXSmp7HCXdz2VepEyTzetpnRMUJTaaI1U9RFGUpOC14XUH2/Qy35rdcdCntAin6Gm58mXr4dsac942ke0lbUn7UP998uq6nck+NJfheE2PsPHPOCQw7Y3F/7TLh5u07Ymgo0lGth9vtR09oik916vmfJ4nPY+WXb5IGBxx8/GdtPKNG4JUztcuCrz4fD509Plxadw4bEzrdWMlGwkczTN/6VlFbhWIu1pHowoWFBkTjNa3j2DEP2PoRXTPC6eTfmhrt9cZKj8+nw97yzvwQd1N1cOC5I7asdMSu8bLqCi48/lyvHf5FfiFLmIu+hFpN3laJV/fOmru2WQXzTZ/plSzzZkDh5GIgoWLrYc5aaZmIjhythuXLy6OfxM3H3SeCNIJpxWfcIp8W/a5F+wfa7yuhMzVZI/Llix0dJK3k2mX8mzk+UhFVN7z7SPwmyqoVq0yVuyGvbiRXs4jxdDDMhyJYqFgCOP73rkU3UMTjnLnOOHF8atuHsJnPnq98DV9Y8jeU53440/eIFxuNth9VJ8v+63j5lxQGvPXWTThhHkZ882O3fn3jWOtOHS2Cwt9sVl6/usn34nv/t0nDcOE9KKKkhTEf3DzWTR1jQmT++p/j49trcUffeId+P7X/8C6QAKHKrvQ0DGCrUeNv0HRcJKDFRex7VhyD9loVMELbzXgLz//Xrz/ncuEk6A8t/s8yur78Pwv/sK2Hmc38yIQS2QaMOccUgMhz+0+j4npEG75prG32NGqbvz+B691dF7yT4bws7Un8Xkp1rMzqijYuK8RR6t78OkPJ3rcipKBt/aM433vMAaX9bkao4qCO55NnhnJKvjm9BTR2e/HPS8khqyW6HpSaIGVu9adxvO3/UX8+e8/cgzf/PMPxx+/eqgZ/+yg53DE1BNBRB+o3K1+/quvWIT+YOxG3XzumwlGLBLaZ8ZyOGA0ufE0G+egXNdeeocnsWb7OcNzonpeNu5XcklBrHHpw+++Uvdc8md843hrPLgpkqrODIjzmqZj27FWfPfvf9/RsqKGhFzwKvCXyffPPMlQqjIpSvpNHXbvS3UfZne/oPWKGw0EDUObrWza34Qli4vx43/8w5TLWsmr4JFwyBqcRQG1RZzcKOsTnZlXfeq8da4QUUuMD4k8Evqgyusphqk4uenNtLvmLU+ciP9tlcdiLBDEtctiQztGdTlitJjLjOmHVtc2jBO1vfEWatHHMLeaDY5OYesR4/4Qzc6iHTvzWF/tcdfghOEkIrq50qLv2rr0raPmXEfRaGzInvS+a5J6Eph7hmldwK10DU7gkm7/HazswnuXL7V9j14oHM24JrF0yULhOGmnt8ypus6K1x2T1Hpm8VlyEdDIBS+CWrHZ1jwozCwy904AYj0FzMf9pbczm3HRqXFTb9Z0WpBPne/Hn3/2PfHHUUUR9jw65SCflxuHKpNzCrj15Bvn8KNvfCrpeR+MPY+6BgPC3Cizx/qL7puFnkdWzNd8UR61VGXba5Mfa0ZtnNHOrafq+/Hdv/tkfDi62Qt7GpJ6IGmTbojOreaipepVI6LlQNQPu2npGRPezFvV4UYDQZTU9qKkthdrfvJlYa/IMjWZ8t5THfjbP/5g0uvdgwHcte50vIeKfr/74Ivf/N3xTHLwRZsBT9vG/2XvzcPkqM6z77t6mZ6e6dn3fUYjTWkkjaTRSKN9tCEksUhIQggQAiEECMQmsEGB2MZ4wxgHm0CwE0Kc93Oc5LPfL46TOLkcv34dL3G8gsE2lDHGNruFBAgJ7dPfH93VU1V9au3qde6fr8toqms5VXXqnOc8q3GBfOZsHJ9yWflNmxD3208l8lHZKY6ffP7NtD7kZAH6i9+KlVovC8rMizCGJH7PxLhpHAO+oiky8Y0fv4SKiP2S4r6//TEkAJ+6camjRd+RpCz5hsbDwzh//jjDSqlmmDloqMYCtZ9kq/pkIczvxjZc96lvp+1TasojlRc0cqu28qbK8y+/g65mczneSiZWMfN688IRh+O3kwp1ucAvmcJT4Zgk/2jIGyrZ5Dx659gpoRzrhLfePYnXDh0TRo/YDSFO83o6fbfHT56ZPJ5H5jh/ACGXIT/GSdUs9wFgnytJJxTYNNmuBDyANLd1N/zu9SM698G/+bp5kmhVUNW6zX39f36Pf/nv3+H+vYt1+wYkCc9bxOCL+GtBUm4RkiTpwkNUtAO0bgyxeIQ/Uw5iw8Iey0SZ33v6NTz1mzexZl4nzl/So/vtR8/qhRW70vEii7Sx+osVZ8/GM3btNx97/Jn43QyoN/zZfwm3i95vKeKHkmw8c31izlGrL2kJBiRhYvhcoE2u/y/ff1Ho8eCEL2oEwDNn46l8J9nkX/8785xd4/G4sCppHEhLeHlc82xyvVjIZ84jK947aS/8ZlINSB2ynVRZBcxD18wwLsJf+uO72H3/t3DtBTP0Oa8sEI1l3zfxchbl/TBiVQ0QSCignn7hENobKtCYDOUGEp4xwERoui5qzWZBoE0Urz3XxAlsm52G6un1lCZXohPlnNHL7bQDWdCsJLRVqgItTucjo4en8aivfu9FxKJhy3McTkYP/OjZNzzPg8bS4pXl2VnK/Mwkz+UzyeS7avv9yHkkohCTVYvwu/hIvnHz2I3507QYc11mm39wWEDlxMnCkLP9ytvoRMHuFx/5W3GhJif82w9+bx5aa6McEjgOC8nVmFESyiM3jyrqwDKixY1b3bOC5LVmQradQJlpBQE7jK56blETiv3QUFrVa8y5EyQpPc/H20dP6qxOWoHXyrvjhVeP4B+/9bzQmqDy1G/eBAC88uZRofInlzz1m4OoLLcWyuwwexyft1CIuuHVN+0TmtvxQh4qOeUDP4St8fG4o3wEhc543FmMfTbQVij8J0FFE6dow3fPnh3HMy7D7gqRlwxeC9rKm7n2ELQayxM5j3LYGA0H37YvkuBWyafNHajKk9pEwLvv/5ar81nx4b/RK03URblaRMIJInf6bMovP1UO4qfKQUTKgnjs9hWm+9l5IVth9HwOBSQYR+zXDh1DW0Ol6TnUa/7apTHN2FJH4c0Z9n+nyuDvP2OvnHTibQGI8416JVuePyedVrDN0vWLhXsNytdi5/XDzhJUA+kJ+4uBbBfbcIoTJwkn2OVwckOhRj+IPI9eP/we/vDGuzqF0X89ZV11VUsmt1oSyqNXDjr/0LPJk8+/mbbNGBahcszGwu3U0ugVq/xHbjAuuJxURPPKz184hHeO6UU4bYleAPjk3024lpsl+FSxUhxpee4P2a+cZMehIydNk6E7xUygzzT3joobTyoz7Dy4yATf+bnzSaKQyae32ee/5s8CRutp9M6xU8Kw22JHm0Qy1zkT7DyPCtkHz22Oq59rqkm++Jo/+TDMcOqZYoXIW++E00V3Bpw8dVZXiMOI4mPFQ5G8ds9f/dCy4ppdHkQ/ybT3F+qCySnZLh5ge/0z41lRYBfLW3GsZCsSnBgFihmrcTOX+KX0yff37wff/In1etSo8PuTz/8gFco7X/ZWOfmfv+uxQjeKrNpaJpw8dRbj437W9HCGlxwCQGl8DH5z8tRZPCwIsdCSSYhAqVMME/yRPFVzKkbeOlparuLFjLYSZSZuzcVCJjkG/EaCVNRVGq0wen8VIqKwjVwojwDgaAHPF68dyp0COVPFRbErj7KV88gp3/SxXLyO4n4tpEBxOz4PdNZkpR3f+bk/Tgy5DFvLFnbzhfGdaXPAhTymSXDrFaulZJRHdz5mXXb50JETuO3Pv1c0McTF0s5c80YRuogSkg3scksUC9kMdSXZoZCU9IGAhP/8cebJw4l/5MpQcefnfpCT65hx/xf9r/DljczkRaeJtYk5P/ilu3xjTnj7WGEZiLKVW8oOt+lGiDVuFdsVGabMMOPbT2aWPkXFz7C1YsTvYixOyOiLlGX5cgB/CiAM4DOKojxq+H0ugMcBVAP4DoC9iqJkxV/OLkQJSMRif9+kikShYZWEjRBCjFULi5X3fAqbJLnjz//3M/Y75QhJch8aRrJLoYRFZJtMLLd+kqmt0c8QP+If//4/5pUY80G+PE7ny034rk+pNkjp4VfuJOIcz55Hsix3APgYgGUA5gK4TpblGYbdvgjgJkVRBpBIKXet1+v5RbZzCBBCSC74TYEsXAjJJ5Ikua6iSrJLrsLWSIL/+VXuLc9k8pHrXHeEOKGQPKEnC5lIXOcA+JaiKIcVRTkG4CsALlZ/lGW5B0BUUZT/SW76AoBtGVyPEEIIISSFJAGh4CQvd1RgOPEEJ4QUF/nKxSqqNEVyh1p5ulBRq4SS3JGJ8qgdgNaP8DUAnS5+J4QYaKwpBwA010WxcGZrnltDvDB3wFnlgynt2UlCSMhk4p2jpxCrjOS7Gb7T21aNge7afDeDEELySrRE8juS7JCNfGPEmkyURwHos/RJAMZd/E4ElFpiuMfvWpXvJuSExT4pegJJC8vYnHYsm0XlUTGyaUmvo/0Ge/K/MByb057vJhCSMS+/fiTfTfCd6V21OHD5vHw3Q8hV62VfzzfPocK9mJk/vTnfTcgqfvaJXRum+3auYmLvppn5bkJBcuJE4VZV9MqyoTZX+3c2VWapJZlxw0Wz8t2ESYfcVWu55uxprcp6GzJRHr0MQNv7WwG86uJ3IiBg4Z1ZV1V81tVABu6ml6ya6mNLgKbacl/Pp6Uyaq30W+JQEaSWXDw7HsfMvvqM20Vyj9MuXwh5WgrZG7yAm0YKjEJJXGzF+oXdrvYv5DwOnU0xX8933YXGdJkTfPy6Rbh0tb+ygBt8G4c8ZLWeNaV4ZICuZv8WLDN7i+e+/aS8rLSMx35RirJAZ7O7MTTok7y4ZWyKL+dRUaMlChG/15CFwtKhNrx++Jjp7zWVZVlvQya98ZsA1siy3CTLcgWArQD+Q/1RUZTfAzghy/LS5KadAP49g+tNCqxie69YO5Dx+XOhkfQLvxe28+VmfOL6RZ6PD1po9iSb6a290ZnVQM3dEc9TVQviHuNA7TQ+vxAEomznEqjOYBKb0l7tY0sIyR7RSNB2H7df2lkf5oD1o+4UVk4JWFm5PFAWFj+/ptpytNZXoCbmznAWDk2Ith/atSCjtvk1UHt5nXZyRSFhJR+5papicoYpBfJvTyI5wu334kdev7+4fQznL+7J+DxanDoIaMfkQmXZbHfeYH7gRUaWJKCvTSwftzdWYvf5g47P5fW9eH6biqK8AuAeAP8XwFMAvqQoyo9kWf66LMvzk7vtAPCQLMvPAYgBeNjr9ZyyYm7hh2Hcb6HAMPsOa2Nlpoupm7YMCber3i7z5QmX8KEpDal/Z7Kwc8OeTblxa7QbXDePTUFLXQUeuGGxLlzHqVXTUnlkM36OO5Qcw0nrwnimtXdJzjC6Ezud4vNV9lZLLMu5BHae617hfdGyPtyydTbGsjiWd7f46zlBJjeOBGiXsn9vARt6jPdbG8uOLKFOg2UuBdzqikR7GmvKHRvMLlzSiw/ump/mEerXVByPx12rguKIY/d5zhcC2aDDoeFLKx81VGfmjWCmTCwkMvGqNyNYyK7AeST/kpI5Xt+YcT1hF5YWylCzraWZmwAAIABJREFUWBEJobws5LvB0Kkhwe0Y7gdmt9pSXwEgkVtWS8ijAnzriimo9qjw9nJFSQK2r56Gj1wzitFBfTj0R/csTM1/TvA6jmX0NhVF+ZKiKLMURRlQFOWB5LbzFEX5SfLfP1cUZVRRlOmKolyuKMrJTK7nhEwnLS3NtVH7nTxQZfFizT7s3ecNmk6odVUR7Fg7kOaiV1EeUk+a2qb1koiE/f+Yy8vS25iJxtldv7beWRUKG2uiGOiaSFY8S6NQs3Lp7G2rxvC0xrTt19hoea9cLzvOZaV6KDWZ9L2NS3stj89XaGN9dfGFVPpFwDipO+yzZ8fzG5Zy7oKurIZyAt48m6Z11WLutMaUIjUb9LS4X5hvW9WfhZaQUsBvTxzAHytoPEvLLuNn3ds6YdjyUwYb7KkDAIQtZJULBDnmKstDuPbCGbjLRc6oruYYelur8ZfvX5m6rhnTOsXFDkR5KG7emjDuxePAZ29d7rg9Kq0NFa6P8Ytrzh/E3TtH0rYf2JH+XLXfwMeuXej5mlYGjYYsyRleFlCRMv/np2yMI6VA3IEG94kDq7PeDm36CdUQ71XRaXzXEZvzZNo39l8yJ6PjzXD66QSDgayHuKlKIRUz+VN9lPVVEd2aymtoYG0sgl0bvCn5ZQ9FMSRICIcC6GiKYc8F5iHfjs6VD+VRIbJoZotv51rnMkeBU6wGAbNfpICkU8JcsKQ3pekMBQNYM9KZllNBjZ82O2c0EjL1pqmNlXmyzos8bNRr1HiwTnp127ZLBKwtOaoNKZvd3yDaHUDCs2nf5nQvr4UzWiwH0JVzO7ByuB0jsn1S0CWzWnFgxzzTHEl2g9un9y21/D1btDUUZjK/XGD8hpz22LN5Knur0t0Sy3pYhNt5aUp7dWrhls2cUF68CTYs9NfdOxv4GTpCnOPkubv51qoqwo6EujkW8xXgrJ97CRFS7zcYkLBrw3SdBdeY/+9aD8LtxqW9+MT1i7BzXSIJc1nIfGElMviMxxOKnIbkYuX9lw3j5q1D6O8wD4Ut14QeGkMCjMltzR7rZedMS9s2vbsOHY2VuGh5H2LRMN63I10ZY0UmjgJW92tEfdZammqjQsPXQFf6giem6UchC4Ph6nkdrtuhcuvF2VkAeyHTubOntSrNiBFk3JqQAnDSRlk4gBm9E0rlnesSXtUpI71LjHOGnXLIahzQeqma5Urt78isum9dVQSy4Lt3o3zI9jrBGH2i/WuW5rlolcXaf2cSGuh1nF41bD0e2l0rFAwgGglheFojHrt9hetzeRUZS26kshIynNCmsfJkSw63snKY/RSQJN1gEwkHUpO6aNC59sIZpm6QW1ckhK2qaNg0PCoQkBwPChs0SitRnga13TN63CVBDEhS6nk4Cy2buLZdtQ5jMlJ1oWqnnAkEJDxxYLVuULJa5KbOGwhgzbxOANYu/mXhIAa6ak2fvV/eGB0+V264wUGVEDvLSrFiFAKaaqOOEtblImG2lQI4Hs9+wmy3AvYOTV63oA8x/mY4sWSKEFnhs4WZd4MV917tLr/LdRszs1qRBE4S3br51kRzukhBVa+x5HpRAs3orfOUE0htX2NtFGNz2rHZwmO3szmGR/ePpW23ygN40fJEiLk6Rpp5L6sVzIxVqoweV4M9dRie1oS9G2cJc0VUlocwRbN9eCDhYbxtVT9u3jKEi41ehybDhzrHaQ150UgIH9mzEN1JRYFx3LdMih0Xy4tTHS4Eb9s2BysdLk5E/dM4Bs+Xm0xzbVRpPIasZNwrzrWuymb1mVh5cPudy8UOScosdO3uK0Z0nvrTOmuy7glcrJjN17NyWVTG8C2qHnJeHRaM47mdAcK4tr1d40kkivjwm7Nnx4XzkuN1cjyeNU9YFeMz1Cq591w4IxU6p66v4nHoBhyv3l2S5OxYUTVFLwpjYwqbz9y8FDdtGULEpB9o9Rp/euV8/Y/0PEogWnDUxspsQ4tUtC7X2gW8n9nLtR3cOBEblQaqG15ASv9NVXSIkisvHGwRWh3j8TgWDCYGu+Vz2tP2UQdCyeGyr6UuqtNorxMk6Axq8vho3Rbtcjo01UVx67bZmDu1EWsXdGG6xr1v8/K+tP2tlF3Gn86cGRf+7thyLxn/FB+nva46AbbWm7uh2ymH/Eo658UabEVFuXjhsnZ+V+rfjQUmGJX5FLZpnDTKwkE8dPMy2+OMscqAv+NMc10UN1qUUfWqPHLj3ZKJcspP5ZpRyPcqwkztqMlJJQvAfy+iSoOFdOPSXtPwWCMij4rJQF+bs/BGJ/kcjMoSYxikNuRYtCgVVWub3l2HNSOd+Ni1C9PGoYHOGtuFzewpDaj3EGamtk+VPawMA5IkXvR/dI/z0Caz56uOb6OD+vs0yzHYUFOOD1w1P237n982ppvD+ttr8MSB1diwsAfDA01pA4bZIigcCuCJA6stE5Ub1wpaGcy4CIxD3BechqBUlocxwyYErzUlY6Zfx5hn5cbNQ8LnN73b3OClxUl5cqvzWC3QmuuinnP4eVnUSpKEy9d6Gxdb6isQDgV093Ngx7yiSCrslUzCWbXfiDY64NzRLsHe2SEOff8rLwvh0f1j2LrCWzi70VBt9/2UR4L46J6F+NwdK3D/3sW6dBuVmn7vxjD2/suGHe975mxcqNx0qkDNhfOYVhHzkT0LdUqTYEDCluS7Ul+jMQ+dV2WwBEkn6243cXYYHWxBS9JLV91fCkC3Xrhj+1zLaz1xYDWa6/RryHAoaNl/2jUeX1Paq3V59LzK6CU3UomSilWUh7HUwaS1d9NMXC/QDC4banO0GHSK9mUZhQDj3KgKTUbtZECSUsm9tN4+6oLDrEPEkcjl9PhdqzA62IJ9m2dhqsbCvW1lotPHKsKWnaomVobH7liB+65ZiDlTJwaxi1f2477do7p91Xdy5uw4PnH9olSCb6uE3ZuW9WH2lAbM6mvALRfPhiRJuGj5hHVz7YKuVC4BFaO3kbYCjlG5Y0xWrP4aDEj49L6l+OiehZg7tVG4jwizZ7VZ02ZVESjKi6Bi5e4N+FNxAbC24DnFSUu2rpiS2q8qGsbjd65ydIwIv3POmA22M3uthW1Af+9eB1+Rl5s2ob0fNNdV4CKBohVIKHO9uN6fu8C5wGb1bER5RbRyT1TgzbFmpNPxtbXWGaNQHo/HbUN+zLjWoqy4HUbhy8pi6CX+/vjJs648ZuMmabeMyqK2POZdySfvuzRduH7s9hVorCnXPxPDM9+6Ygo+bJgH5a5aneXRGAapDb/SCrFTk9bTFo3AWBEJ4bqNMzBfbsKOtQNoa6hME3wPXDGC3tZq7Fwnm4YzSx4UlItmtKCpLorV8zrS5mAhyW9apCx3SlijnHIyD9itnzYv79OFoNgRqwjrCo/Yrs8sHqtWSTU2p013smBA0sljJ0+dFY6hbpQMdhZxNcS/pS5dkexUgd2bNIJeuKTXUr5RqwBZnderUSccDHgOIfKCJAEjsrc+rd6/9jFIkuRrziOj/JpvrGQBu36mHdu0+3pZ7HvNuxOPp8tn0UgIAUnCfbtHHRfeUTG23e4ZSEgYIMrCwVQ+3vt2j+KTexfjqvXTU21z41Q93ZBvZ2ZfvdBLFEis3y47ZyDNe8bpK8hFDSDtM5Sgz0dVWR5ONUJde3a3VunWAZ6NnQYvRJETRfohUqrNWoPkzL563/N3Gef5ZbPbcPHKftyydTZzHqmIPI/OnnWWmHZ0sCXRwZJkK2hC+7Ji0bDO4mh8kWougeOnzgAA1iU17ZIk4doLZ2B0sFkXgvShqxfgklVTbT8ItaOPyM24+4oRXHHuAD60awHqqiK4ar1s2anWzu/CHZfMRSQcRDgUSFNsGd/BjKRb9qrhDgQDgVR7ApJk6mq/aVlf2kSqWm7bGysRCQcxPK0JF6+cECSNlg1tKEEoZFAeJT2PUhOsxvOoriqC9sZK3LRlCJ1N4rCftEV38s+Brlp84rqJanpaa3F9dTkev2sVllvkY7LL9u/VG8P4nL16Ndxz5Qi2JhOzOxF0QqFAyroxHnd4jMk9+p1zxkzwuEOwYDRyr2FhKEKUyFWLSFj3c9BRE+mdMeRWWjqUEO7j8bin61kl/DeiHUOMi4JegVeH1gJszJ0CwFQRJkKbcDhdeQTcuNlbFUgz12BHxxo8NEQ5BFS8CMb11RFM65pYFGtzvxmFt3hcX9Vx0YwJ742Vczt0i49sVBYqBkRK9khZEA/csAQfu1ZTNdXwbOuryoVWWqOHjJalQ234RLISq3ZK/dTNy/H5963AgsHmlKdyKBTAohmtuu/LbGhdNdxhWkjB+F61Cqyls1rFCYqTgvIV58roEMyP07v1Shn10SyyUCpoefDGJYJ2Tvxb681qht065cKlfULFoBkBScKNmnyHmSyEZk9txNUbpuOBGxbjynXTdflcrt80MzUk97cnFH+ia4WCAV2Ir13brVg32oUHb1yCrub08dhp6LC61+axKWnK9RG5CQ/csBh/fttEsnCR8uuCJT3YvnpqKhTpE9ctSlvol4UT+T0vWJIuC7TUV3h2bzA+IydeMpLkPeuRej3joq6Ux1mre7PzgL1Eo5jRGlWMcqxZrlAtVrlHP3H9IvyvD60zUbbHTY2unc0x14pE47flRSbvbI6hqTbhcXfeosRaw5iSwwrjGk+CuWH59NlxRMLBtDksV322uiKM27dbe1zqlbGJ/9ZXR1LrZnV4aGuoxAeump9cK2uOyUAAd6qEUdugXQdng03LJmRlUdc6b1EP5k5r9D6GeTyuYBF9gO8cO+XpXOpCN9s57LRhTAumTwxA21b146r103GuJmRLK0h0NMWwd9Ms3WK7sykmdG9PYTK5rp7XmSppu2Juh2lyNCBhle5s1guNf3LFPLzv0oS7nVEwaKiJ4okDqzGjt153D5IkFhTNiEXDeOLAanx0z8LUh3reop5UbpB4PI5tK/tTOZi0fcGo4FJdPo0LfO3EFAhIuPfqBbgjeV9VGu2w8XtXB51ZffVpGf+12A0Udt4GWk8FNx4QxsVDICBh/cJu1+UlJUhYlPTiczLZBTTWNLP8WqJjjJjlWXCL1nIUkICVHsvBO/MAs77fUDCAXRumY7EmtMTPaUTNi2FUnqvjhUfdEQISHPcb7flvv0Tvjrt6WOBFpHlkIgHezUSrs1Ya3lccCVdfL2Qy2ZuFHotwK0w+dscK1FeX4wPXTIQDLZ8zoUAT9UZteE9dtdaIAdxy8ezU341ZqjxayLjNI/HYHRPJKhtqytMFc0G/uX/vYt3f6vvQJ/EMIBwKIhIO4vpkjipR1/BiQTQesmHRhOxwzQUzMEfgvWC2sL7/+kV46OZl2LaqX1dtSw2jOH0mfVFz//WL8PGksWXVcAcuXT1VGEanGoJGB5sdGVC85jSzo7Mplhz70s+v9bixCp+SJAnL57SjsSaqM6bcsX0uZvXpvbi7mmM4rRm/d22Yngo5FxofhNez+11CfXU5wqH0Hf0Ind23eQiNNVGdYXbDonTlTzQSwrrR7lQ/bqmvwAM3LMETB1bjsTtW4N6rF6CyPIwdawewZWzCaPjo/jF8aNcC9LVVO5YxjIzNabdU5IuQUv/nHlUcNc4lfnoeFZoeysrL0e6tab+nkIVc78abUERLXQXqqstRVxVJ8zKy61rVle5kaeO3VZ5U2mgjJtygGrVOnj7r6Xg7zO7f1byTwbB8dtzeU177/ajt+tsPrcf21QlPau3as6+tGqFgQJ88O5OcR04P1bQByJ7yyCqyRwvD1pJoO7KqRDBawkRcLsjpMDrYglXDHa5jWlVrnSgvjxZ18FA1vZeunoqtK/oxs7cO60e7sWFhD2LRMC5dMy210IkbOp5bRmc4T+62xSR8SMS0ztqUcsguafmM3jrIXbW4eGW/5wWcFu2j2LCoB9sceMZMaa/GEwdWp0JbtC6EWgIBCTN66rBznYydFoke/fr+7YQ1rdeDm2vWxvTKo0g4iEtWTcUaB1ZcLbokkSbXv9CgkFN3Fwn0onLUxvd2z5UjuCNpccj0MWtzFAQCEq5cb51Y3Qyt941ZnioncuzYnHZc7UP8sRXGJPbqGDnuVXuUOInD3Sb20yaKj0XDQqu2tqWiErhen48xnNlqcWlMRuhXG4B0QcEqRMPNwm2wpy7l1VQTM8udo7/nOJBK4nvO/E5UaCyOxnY210ax1IFVt1T4/PtW4LO3uCurrn1fA121joTCZoNSLqU8Mnn36vckTFzqQfA1zgtmCwGtF5rWoqmlua4CNZVlCAYCaGuoRFfSwKR+anJXbZpVu7muImU827lOxrkm7v6xaBgf3DVfN1ZaYZbzKFPuu2YUn7lledrYfumaaTpjjpsFgZoHSPWsNh6peknLXbUYm9OOxcnv0OkdGhVZf3LFPGH7RIpsp8lc3SouL1zSi+5m59V8I+FgaqwyEo2EUoZPrzrDcCiAyzWeXI5yIEneF37qWOu24la+8CPPn+WtuXhxurC1tEq39s/P6aXcKqDDoaCrcCNj11H7hFmCe7u+oc7/J09lR3lkhvOwtbhn5S6QlGNtrqULW3PYLq33rGdxGBJOCYwjIoxjS76VvAxbw0QitUf3j+EDV83HxSv78akblgjzGBk5R7CIDocC2LlOdhWmsWPtQMp90UpRc/3GmamEkaqmORoJIRCQcMelwzo3TS1qx/Pa39xMAsFAwNPkaBePX14Wwl075qXKNn5o1wJdqJfTSiJ2eGm7aMEmSRJWDXc4yhPkdWic3d+A8xf32FbM0Ya9uLk/Nb/M3k0z8eCNSyYq9bl8RJJkPtjt2jAd1144I63yjjopNtakW0qNiycgfZKc0ladyhORsXCleUHtFmVD1492W4YFaAXyTJNc+pUY2qzEsTEPxFAyLKC3tdqzm67Trqfdr7E2msobcuLUGU+CvteJzugpZnbtWy6ebftdZWIpMq7FrBItW4WM3HW5PuSmx6b4ACC+54ryEJ44sBqXnzOgU9aJbrEug4SnxUY4FHT9XactZAzP0MliRPW6MfMeVs8g6oNuvo3u5hhu3jqE4Wl6zyKzvq0t/+x0vDKeqbqyDI/uH8PdV4zoEnY6pbe12nHFzmzn1/BTObV4ViueOLB6wjvY8A5U5X/YYy6g/o4a7NOE6E7rrE311QFNfiXRu7eabzcu7U3928uQqC4kvVQJNMfbe4nH9e/UGOotIpN5QFXwp3ke+biS9DpXiviIIbn9ZWvcJwoXVWJWcaNUsApbE4kzq+e5L4UuapPfY4rRyK6GmM/pF+eqslPkppRHp88KwzqzhRuZ/J2j3qKAAOCEA6VYQPOMRK0SKYVn9zegRjVsevxkVE8mLecY8nOODCRkX7UfTTiC5Fd75HX1UfDKo2Wz27DCYWjJdRcmlETRSAh9bdWQJAkNNeW+lQgXLXSNrJ7XgW2r+nH/3sWWcdMLZ7SkwpvUhfxxJxrjHHc4VeB1EzbkVujuaa3ShXq5LoedfBbGwV19RC11UdyqCcEQobqAe862rx7mcYbpaKzE1hX9ae/1gb2L8ZFrJvLrRHQLPAmz+xtQb8hLIUpMOiI34WPXLsSC6c26sAC39ytBmojXN4y0Y3PahckyO5piuGnLEK4UKDdEC6o0ecAi/MgtWku7VQXGS1ZPdZyc2SzJubeu4P3++jUeM1rX5/MW9eiSyQ8PNOHR/WOY0l7tzeohSY77jXavgCSZ5mFKYfPMRHJKIizCWrGhCpyqK6/a77aumDIhOACY099gq1DNZOw1Hmv1HK1+kw3etGb7arenP1r9llUai6foHv2u/lZq2C0ErRZPKtFIQpm3fLZY5okLwtq8EAwGMDytKfWetadbM9KZWhxmsl5SFU5G5cDUzhqhx6m/ZFd7dOzEGcPl/Lue+irU7iJ312LVcAeu3qCfr9xc0piPRQ1Ru36TOO+bGpasLgz/7KaleMAQYnnR8ilphiItV66Xcf1Gc8Ot+j2o4aF+KOS8nGJWXz02LOrWLSyd5El1FapiQFW8nTh1Ju23necOeBprjQpZv0brT+9bmua95sWIZ/V+3fRlrTLI+JyMraqIhHCeIETSCWk5An0eU4xGvZ7WKjxxYDUGumqxY+1AWkEPO9m3JlaG7uYYrlo/Pc373zGGS8x2UFREKyv023ht79owPSNjqV2v03sepe89oycxJ82aUq/b3qauPzN4xcZv5PK1AynjzBXnDuA6k7Ewa0t5hx+VV6NEwSuPdp83iKschpZEyvy5nfuvXyRUYBjzE2i5ar2MXRumQ5IkBAMBNNdGhROAKI+CWlXo+Mn0icSIqphxoqDxY7BTF8Z375zn/BgfS2xngjrB3XDRLAzYxLPv3z4XN20ZcpwM1+yDd/rE0yphmJyvsTaqc6vU9h8JwG3b5uDBG/XJ/UQCmxpKYBxQzVxkVYxxs5LkTXCYN9Ak9NwSPS9tG//sJv29eV3AlpclXIq177fch4pziXO7P8/YnMwXT39yhf6b1E5eH756QuEYCgZ0iZOBCYW1V0WIc88j/Y6qd0t/R7UuR4BqpWmpt1bQG8/3mVuWYURusu0XKc+j5ISq9rvzF/fig1ct0J3f7pmY/WxWJdDqWK9lqYGE94ga9mZ2GouotTTsxm2/jDB+sW60S+cRUwgMdNakxl/jO8nEZd94Di9V0v7kCvNS4B++ehSXJhVGO9YOYK2LiopmbF3Rjwf2LhbmMMo2G5f2ZfX8pw3KBT+XlcZ+EwomPOCNeQv9CCUyC5tV1/lqW2pjEWHes55kKJnIuLhybgcWWnjfq9dQPTCyFWpox+3b56I2FtGttczG5W2aAi0J45m3+VP1uldzin3mlolqzqvmdaLVQ3XLNIWsT4tScX419+exGv+shsZ9hsIWXc2xlMHUOA52GUIhH9k/ljb+eA5b87l7VljIn2tGOtFgMIjZyTjBQAD37h7FnKmNtjKMlcczMJHGxcmz0l7qfAulVTye8ILcYJWT1wa7Z6D1vhft2dNahb+6c6Uut5wW9Zk7SZivRVUSXbyyX2gkr6mMCIu2ANl3BFk53GF5Dbtk9WYUxirfhNUCy7+VAOs0PtuO5roK09ApMwF7bE572gLN+MIGOmvwgavmpx2rLuTeM1qzBGxc2ocLl/Q6styVhxPnrYp6FzLu2TmCi5b1+fZsc4lqnXUyANZUlmHegHkVhnSMH6O6OE38Z77cZFqpDUhoovVHWw8galLwiEZRYWaJEA0UZslf7ULxjAnNdYtrP8a8OHQhi4Deqm7MyeHV4u7HvD+tUzwmtNVXiL2qTK66dFYrdm0Qez25ub1pnRMK0Uf3j+nesdMEx15fodPjJAm49oIZOrf3+/cuxu2XzEUwEEhZqkZntOCJA6ttQ4SNz6c6ub/dBKzmpVLfiHZMSPd0szyV6bVWzLV3jzf2X6tr2SmP7t09ivOSFQjNvgvtfWZqTFgz0mFdjMFH5k+3r1xTFgpaCuBuMJYsdsuWZF7EA1eMpBbMxn6SyTysoi60OxrNQ27NmNZZizsvU8Md9X2hszmGc31QGGkJBKS8JFp/4sBqy4qmfnD7JXNSlXABsYyxargjM4WrjeDS01qFe6506aVtwDhq3LxlCB/dsxC9yTBYs3x+KrP7G/CpG5a4lJ0SqF50qoHSD93RTVuGTCsL2qEdQ82qdmkrdVmF8DtlzUgnPv++lal5zE/8WpKK5jsvcpiV56XV3KSuxdRiQpIkTeQwNHwjHU0x3Ht1whhkpmhwOg8am6v+uW/zEK5zUazGDG0CeScY8zZmwieuXyxci6osn92OqZ012LbKPt+v076gPr9MvplpXbW6cFkjVpXLVURrWXXf2lgEj92xAg/cYO4oIkLN3Xveoh4Tg7zA71s1BNk8D9HawgnaK1pdwm0/VClojcB6QfLEh29dpvvbTdI9LZesEucUsuPDuxcItzvRHl5xrpyyOGipTLovGq1ZIiJlQWwem+LIu2fO1AZcce4ALnYwAJjR3VKFjSYJMq3Yu2kip5NT3n/pXHxol/j5WpGKGDNsTymPsujCrr47Yxtu3DyE+64xL+ee5m5r031uvXgO3n/pXMQ05cuduJQCiUTsTvI1iTD2MwnOBv87Lp2LPReIFST9HRNWyvF4PK06ndUcaVeNzhRBF3BrvDd7hnHExROGi26381xnZZdVKg0uz2q+tFwhGu/MvvfFs1p1i93m2qjj/jjVoLAzG2ft7j2oqTCX+O/Ey3FSFUt3LcHPiQTJ6u/WoWi9mvxEVgpmJ1524zYCiG7si2eWnyscCnqeN92i3vslqyZKdxvxc1QXJWd3g9VY3NOSCEcwhikY93FCQ005bt8+Rzi2Ovn61e8k2zmBss0jt43h4Vv1Cc1nZlhpyQ3dLVW42KaQys51sq4CXzbob880P6S+1wwPNKG9sRI3XDQL91w54micNnpIOEUdu9QxyUlYpx19bdWeF/bdLTFsXTEFD920FN0t4nG5rmriXp0qj9R8kyIkSco4Z6LFyX06j/tTi9YnXsPW1Pn42gtnpL551XAqOmW5STJyIFnZOsOE2SNyExYJ0jO4xapYBpBuUHaTssFOoVNXFRGnIknecqQsiLuvGLGUTyauNfFvNz1u49Jey29DfC0JFy2fIny3xpA5N91fPV08HkckHPTNG0h0nrT0KjbnUPuh3FWbFm3gqA02v7utKqvij9kuh2irc40ONmPvplnYff+3XJ1jbE4b1i/sxv/7f3/j+vptDZWIRkKOQsy0XLp6KjqaxNbCRTNb8fs33vWkpLFCkiSsnucsb4vfjA46r+qmMtjrLQRBdWE1fgTqdzvuLAm+K9Rzf/TaRbq/nVZocBt2UFEeSj2fz9yyDBWRkGNvMK/CnYhEnH+i7aGAhE2rpqa5CgPATIt3+b5Lh/Gl//w1vvv0aybXMH82Xsd00Xvxa4Iwe+WmPUEkjDlY1O1cJ+PwkRP4tx/8HsPT0i29XkL6vD5YIAeZAAAgAElEQVQC0XFezjV7aiNeePUI6mJia/Gdlw3juk99e+Iamt+0i0d7YTaxQ11VBEePn9b3WZeeR0bB7KN7FqKpNoozSeV/MChh/EziRV5z/iD++t+enTg2IOH27XPx+9ffxcy+ejz9wiHH1xGhCs9m+2rHvoryED5w1QL87X88h6dfOJRTBUIoGEg9HydctmYaYtEwzpnfiVBQwi9ePCzYy78byFY+p3uvXmCbj+tzd6xwpfg1c7l3g+N3bwhfKhREirj92+e6rpC0d9NMz6Wts6WsVxWZ+UykGo2EfFBMWaMqi9QQGrfvzoxOjwZlSZJw/uLeZFvSf+9uiekUPZIkOSo4ccpL//LhUfjVe4SJ1G365vUbZ+DYiTP4wr8/l9p21iIJuWVIb/JSoWAAsWji+avjtUghFUy2TaRs2XPBDLx38jS++dOXLdtv2yYLOpsq8fLBY7b72X7fhp9dzVEeX/50l8ocQH8f6j+7W2KY0l6Dbz/5imZPQX5TH8fQYYP3o6vxM+VokH2aastx6MgJBJMykV071Ta1NVbqog1ckbyEyGtr0iiPtKgD2L7Ns/Dqofdydt366gheOehOeWRWghZIWF6usCgDXyjcvHXIVeW5XLFznYyhKQ1pmnR1YPIj14QZ6tinaujbHYYTGCcCN+EXIhfnnpYqVFX6WbXEBElKTRDBYMBTGEskHEzFFHt9NQtntOCHv3rD8f5+9IB4HLhj+1xdgmW/LqqOZVZ9dXSwGT9TDpr+bqdMvPfqBYLnnbhuWSjguNRo4qj0Cc/LYuf8xT1YMac9LbeWSigY0LVNew29xSv92tpnqT6bnpYqXH3edHQ3V2mO1WOXS8R4m5XlIYRDE8qRSDiI08n2Lh1qw8G3j+Nr3/9d6thYNJzK1WP1yJw8zpTrs4kQpn0GB3bMQ11VBPMGmvD0C4dMn3l2cPcFVleWpaodmh0ZjwOLZrbgx8/9McO2efdo/PS+pZbvyay8uJZMvZ5UnPSXlJHD4ftIhRp4a1JOCXiII/Ji5FLRepv56d189XmD+D8/fQkDGYZSFjrq2KWGxvnheQQkwjB2njuA/+cbv/Z8DnXcXDrUiu8/8zqA9DlG0shCVpzwqJzMFN8cj4SGIuuTx6JhjMjNeuWRx5xHIkXV+oXdePxfn0VjbbpiXpX7xeFJCeX7ngsG8fi/Ppv2u6hNbvvSfdcsxFO/eRMPf+Vpx8eIMN61m9yaXl79fbtHTR0cjAxPa8STz78JYOL9aK9ZXVmGbSv7dcojY46feNxfo00myme3xn+3aE974+YhKH94C9/48Ut4/uV3TKOI9lwwiINvn9A8N+/XVGmpS8+lFvO4pi9u5VGy443Izcgs8tsd21dPxV//27O4acsQ/vJrv8TSWdmuHFIYiLwdCoHyspDQjXQi55H/A4L6HasD4fzpzfjw7lGhF44ItW3hUAAXr+zXVTrywgd3zdcNFjWVZXjnWKIspldLnIiA1vMok8pnLhcxhsNc55IQdQG3cftxxIUJetVzG2PIze5NpOhQE7qPDjbj7aMnsXRWG37x4qGU4Gp2nO68NrcjWsiqx4QtlEehoKSrjtbbWiUWKIVtsm5UQJJslRjmPUSsSFLRWiXVvhqPx9Hbal0RxC6BoNk9lZcFsXFpLxYMtuADj/9QuI8xH4exQof+fPbTs7rgCpkpj5K/T+2oQXNScFg2uw1l4QBGp3tfOLsloyHY4li/5iSvQqyX/CpTO2rSwjH9wFFy06JQAxUHoWAA60e78R8/+oOv562pLMOWMe+pBpxQVVGG4yeP59WjTB2eVW8ePxNmZ3oqYTJbo4cqnC3oqpJj/My+evxS6EEpuH7yv8PTGnHDRbN03rdO8S30Rmgocn/tSCiAk2YVpS0GL9G1lsxqwxKbdZfVmO7E4yU1t2axANB8uQk/sTAIajlnvvMoEi/vvrG2XHicdi2hsm/LEPZ88v8mL5b4T8LTa+J49bsem9OO7/z81dR2NWy/p7UKL/3xqO683c0x/MGwzSnGLuTOUcve898LoiaoitVpXbX41YuHdTKEdl2j9u9vP5VQwNklOTei7h8pC+J4sqqjaE0yX/YmQxV0ziMt0UgwreRrLnN8aJnV14CHblqG/vYafHLvEt/DzYg/TIStZc/zSDvWOlUcaY8LSBLWzu/KeIKSJEn4PXzs2oVCbbMVTisYZZLAz9jSz79vRWoQs/qq1cnN/WJP0AfcavJN+pE6IPe1Veu839SJyEmemNb6CjxxYDVm9TXg9kvmCqvUSJq5WTsJGBWZblCPCFlMTB/ctQCXrJqKJw6sxsO3Lk8ouiy0R7VOPbMcYjah6+R6QXu0lmzVs8TJUGCntEm7lGp5S8bjG5MZz0iGcK6Y244r1uo9TPvaqrFrg7iaqCQBWyxKYQPA6dMJhZ/x/anJfFXFufZzCUgSFs1odTR/3njRLF/KqmczRO6Wi2d7Oq5aI09sWNjt3KMwQ+7eOZKz3FGmOHwfar6pXlF+DDJBkeSQUhd07790GLs2TPecC9EPVLlMTUXhl+cRkLnBcDw1bmpCcgz7JBzdrMfQe69ekDLaWIXym7HFQX7TSDiIy5LVsT69b6I6rV+rI9EtekmYvcDCWGH16t0qvM+OT4SPZ3LOt949CWCi+IirVth0P9XDZ7FJYnbRBbNdxdqsL4uSR2vfvyqLGwtGhYIB/OX7V6bmOvWRzJnaiAf2Lsa8gSbPa3hRU9Od6p2fe8IjN3dUV5TpnB4+du1CfFJQ0X3ZUBvOX9yDTS71DEuGWrFlbAo2LetLecl2NacbkL32q6LxPDImRwTE4TtuCAYkXycsETdtGcpbCdLJjptqa66RdP9xjepSOyPLST69hGNYCV4BSdLldvGM4d2EQ0GsG+3GT5SDjuKu3SqPxJ5Hrk6RJuCkXNrd9i+H1013k9dsS17z/usXuXJnTruG6gFn0U86m2KpsEzVU0ZYvtdzK+wQP2CdYO/U80hU9cL4t82AkVYxzXLvhFfZ43etMhW4505rBP5dfKzdxH76bMKSa7RKffCq+Xj3+GkcPpIQgL0KafOnNzuqfGZHNosWzE2Wu3bL5WsH8JPn/oifKAfR3VKFh25aZps/8bZt3hRVucBN2JpTkWTeQBMeu30FIsm8CHZJXicdReTI9fCty1PzZkNNedpiL9eo47Pap9zKyTdvGULYpD9mKvOpx+tCo42eRw4+uO6WKnz7qYTXhZvE2G6UX5+5eVnq+/Sr+qQWoZ3I5laEj0azzeiN4vpcFtTGIuhvr8ZmG8MLkAg9XTbUhr/46i/Sfrt+40x862cvp3KG+uWs8Mm9iy09jkXkwkPQ7PZU5a5Zm0PBAP7i9jGUhYITuQnjE7+pXXn2lIkwX1Uhl3bNTO4zk7C11Cnyt1YXFdMCEs9wq01xBhHBQAAXLOkFACya0Yq5UxszWiuktcu3M2UZUfyqW02cyqIZCW3fgzcuwf5Hvp9Ru+zwUsKU+MNAVy2Ul97OikVZXcR7dQ0OhwL4+HWLUO+xrKxTvIj68Thw1XoZb75zIv1HCal8LplYQiYG64lt/R01eOLAakfHW1UuEiGeEzKbke2sV15jlU2vJzhRs0uvsvSTJv6jFWw/vW8p7njUelwU9nsps2/CLXaeRzrlUUBfbU1L1DChZiNHmpWl1sqDz66fnz6jWu/156goD6OiPJwSFlY5LJywa8N0/MSHHEJpWDzSGy6ahR/+6g387Ndi932rnEdeeejmZaipLMOI3IRrzjg70aP7x/LqqeEvzh+eujB98MYlvuVnKjWKwTzodsGabVLV1lJeoe6eojFBrhbtmWpiZXjn6CnhfmbyxkQZbQvvFcmZB87pZM4jT4pXB+fXz4OuDnXYhPQTefE8Ul/KZedMw9r5XTrlkdWi3e2lQsEA7rlSXIbeeK7ysqCpcWSwpw6DPXU4lJSD3RgsrYwldmHxKqp8OdhTh6vWZy8nrpqWwOrze+S2McsqyKqcIXpX4VAAD+xdjBpBUZRsRg+5OXOqj3sYyPdtnuVPI7KMn4ojoIiURyK8lrhUPRtEnZmUDpuW9WHRzBZTjW6+aa3PcOFvQSrRqYdJPh6PY8XciRxMkbJgKlZdkqTUuY3l4t3gNnGr8bglQ22pJMROEF3HfQI6/Tlm9zfge8+8hp5WcVJc9Zp+GVeyMc+qp9RXkXFwXA49j8zD1iauKMx5pDlQXfSLhNRwKKCroLl6Xif+93/91rQ9ad9UhjduljtMktItybFoGEePn079ffpM4rvUViHVUlNZ5lghCyQswtnwSLD6yruaY1gwvdnc6ycLyjw1KXowEEDQxrbwyb2L8d6JMyWhOEp543o4tr7av6qdpcLa+V34zSvv+BLa6TcXLfdmXM0VqWpr4eyGrTXVRE2VR2aohgf9UK8fp6d11joa+zct68PbR09ivtyMv/n6c/YHCPj0vqU4cuwUPv7Fn6aMd6lWmXrg+jMje5E73IaaWYat2QgkW1dMwfRuZx78PQ4KGBhRFRyuKiQ77cqW95347+z+hsyNhBbcvXME//PLNyzX006NtWqbje+s0URh5qfyKJPRY0ZvHZ76zZumir1oJITqijDeeOt42m8jcuae2cVI8UtDhJgQCEjZUxwVkEbZCi8GIqP7+KO3jWH/I9/Du++dhoSEh9CWsSlYnoHA7FXTr95OQEp4lv36pbedHehDwmyjgDN/erMupMP0msYwJ499Rzsh+yVmpxJma7zInCXedbbNT4zKSu1zFFnV1cVITawM/R3V+M+fmAupH79uEY4kk0LaKQmc6I4+uXcx3nw7XdAQYeXB19umF3Y/umch3j56MvW32la3nniZ4KRSjRvs+s2y2W34h2/9BgDQ11aFcCiIX7/0tqXied5AU8qTSasY9IJTS3GhMKuv3jzUUB12i8FVpgioq4rg7ityWa7FOf3t/idl9xNVCaKWivYzvcPYnHb8Y3LM0A4wl58zDZIk4e/+89epvHAihAmzDWxfPdXRnNdYG8Udlw472NOcuqoI6qoiaKwpx2uGytJajxBzRZJ3PHkeZWiY01/L+tjzF/c6vo7V+2wwUY6r1w/mKbt8tsfq3tZq2yIiThnsqcOaeZ04b3GPo/29P1MJaVJw8s+qijDefe902hFWrBnpxIjcbFoA45HbEmlzrlGThLukFKdbKo8IKWG8aPaNA10gIKUmXTVJpBpL6xVR2Jor4u4sYn5ErYkEHFPFkeaankWOtBwLQF11YnJr8c1rLXERrUu2k7hvkRCm3dZSX4E3Dr/niwCrehA9cMMS3XatAHvNBTPw38+8llIyfOSa0VQJ9xVz2m0rL9ZUlqW8UexwcktNtVHHSgerb7SxJorH71yFv/vPX6MyGkZ1ZZmuOt2la6ahp7UKMxzkCfOLJbPa8I0fveS5KopbKsrDuPfqBfjsV57G/kvm4r+eesVWaXzTlqGUJ1OR6Pl9Y/vqqehoEhdvmGzPghQ+6hzqZ7iw1gCg7fPzBppQX12O+dObEbEII1PHbmPxAy2hoGTrFZMpTs6eDYWR/TXdH2PmiZ34zfJq7i/mkkf3j5mGpanP140s7bgnl9iAHAwEsOPcAcf7G7253HqsfWTPQvz42Tfwte//LvXMvQwjkiRZVk5V+8DDty7Hy388ih/88nV89+nX3F+ohGD2w0lCLBr2XI6YpFMsT9JNO+uqIlg1rwN7LphhcT6/zFmJ/7hPpDsRdpGp4Ob2aNeTkkZ79OCNS3Dxyv6JDR6QIGFmbz3ef+lcnL/ImWXH9pwCN2P1PoMBSVe9RXSc2bZY1D+7hDqpq2VMU5XoDJ5H5452p/7uaIqlPI+CwcBEmKQf65M0T7JsjQYTQuvOdbKw8lo0EsLqeZ05yzOVapmfc4mDU3W3VOHT+5bqPcwcvss8GYxzjps+kM/EoIRoKQ/773mkRfRV1FSWWeYAmTutEffsHMGKueYhvKos9KlblqOhOn8pMLT3lw1FktjLyPrkVgoi0ThllfszF+N3NBIyzeeWqryXjfVTjoZhtdpWoZG2JnX5iLW7p81pWXhdsWgY03vqcPV5g472n9aR8P5sqi29kG96Hk0S/uympXRV95HW+gr87vV3S2phEg4GsPNc68R8vrlCq0ogt2Frmmg3u8l82VAbvveMuXXAKMQc2DEPtRZCjNsFl9bSVl9dnlJ+eFXiqs0d9FDy1/SchnMDE/dZGysztcb4pkR0wIEd8/D8y++k3vc15w/isjXTbF3na5M57eqrIr5WoymhT94zahcOBQOp6ou5wo2SxFNi1xIm10pGkn2GpzXiyeffTNuezQqHfhLJQtiaDo99vr/DOuxPPe30nnpUlIdx6MhJy/39QCSC6BRGmu1+jX2i09iKMA4ufdu22fjMl58GkMgfteeCGXji68/ilYPHDNfK75il5gIa6KrN6XX9uu3P3bEis8rIJnzs2oU4dTqzuT/Td6tGQgCFGYq9dkEXZk9tzGp+23xRtMqjgU738dxrRjrxvNMcKSVGJpWxSDr7L5mD3756xPcM9r7hYSS1mmAmlAz+CiSZDPh2TbGqDiGipS5qmUTfrWxrtLSdOJXIu1IecVaxyHh7Tp79vs1DqK1yUV1QcMq66ghm9zfgAqtcAjmU5xpromismQgBCwUDutAtM1bN60BdVQTD0xKl3C8/ZxqWDvmQ2DZXoQG5uYwn1L64/5I5+NTfP5nZuTzub/c53rd7FLGKMD7w+A89tKr42HPBIP75uy9ahrSqQ0i21ukk9+zbMoQ9HnNxFAKqMcXPhNlasuYXKvDW9Quz89ldRtsmvyojiiurTvxzsKcOz/7+Ldfnnd3fiCvXy/hf/6EAiKOvrVpslMrzRFiZDJt2owBw2h+sdksZWDNUAmerQqYf+WSNBmCnr1o1cAYkKU0e6G2twi9ePGxZxTZXSJJUkoojIAPlkSzLSwE8BKAMwCEAuxVF+b1hnx4AvwDwQnLTG4qirPN6TZW/unOlp0XsjrXpsZgP37o80+aQSUhVRRnmTG3MdzPscfGdOPGI8c/zKIHZxHhgxzzUxtIVBHVVEbz5zgmEApKt1SLgcvKwH1Mym8SPn0xUxjKWhveTEdm8fLEIderV3nswEMBt2+ZYHtdcG8XvX39Xt01oFc2j5BeQJMzTlHM+Z36Xb+fVMhmdOdRn4EsotNsHaKM9WjPSCQDobBbn/SlVelurcavNd6t6Em5Y2G25HykeTOfBAlcQyl21UF56O7WAzFrYmqT9d3YGa60cc9k50/D333zel/MW6tyifY471g7gTw0KeuG8b1G0ZCJBueBanlvpH90eqrS5ISJS8Di1khQxXj2PVEWzqELcDRfNwisHj2VcRKSlLoo33jqOz96yLKPzlCqZPN2/A7BRUZSnZVneDeBhAJsM+8wH8CVFUa7P4DppBH3UKIqq9BAyGcmle3BZ0lW93CThtJmL8L7NQ3jmt4dQX10ubG91ZVmqapbbda3d7buWbQ37nx1PuPhWOhxzClVwBIBdG6ZjdLAZb75zYqKqTRJJQkkLPLFoGJuX9+GfvvsigOwJt1YJHPON+m3ZhXJWV4SxZn4X/uk7v/W9DWaK5wL+bPJOeVkITxxYne9mEILbt8/BiVNn8eJrCSPE2UKMO3GItund2VRaO3xGC6Y342wWw4n1eZYEvxu2PXLbGL7yXy+Y7m/pgeODIPTJvYuFCprsdTlnJ1bvbNCi4EUmTSzUXEcqRuOT9lXP6W/Az184ZHl8KBTQdMbEk4pGQpjqITLJyEf2LMT4eDxrnlvFjictjCzLEQB/qijK08lNTwMQmbIWAJgly/JTsix/S5blIY/tJIRkGSdJcP2abJfPbsPWFVOsQ6MEVFeWpUKPRDKFdjJyqwyzE1Lc5zxSz5v474VLerFutAvLXIZOnTO/E1e4qGDhhlRepmQbnbrYRiMhjMjNWDeaPuzrHlOJruQvXNqn+cv/m9y3eRbGLJK15hv1W7FTqH7mluW40KYyo/uwNZvv1Lh/IWthCfGRD1w1H51NmYeT5IJwKIiqirJUeHn2PI+y//1rZQM/rpfJk3jktjFct3FG1sIAgYl7XL+w21FV0YryUKq6XViTQsOw7s8aTbVRXah7truEH2FrS2a1AgBGBtx5k6t8/n0rcPPWwl5ySxYaiF0bptseHw4GMq/cbEIoGKDiyAJPnkeKopwE8EUAkGU5AOBeAF8V7Hoiud/nAawH8FVZlgcVRTnl5DoNDZPL7byUaWrKrtsn0bN3yxw89v/9HL1ddY7zXUXKgqbvSc2H1JCMc/bjfe7amNnEVl6e7sGjdWOtrNR7bqhtntpZg9+8/E7aPTQ1VVl6IgaDAVf3rbavqqo8ddxN250nu45GE8KO3NuA9S6VbE6pOXQcABApC+HhO1aisTaKqgoXOZM01Cf7RjAgIZScdOtqK3L67U/tqkVncywr1zQ7Z2NjzLE3mVPWL+u338mCbD/zSDLxeE219cLBSTsaGmJoMigtrY5Tv+totEy4XzQa1m0XLebs2lVo81WhtYdkRrbe5+jsDlRVRfGxL/wQC2Z3FIVnff3bJwAAoZC5/JEJZRrv5sbGGOqrvVU+uvvqUTRp8rxo2xrUyFi1tRXCfbTY3WcoKW/V11fq9g0YZLlQUDI9157NsyEFA/jOk69YXsuKv7hztfD8tbVR/MunJwJN+jtr8MLL76T+rqvTz/tNTVXYc9FsNNRVYtOqaannVZ18F2WREJqaqhAOTbyr6zcPYcOSvqxUia5++QiAxDwmur9M+2H1a++a/qY9d/XrR03b0dRUpXvGpUhVTP8thsNBSFJCEdTQmL7+Nz6jttYaVMb+CACoqBDLA6Lj/ELurpu0c7Ot8kiW5W1I5DbS8pyiKOfIslwG4G+T5/m48VhFUe7V/Pl1WZY/AWAQwM+dNO7QoaPZq8BAckZTUxUOHjQfTIn/TO+sxmdvWY63Dh+z3znJyLQm0/ekWrEOHTqGhppoQbzP06fPpm3TjhcnT57W/aa2ef+2OXj76Mm0ezj05lEct4iTPn36rKv7Pn48oSM/KriWs+MT7X/36ImsPe+33n4PQOLeYuEAThw7iRPHvFWNOXwo0dfG43GcSb6bt95+DwcP5m4Bc/eOeQCQledlds5Dh47iPR+quDm5lhNyMd6eOZN4v4ffth5fnLTj8KGjCJzVf8tWxx1L9s/33jsl3O/E8dO67UaPwZ3rZNt2FcL4psL5s7TI5vs8ePBdNMbCeOimZTh+9ASOHz2Rlev4STSpKJnb35CV53JGIyccOnQUZw1ygVOC4+O69qn/bmqqwpkzEyFip06cStvHiN19quc7fPgYIhrdydypDXjtzWPoao7hpT8exZmzcctz7VonZ6Q8Kg+I23rkyHHddqMs9vbb7+GgRpZS9z1nuB2HNTLpu+8mxvITJxJj9qy+Ovz21Xcwd2ojhqfU4/Cho57bbsWRdxNGs5Mnz6Tdnx/fZ9Sk+Myn9y3VnfvIkUQ7Tp1Kb8dk4MRxvR/JaU31NlWeBID1o92orixLe0ZvHT6KuoqEfFlXGRY+w2yNt39x+xhCwUDRv7dAQPLkqGMr8SqK8mUAXzZul2U5BuBrSCTL3qQoStqILMvyzUjkPFIDFyUA3kZuQkhWOWd+Z76b4Ao7g5Q2bG1690QOpWgkhKhgsW/nyuw24XIqCaSro3JNdhpJlb87prRX47evHsl3MxyjflvjfqTV8Lnv9bRaWwJXDXeY/nbeop6U1Z8Qkn3qqiL4y/evzIqHCQDdxO7lCpGyIE6eSjdUadHOdy11Fbjr8mH0tVV7uJoeo9fk1rF+bFjYg1g0jN33fwuLZrRkfA1P7bJ5kk4LZRir7m5c1oc1I52evZ8Lha7mGB68cQmqKsrw6X94Er9OemUVch7DfPDeyTO6vyUp0XfiiOs+1q0rpwhzHUuShOFpTfjINaPoaMptpFLBVtrOEZnc/RcB/AbAXkVRzETIFQCiAB6QZXkFgCCA5zK4JiEkSxRbbpDe1mr86Nk/mv6uLQN668XWVYgA6xxJ3pLM+qSYyaImRhXa/EiWLkpgXFw9yhw/FgKlhDpWuM0DJjxXspfcdfkwPvmlJx1c2/y3T1y3CM119jk4zLh4ZWbhgoQQ9zgNrc8HH71mIV47ZOPBrct5lAhnyQSzUTUQkFKhiI/cNoZIWfaeW2ONeXhf2hjscRqY2pFIbDw62AwgIYcUu+JIRQ2P7O+oSSmPiJ5XDqZ/V2rBFV1SdoMk2dZQgdcOvZf6O9eKI+JReSTL8jASldV+BeBnsiwDwKuKopwny/JeAO2KonwQwK0AviDL8pUAjgO4zELRRAgpUGoqyvDO0VOuK5hlk3NHuzDYU4cPf+HHwt+1lsyISVU3LdnSnXk9bVNtQvioqcyeMJUNvZSEbFYxyT0P3bzMtCog4E+/KaDPyhEBg8XYD5wuuNTFU1VFejhkiyDhe5HpxAkhPqL7/j0MBg015WiwUKQA2ZvvrFqbaSlyOz68e1T399JZrfj+L14HkN6u9CIFzq7RUl9R8tUfS0gU8p2Asdqa9t/aTmToT/fsHMG77zGIKZ94TZj9JEzGNUVRPqf59ysA1nprGiGkULh12xw8/cKbqIkVjtttQJIsQ1TcKrr89rzKVKDcsLAHnU2x7JZbpWQjZL7chJ8oBwGYK++SBjLHLvqlxES1NR88j1w+vsXJKjSLZuYnZIOQQqStwVmlzMlGLsZnkddtJpy3qAdf+PfnUBPLnxeOcVy++vxBvPzmMfz+9XfTZKVSMhZli20Cr9bJ/txEoaqS6nqk3WbYp6I8jApBwRySOyZ30B4hxBF1VRGsmGueK6QQaaxxF77it4dCa1KY91rdJRCQMGdqo59NSkMVejO59RG5CePjcdRXlWPu1Eact6gH3/zpS3jxtSOOPL4KkRs3D2H3/d+y3ildxvFOkemfLl0zFfF4HM9jTRsAABkySURBVDP7nFcP9IuAJGHpUJvj/Yvs0RLimgduWIxKLqZs8WMsWDyzFT/45eu6bX4rAcbmtGNsTru/J82QgCQhnAwvTJeVJrkWhHhClC5B3aRzPKL7cMFB5REhk5xlQ2343jOv5bsZvnLN+YOY0esu74BoIrtoWR9efM1bIuN1o93oa63G9J7M8h9kk1RS7wwm532bh1L/vuXi2QCAjqZKzJeb0VnCseiixI6Thea6Cty6zT6PmIhNy/rwz9970ecW2dPfUY033yn86lOEuMWtoWQy4fe6c88Fg7jm/EHdtmWz2/DV776YlevlC5HHVsrYZHOTXOxroF7NlDTPI2lCnGIPKmyoPCJkkrP7/EHsNghDxc60zhrEBDlRLBHMVhuX9XluQ0CSClpxBGiVR/6eNxoJYf70Zn9PWmCIEjt6PtckEpUqDJUOc7XQ2Ld5CLUFFHZLCMk+kukfHs8nSWnz5YVLelPKo5LBxbOifsSc7taEAa2jqTLttzlTGzA2px2bMpAzixpRH5OsfiSFApVHhJCSYOmsVigvvZ36Wy3tOaXdWaWsyTlVUezzisi9ejLiZ/ReVpjsL4iQSchDNy2FFJDwha9PFHjO1kigVYCXtCHApDrr0JQGXeWsjsZ0RUkhMTytCUuHWrFlLPvVNRfNaEVvazVaBcUcQsEAdm2YnvU2FCrGcE8p+T+A03ahU7j1MQkhxAXXXDADC2ckkuhWpsrZLsddlw87On4yulrHTYRB4gQ+MwAIh92JEQWtaCKElAQ1sQiqS6Tsez4QzW5xkx8vXtGPm7Ykwtcry0NpVbQKjXAogGvOn4G6qtx4oooURwQYH0+XBiiKFgdUHhFCipplmuS5m8em4JHbxlLJQyvKwwiHijNpcy4wEwaJcyZ7xZTWusIWjNm1CZm8aBejORmqJ+GAEwhIKUXMZDTCEW/E012PUv0n7TdSUFB5RAgpaq4+bzoev2sVgIQHTUU5o3HdQnHPPapx1RcRp4hfwP7tc/Oe3+qO7XOxbrQrr20ghBQ4XI86RqQDSuVIFOxP72XiltUjnQAShWlU1F4kcEoiBQSVR4SQokaSJAouHolnK2P2JGDHuQOoiIRS5Yv94pJVU309X7apqSzD4pktzg/IgkVxZl89tq+eluvLEkIKHK0nTC6GgNKZSS3uxOFN7t00Excs6fGnOaTkGJrSgCcOrE4VlpFAUbRYoPKIEDKpmd3fkO8m5A0rSyKxZvnsdjyyf8yX/A7aM6xf2J3x+XJNQYcqFHDTCCHZhZ+/n5ir30RTwOhgS06SUpPiRhuitnFpwgupvIzpJgoZxncQQiY1N20ZwolTZ/PdjLwQTwqDhbz2J4WP0+5z7oIuRo4QQnJHjue2glakWyB31eqq1VrdhlVFuSK9fVIASADWLujC2gUMQS906HlECJnUhIIBxJLV2SYdqag1SnzEO077z6VrrEPLsoHaMibgJGTysX21JgyYY4Ap4w6ejdUuauoAShLEM5RDiwZ6HhFCyCSlu6UKADBvoCnPLSFA8bpq+1WZ+eatQ77nkCKETF4aa6KorizDkWOn6PVogahsuhnCNT7X/YRMGqg8IoSQSUp7YyX+6YEL8dbhY/luyqRGlbtvvXh2XtvhGRcLByvr9fA0KjEJIf4y4X2Y12bg9kvm4PC7J/PbCBPOGpRHwmprFsendqf3CCElD5VHhBAyiQnR04NkiFUODADYuU7GD37xOgCgv6M6F01KwZBMQiY5BTIEzJqS++Icd10+DAD45JeetNzPGLZmN6anwbA14pF8K3WJe7hqIIQQQvJJkSs47Jq/argDd+8cAQBM66zFo/vHUBMry0HLCCFk8iJ310HurrPdz1HYmsUuUto/CHEHu07xQM8jQgghxMCdlw3jxOncVuErVgucW++eaCT3okexPltCSGZcvWE6vvztF1BVMUkLYzjAGLZmtZIXDffqNioAiFs4NRcfVB4RQgghBqb32Ftr/aLYBe5ibz8hpHSZ3d+I2f2N+W5GQeNEdxS3WOYzPJhkCrtQ8cCwNUIIIaQAKFYLXMRDlTjKiYQQUhiMj4873leUD0ndQiUScQ3dgosOKo8IIYQQ4pne1irXx+RKXFTXMlZWc0IImcwYcx4JlUCOyq0RQkodKo8IIYQQ4plCtjYXbssIIaQwSMt55BJ1DijgqYAUKDTrFB9UHhFCCCF5ZDIK3Dm/ZUqohBAixEm1NToekWzQ0VgJAFgxtyPPLSFOYcJsQgghpBBg7H8W4LKGEEKscON4JKy2ZvgvIU6piUXwxIHV+W4GcQE9jwghhBBCCCFkEuIkbM3KtjHxE9VHxB9qKsvy3QRiAj2PCCGEkAJgMvkdtTdW4u2jpxAK5maxMZmeLSGEuMFJ2JrVKKr+MhlDsEl2+PDuUbz17sl8N4MI8Kw8kmX5KgD3A3gjuenfFEW5x7BPLYC/AzAFwEEAlyiK8rrXaxJCCCGlRiEnnPbCB66aj1DQ2rH5xotm4bevHUFVRXati0uHWvG17/8OsWg4q9chhJBipaGmHK++eSzfzSAkRXVlGarpfVSQZOJ5NB/A7Yqi/L3FPh8F8F1FUc6XZXkngM8C2J7BNQkhhBBSwPS1VdvuU1Eexqy+hqy3ZdOyPpy/uAfhUDDr1yKEkGJkw8JuVEbDePgrT5vuM+FdJDB2MF8fIZOGTHIeLQBwlSzLz8iy/EVZlusE+5yPhOcRAPw9gA2yLNP8RwghhJCsI0kSFUeEEGJBQJIwd2qj5T69rVUAgIpIut8Bw9YImTxk4nn0GoAHAfw3gI8DeATADsM+7cn9oCjKGVmWjwBoAvCqkws0NMQyaB4pJJqaqvLdBOIjfJ+lBd9nfgmHE8qNmpqoL+8in+/zqw9ciKBNyBpxB7/P0oLvs7TQvs9iereDvfWIVYTx41+9gVhVue193L5jPra8dgQD3em+AqeTibJDwWBRPQMRxd5+oofv039slUeyLG8D8JBh83OKopyj2ecBAC8IDjfqoCUA404bd+jQUYdJ3Egh09RUhYMH3813M4hP8H2WFnyf+ef06bMAgLffOZ7xu8j3+zx8mHkz/CTf75P4C99naWF8n8X0bt9/6Vz81b/8EgBw5MhxR/dRFw0Jfzt8+D0AwNnx8aJ6Bkb4fZYWfJ/WBAKSJ0cdW+WRoihfBvBl7TZZlmtkWd6vKIqqVJIAnBEc/gqAVgAvy7IcAlAF4JDrVhJCCCGlDm0lhBBCcobexj+tswbPv/yO67Nw6iJk8uDVt/wogDtlWV6Y/PsmAP8k2O/rAK5M/ns7EsmzT3u8JiGEEFJyME8EIYSQfHP7JXNx//WLXB8XTybM5lRGSOnjSXmkKMpZAJcAeEyW5WcBjAC4EwBkWb5PluW9yV0/AGCRLMu/BHAjgH2ZN5kQQggpPeK03xJCCPGZuy4fFm5XDRdqsbRIWRDNdRWuz19VkSipPk9u8tQ+Qkjx4DlhtqIo3wUwT7D9g5p/Hwaw0es1CCGEEEIIIYR4Q+6uQ0djJV55U5+Tzi9PoVg0jM/esgyV5SyoTUipk0m1NUIIIYQQfHDXfBw9zqh0QsjkY0Ruwk+Vg/luhntUzyMfvF5V7yNCSGlD5REhhBCSR0ohT0Rva3W+m0AIIXnhhk2zcOas42LSBYM0oT0ihBBHUHlECCGEFAIU4AkhpOgIBCSUBYL5boZnOPUQQpzitdoaIYQQQnxA7q4DANRXl+e5JYQQQiYLCwabAQBTO2ry3BJCSLFAzyNCCCEkj5y3uAejM1rQXBvNd1MIIYRMEoamNOCJA6vz3QxCSBFBzyNCCCEkjwQkiYojQgghhBBS0FB5RAghhBBCCCGEEEJMofKIEEIIIYQQQkoUJsUmhPgBlUeEEEIIIYQQQgghxBQqjwghhBBCCCGEEEKIKVQeEUIIIYQQQgghhBBTqDwihBBCCCGEEEIIIaZQeUQIIYQQQgghJUo8zpTZhJDMofKIEEIIIYQQQgghhJhC5REhhBBCCCGEEEIIMYXKI0IIIYQQQgghhBBiCpVHhBBCCCGEEEIIIcQUKo8IIYQQQgghhBBCiClUHhFCCCGEEEIIIYQQU6g8IoQQQgghhBBCCCGmUHlECCGEEEIIIYQQQkyh8ogQQgghhBBCCCGEmELlESGEEEIIIYRMAoIBKd9NIIQUKVQeEUIIIYQQQsgk4MF9S/PdBEJIkRLycpAsy80AvqHZVAOgSVGUmGG/HgC/APBCctMbiqKs83JNQgghhBBCCCHeqaksy3cTCCFFiiflkaIofwQwFwBkWQ4A+D8A7hHsOh/AlxRFud5zCwkhhBBCCCGEEEJI3vCkPDJwNYD3FEX5kuC3BQBmybL8FIDDAG5VFOUZH65JCCGEEEIIIYQQQnJARsojWZaDSHgcbTLZ5QSALwL4PID1AL4qy/KgoiinnJy/oSFmvxMpCpqaqvLdBOIjfJ+lBd9nacH3WVrwfZYWfJ+lRbG8z2BwIs1tsbQ5H/DZlBZ8n/5jqzySZXkbgIcMm59TFOUcJBRCz5t5EymKcq/mz6/LsvwJAIMAfu6kcYcOHcX4eNzJrqSAaWqqwsGD7+a7GcQn+D5LC77P0oLvs7Tg+ywt+D5Li2J6n2fPjqf+XSxtzjXF9D6JPXyf1gQCkidHHVvlkaIoXwbwZZOfLwLwD2bHyrJ8MxI5jw4lN0kATrttJCGEEEIIIYQQQgjJDwH7XSxZDOC7Fr+vAHANAMiyvAJAEMBzGV6TEEIIIYQQQgghhOSITJVHUwC8rN0gy/JeWZbvS/55K4C1siz/AsCDAC5TFGUchBBCCCGEEEKyTn11eb6bQAgpATJKmK0oSoVg2+c0/34FwNpMrkEIIYQQQgghxBvXb5yJWz5rFSxCCCH2ZOp5RAghhBBCCCGkQIlFw/luAiGkBKDyiBBCCCGEEEIIIYSYQuURIYQQQgghhBBCCDGFyiNCCCGEEEIIIYQQYgqVR4QQQgghhBBCCCHEFCqPCCGEEEIIIYQQQogpVB4RQgghhBBCCCGEEFOoPCKEEEIIIYQQQgghplB5RAghhBBCCCGEEEJMofKIEEIIIYQQQgghhJhC5REhhBBCCCGEEEIIMYXKI0IIIYQQQgghhBBiSijfDSCEEEIIIYQQkj0+tGsBfvX7w/luBiGkiKHyiBBCCCGEEEJKmJ7WKvS0VuW7GYSQIoZha4QQQgghhBBCCCHEFCqPCCGEEEIIIYQQQogpVB4RQgghhBBCCCGEEFOoPCKEEEIIIYQQQgghplB5RAghhBBCCCGEEEJMofKIEEIIIYQQQgghhJhC5REhhBBCCCGEEEIIMYXKI0IIIYQQQgghhBBiCpVHhBBCCCGEEEIIIcSUUL4bYEIQAAIBKd/tID7Bd1la8H2WFnyfpQXfZ2nB91la8H2WFnyfpQXfZ2nB92mO5tkE3RwnxeNx/1uTOcsAfDffjSCEEEIIIYQQQggpQZYD+J7TnQtVeRQBsADAawDO5rkthBBCCCGEEEIIIaVAEEAbgB8DOOn0oEJVHhFCCCGEEEIIIYSQAoAJswkhhBBCCCGEEEKIKVQeEUIIIYQQQgghhBBTqDwihBBCCCGEEEIIIaZQeUQIIYQQQgghhBBCTKHyiBBCCCGEEEIIIYSYQuURIYQQQgghhBBCCDGFyiNCCCGEEEIIIYQQYkoo3w0gxYssy9UA/hvABYqi/E6W5V0A7gRwFsC3ANyhKMoZWZZHATwKIALgDwD2KIryuizLZQAeBLAcQBmA/YqifCMPt0Lg2/v8GwCzk8e8T1GUb+bhViY9six/CMD/3969xtpRVQEc/5dLW8qzicVQQHxQuzCm0IqIgohRwBdaA0WEBjHyEBVqRKlNUw2CCgQBFSHyCG2xlocgb6oxoIIRNAhtEzELxEfEQoCqUPFRkOuHvQ+91HukvWc65yb8f1/uzJ45k72z7szsrLP3Ph+qu7dk5tyIOAA4F5gAXJWZC+q504FLgW2BO4ATapx3AZYALwcSmJ2Zf2+5KaKxeO4LnEd51q4GPpaZf2y5KaKZeA651gzg7swc32YbtE5D9+fkWr4j8A/K8/YP7bZE0Fg8XwVcXsv/Bhzt87Y/NiaeQz5zOXB7Zi6q+/aHRomG4ml/qAeOPNKIRMTewM+AqXU/gC8D78zMacBYYE5EjAGuAeZm5u6Ul+nF9TJzgUnAGygPgoX1fLWsoXgeBQzU848CFrXaCAFQX6IHATOA6cCeEXEEcBkwE3gdsFdEvKd+ZAlwYmZOBcYAx9XyC4ELM3M34B7gC+21Qh0NxvO7lETv9Lr9zfZaoY4G40lEbAmcT+kAqw8ajOd3gJsyc0bdPqu9VqijwXieDlxRn7fXAl9prxXq2Nh4RsSOEXETMGu9S9kfGgUajKf9oR6YPNJIHQd8ClhV93cH7srMR+r+zcAHKcmhCZn54yHl746I8cDhwJmZOZiZvwYOpLx81b4m4jkAbBURA8BWwD/bqrxe4BHKKLG1mfkM8BtKUvDBzPx9HbWwBDgsIl5Jiefd9bOLavlY4G2UROHz5S22Qes0Ec/xwILMXFnLVwK7tNoKdfQczyHXOgf4entV1zCauD8nAXsAF9XyhcALvjlXa5q6Pwcoo47A/lA/bXA86/mzgRuAqzsXsD80qjQRT/tDPXLamkYkM48FKANUAFgBnBsRr6AkIGYBOwBPAE9HxEF1StqHKaNYXgZMAfaPiAso/4vzM/P+VhsioLF4LgI+Ws+fCBzRXgvUUROxAETEaymj+s6nvHQ7HgF2pkyRGK58EvDUkOkxnXK1rIl4Zua/KR0qImIz4FTg+k1acQ2rofuTiPgAsGVmXjPkua2WNRTPXSlTwM+JiP2AR4ETN23NNZym7k/KyJSfR8QcysjAt2zCaquLjYwnmXl2PfetQ47bHxolmoin/aHeOfJIjcjMB4B5wI3AnZRM7trMHAQOBeZHxH2UpMJqYC0lYbQzJaP/cWBpRGzXh+prPSOM56nAXZQk0zTgG/WbOfVBRLwe+BFwCvA7YHDI4THAc5R3wIaUU8vVJz3Gs3ONcZQh2psDX93EVdb/0Us8I2IHysiUk9qprV5Mj/fn5pRpGLdn5l6Ub8oXt1BtddHA83YxcHxm7gScAFznsgz9s4Hx7Mb+0CjTYzw717A/NEImj9SIiNgC+GVmzsjMfYA/Aw/Vw89k5tvrXP4llOG8f6F8u3Zlnba2EvgT4Feoo8AI4zkTWFjj+QBwN/CmPlT/Ja8uBngbMC8zFwMPA5OHnLIDZYRYt/LHgO3qFETqOatQXzQQTyJia+AHlI7SzDrkW33QQDwPpoz2vCMiltdrLo+IbVqovtbTQDwfBdZk5s21fCm+O/um13hGxPbAbpl5A0BmXluPTWqh+lrPRsSzG/tDo0gD8bQ/1COTR2rKVsBtEbFNzeaeBFxVjy2MiL3q9snA9zLzOeAmyrpHRMRrKHNOs91qq4uRxHMFZV0kaufpjcDydqutOtXweuDIzLyyFv+iHIoptQN0JLCs/rrEv+rLGMpC58vqi/RO6v0JfARY1loj9Lwm4lm3lwC/BQ6vw7bVBw3dn5dm5q6ZOb0u+EndXtNyc17yGornQ8DDQxZhfj/wq/ZaoY6GnrdP1PL96jX3pSQHH2+zLdq4eHa7hv2h0aOJeFb2h3rgmkdqRGaujogvUUabjAWWZubSevgTwEVRfhlmJXBMLZ8HfCsiOnNYj83MJ9ust4Y3wnh+Bri4xvM/lDWsHmy56oLPAVtQ1qzqlH2bsh7VtfXYraxb/HE2cElEbAvcy7pfnfgksDgiFlDW43ANq/7oOZ5Rfs59JnA/cG+9zqrMfG9LbdA6Td2fGh2aiuchlPfq2cBTwNFtVF7/o+d4ZuZgRBwCnB8RE4A1lOn+at/GxrMb+0OjQ8/xtD/UuzGDg+tP45QkSZIkSZIKp61JkiRJkiSpK5NHkiRJkiRJ6srkkSRJkiRJkroyeSRJkiRJkqSuTB5JkiRJkiSpK5NHkiRJGyAiZkXET17knC9GxMyWqiRJktQKk0eSJEnNeQcwtt+VkCRJatKYwcHBftdBkiRpVIqI04DZwGrgQWAn4HjgAmAbYDKwHDgcOAY4C3gcOBm4pe7vDwwA9wFzMvOpdlshSZLUG0ceSZIkDaNOPzsUmA7sA2xXDx0HLM7MNwNTgFcD78vMC4B7gFMy8zpgHvAssGdm7gGsAs5stxWSJEm927zfFZAkSRqlDgC+n5lrACLiMmAO8HngwIiYC0wFdgS2HubzBwMT67kA44DHWqi3JElSo0weSZIkdTdmyPaz9e8VlD7U1ZSpabusd17HAPDpzFwGEBFbA1tsuqpKkiRtGk5bkyRJGt4y4LCImBgRmwFH1fJ3Aadl5lV1f29KoghKgqmzYPYPgRMjYlz9/CXAGe1UXZIkqTmOPJIkSRpGZt4aEdMo6xj9FVgBbA/MB66LiKeBJ4GfUtY+ArgROCMixgGnA1+jLJQ9QFlY+7OtNkKSJKkB/tqaJEmSJEmSunLamiRJkiRJkroyeSRJkiRJkqSuTB5JkiRJkiSpK5NHkiRJkiRJ6srkkSRJkiRJkroyeSRJkiRJkqSuTB5JkiRJkiSpK5NHkiRJkiRJ6uq/sVmRAAWO11EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.returns.plot(figsize=(20,5))\n",
    "plt.title(\"Returns\", size = 24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.sq_returns.plot(figsize=(20,5))\n",
    "plt.title(\"Volatility\", size = 24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_pacf(df.returns[1:], lags = 40, alpha = 0.05, zero = False , method = ('ols'))\n",
    "plt.title(\"PACF of Returns\", size = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgt.plot_pacf(df.sq_returns[1:], lags = 40, alpha = 0.05, zero = False , method = ('ols'))\n",
    "plt.title(\"PACF of Squared Returns\", size = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The arch_model() Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from arch import arch_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     39,   Neg. LLF: 6972.734752397977\n",
      "Iteration:     10,   Func. Count:     73,   Neg. LLF: 6970.088043671654\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 6970.058366189876\n",
      "            Iterations: 13\n",
      "            Function evaluations: 91\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - GARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>returns</td>      <th>  R-squared:         </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>GARCH</td>       <th>  Log-Likelihood:    </th> <td>  -6970.06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   13948.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   13974.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Sep 16 2019</td>  <th>  Df Residuals:      </th>    <td>5016</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>16:56:49</td>      <th>  Df Model:          </th>      <td>4</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0466</td> <td>1.183e-02</td> <td>    3.939</td> <td>8.187e-05</td> <td>[2.342e-02,6.981e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    0.0109</td> <td>3.004e-03</td> <td>    3.640</td> <td>2.724e-04</td> <td>[5.048e-03,1.682e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.0835</td> <td>1.071e-02</td> <td>    7.794</td> <td>6.476e-15</td>  <td>[6.249e-02,  0.104]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>beta[1]</th>  <td>    0.9089</td> <td>1.148e-02</td> <td>   79.168</td>   <td>0.000</td>     <td>[  0.886,  0.931]</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                     Constant Mean - GARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   R-squared:                      -0.001\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
       "Vol Model:                      GARCH   Log-Likelihood:               -6970.06\n",
       "Distribution:                  Normal   AIC:                           13948.1\n",
       "Method:            Maximum Likelihood   BIC:                           13974.2\n",
       "                                        No. Observations:                 5020\n",
       "Date:                Mon, Sep 16 2019   Df Residuals:                     5016\n",
       "Time:                        16:56:49   Df Model:                            4\n",
       "                                 Mean Model                                 \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "mu             0.0466  1.183e-02      3.939  8.187e-05 [2.342e-02,6.981e-02]\n",
       "                              Volatility Model                              \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "omega          0.0109  3.004e-03      3.640  2.724e-04 [5.048e-03,1.682e-02]\n",
       "alpha[1]       0.0835  1.071e-02      7.794  6.476e-15   [6.249e-02,  0.104]\n",
       "beta[1]        0.9089  1.148e-02     79.168      0.000     [  0.886,  0.931]\n",
       "============================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_arch_1 = arch_model(df.returns[1:])\n",
    "results_arch_1 = model_arch_1.fit(update_freq = 5)\n",
    "results_arch_1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Simple ARCH(1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     34,   Neg. LLF: 7660.088789376147\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 7660.08878204096\n",
      "            Iterations: 6\n",
      "            Function evaluations: 39\n",
      "            Gradient evaluations: 6\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - ARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>returns</td>      <th>  R-squared:         </th>  <td>  -0.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>ARCH</td>        <th>  Log-Likelihood:    </th> <td>  -7660.09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   15326.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   15345.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Sep 16 2019</td>  <th>  Df Residuals:      </th>    <td>5017</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>16:58:41</td>      <th>  Df Model:          </th>      <td>3</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0345</td> <td>1.603e-02</td> <td>    2.151</td> <td>3.147e-02</td> <td>[3.063e-03,6.590e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>        <th>P>|t|</th>   <th>95.0% Conf. Int.</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    0.9206</td> <td>4.309e-02</td> <td>   21.365</td> <td>2.855e-101</td> <td>[  0.836,  1.005]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.3684</td> <td>5.040e-02</td> <td>    7.310</td>  <td>2.673e-13</td> <td>[  0.270,  0.467]</td>\n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                      Constant Mean - ARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   R-squared:                      -0.000\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.000\n",
       "Vol Model:                       ARCH   Log-Likelihood:               -7660.09\n",
       "Distribution:                  Normal   AIC:                           15326.2\n",
       "Method:            Maximum Likelihood   BIC:                           15345.7\n",
       "                                        No. Observations:                 5020\n",
       "Date:                Mon, Sep 16 2019   Df Residuals:                     5017\n",
       "Time:                        16:58:41   Df Model:                            3\n",
       "                                 Mean Model                                 \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "mu             0.0345  1.603e-02      2.151  3.147e-02 [3.063e-03,6.590e-02]\n",
       "                            Volatility Model                            \n",
       "========================================================================\n",
       "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
       "------------------------------------------------------------------------\n",
       "omega          0.9206  4.309e-02     21.365 2.855e-101 [  0.836,  1.005]\n",
       "alpha[1]       0.3684  5.040e-02      7.310  2.673e-13 [  0.270,  0.467]\n",
       "========================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_arch_1 = arch_model(df.returns[1:], mean = \"Constant\", vol = \"ARCH\", p = 1)\n",
    "results_arch_1 = model_arch_1.fit(update_freq = 5)\n",
    "results_arch_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_arch_1 = arch_model(df.returns[1:], mean = \"AR\", lags = [2, 3, 6], vol = \"ARCH\", p = 1, dist = \"ged\")\n",
    "results_arch_1 = model_arch_1.fit(update_freq = 5)\n",
    "results_arch_1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Higher-Lag ARCH Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     41,   Neg. LLF: 7449.870533644225\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 7449.545164098214\n",
      "            Iterations: 9\n",
      "            Function evaluations: 67\n",
      "            Gradient evaluations: 9\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - ARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>returns</td>      <th>  R-squared:         </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>ARCH</td>        <th>  Log-Likelihood:    </th> <td>  -7449.55</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   14907.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   14933.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Sep 16 2019</td>  <th>  Df Residuals:      </th>    <td>5016</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>17:01:44</td>      <th>  Df Model:          </th>      <td>4</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0484</td> <td>1.401e-02</td> <td>    3.455</td> <td>5.495e-04</td> <td>[2.095e-02,7.585e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>   <th>95.0% Conf. Int.</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    0.6978</td> <td>3.564e-02</td> <td>   19.580</td> <td>2.272e-85</td> <td>[  0.628,  0.768]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.2202</td> <td>3.474e-02</td> <td>    6.339</td> <td>2.311e-10</td> <td>[  0.152,  0.288]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[2]</th> <td>    0.2783</td> <td>3.645e-02</td> <td>    7.635</td> <td>2.260e-14</td> <td>[  0.207,  0.350]</td>\n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                      Constant Mean - ARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   R-squared:                      -0.001\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
       "Vol Model:                       ARCH   Log-Likelihood:               -7449.55\n",
       "Distribution:                  Normal   AIC:                           14907.1\n",
       "Method:            Maximum Likelihood   BIC:                           14933.2\n",
       "                                        No. Observations:                 5020\n",
       "Date:                Mon, Sep 16 2019   Df Residuals:                     5016\n",
       "Time:                        17:01:44   Df Model:                            4\n",
       "                                 Mean Model                                 \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "mu             0.0484  1.401e-02      3.455  5.495e-04 [2.095e-02,7.585e-02]\n",
       "                            Volatility Model                            \n",
       "========================================================================\n",
       "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
       "------------------------------------------------------------------------\n",
       "omega          0.6978  3.564e-02     19.580  2.272e-85 [  0.628,  0.768]\n",
       "alpha[1]       0.2202  3.474e-02      6.339  2.311e-10 [  0.152,  0.288]\n",
       "alpha[2]       0.2783  3.645e-02      7.635  2.260e-14 [  0.207,  0.350]\n",
       "========================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_arch_2 = arch_model(df.returns[1:], mean = \"Constant\", vol = \"ARCH\", p = 2)\n",
    "results_arch_2 = model_arch_2.fit(update_freq = 5)\n",
    "results_arch_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     45,   Neg. LLF: 7278.805807411393\n",
      "Iteration:     10,   Func. Count:     84,   Neg. LLF: 7277.050453152619\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 7277.050452148393\n",
      "            Iterations: 11\n",
      "            Function evaluations: 91\n",
      "            Gradient evaluations: 11\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - ARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>returns</td>      <th>  R-squared:         </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>ARCH</td>        <th>  Log-Likelihood:    </th> <td>  -7277.05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   14564.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   14596.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Sep 16 2019</td>  <th>  Df Residuals:      </th>    <td>5015</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>17:02:14</td>      <th>  Df Model:          </th>      <td>5</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0529</td> <td>1.316e-02</td> <td>    4.018</td> <td>5.875e-05</td> <td>[2.707e-02,7.865e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>   <th>95.0% Conf. Int.</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>    <td>    0.5012</td> <td>2.834e-02</td> <td>   17.685</td> <td>5.505e-70</td> <td>[  0.446,  0.557]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th> <td>    0.1570</td> <td>2.649e-02</td> <td>    5.926</td> <td>3.108e-09</td> <td>[  0.105,  0.209]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[2]</th> <td>    0.2197</td> <td>2.588e-02</td> <td>    8.489</td> <td>2.077e-17</td> <td>[  0.169,  0.270]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[3]</th> <td>    0.2804</td> <td>3.354e-02</td> <td>    8.359</td> <td>6.302e-17</td> <td>[  0.215,  0.346]</td>\n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                      Constant Mean - ARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   R-squared:                      -0.001\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
       "Vol Model:                       ARCH   Log-Likelihood:               -7277.05\n",
       "Distribution:                  Normal   AIC:                           14564.1\n",
       "Method:            Maximum Likelihood   BIC:                           14596.7\n",
       "                                        No. Observations:                 5020\n",
       "Date:                Mon, Sep 16 2019   Df Residuals:                     5015\n",
       "Time:                        17:02:14   Df Model:                            5\n",
       "                                 Mean Model                                 \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "mu             0.0529  1.316e-02      4.018  5.875e-05 [2.707e-02,7.865e-02]\n",
       "                            Volatility Model                            \n",
       "========================================================================\n",
       "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
       "------------------------------------------------------------------------\n",
       "omega          0.5012  2.834e-02     17.685  5.505e-70 [  0.446,  0.557]\n",
       "alpha[1]       0.1570  2.649e-02      5.926  3.108e-09 [  0.105,  0.209]\n",
       "alpha[2]       0.2197  2.588e-02      8.489  2.077e-17 [  0.169,  0.270]\n",
       "alpha[3]       0.2804  3.354e-02      8.359  6.302e-17 [  0.215,  0.346]\n",
       "========================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_arch_3 = arch_model(df.returns[1:], mean = \"Constant\", vol = \"ARCH\", p = 3)\n",
    "results_arch_3 = model_arch_3.fit(update_freq = 5)\n",
    "results_arch_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      5,   Func. Count:     93,   Neg. LLF: 6996.50004371243\n",
      "Iteration:     10,   Func. Count:    188,   Neg. LLF: 6985.661373689021\n",
      "Iteration:     15,   Func. Count:    283,   Neg. LLF: 6984.395232187267\n",
      "Iteration:     20,   Func. Count:    378,   Neg. LLF: 6984.217022569693\n",
      "Iteration:     25,   Func. Count:    468,   Neg. LLF: 6984.175137692235\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 6984.175062617066\n",
      "            Iterations: 27\n",
      "            Function evaluations: 502\n",
      "            Gradient evaluations: 27\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Constant Mean - ARCH Model Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>returns</td>      <th>  R-squared:         </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mean Model:</th>       <td>Constant Mean</td>   <th>  Adj. R-squared:    </th>  <td>  -0.001</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol Model:</th>            <td>ARCH</td>        <th>  Log-Likelihood:    </th> <td>  -6984.18</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Distribution:</th>        <td>Normal</td>       <th>  AIC:               </th> <td>   13998.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>        <td>Maximum Likelihood</td> <th>  BIC:               </th> <td>   14096.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                        <td></td>          <th>  No. Observations:  </th>    <td>5020</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Mon, Sep 16 2019</td>  <th>  Df Residuals:      </th>    <td>5005</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>17:02:36</td>      <th>  Df Model:          </th>     <td>15</td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Mean Model</caption>\n",
       "<tr>\n",
       "   <td></td>     <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>     <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mu</th> <td>    0.0492</td> <td>1.206e-02</td> <td>    4.077</td> <td>4.566e-05</td> <td>[2.553e-02,7.281e-02]</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<caption>Volatility Model</caption>\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>       <th>P>|t|</th>      <th>95.0% Conf. Int.</th>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>omega</th>     <td>    0.1871</td> <td>2.210e-02</td> <td>    8.466</td> <td>2.538e-17</td>    <td>[  0.144,  0.230]</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[1]</th>  <td>    0.0568</td> <td>1.729e-02</td> <td>    3.282</td> <td>1.029e-03</td>  <td>[2.287e-02,9.065e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[2]</th>  <td>    0.1156</td> <td>2.017e-02</td> <td>    5.733</td> <td>9.841e-09</td>   <td>[7.610e-02,  0.155]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[3]</th>  <td>    0.1265</td> <td>2.625e-02</td> <td>    4.820</td> <td>1.433e-06</td>   <td>[7.509e-02,  0.178]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[4]</th>  <td>    0.0884</td> <td>2.159e-02</td> <td>    4.093</td> <td>4.265e-05</td>   <td>[4.605e-02,  0.131]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[5]</th>  <td>    0.0695</td> <td>1.750e-02</td> <td>    3.970</td> <td>7.189e-05</td>   <td>[3.518e-02,  0.104]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[6]</th>  <td>    0.0865</td> <td>1.926e-02</td> <td>    4.491</td> <td>7.092e-06</td>   <td>[4.874e-02,  0.124]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[7]</th>  <td>    0.0404</td> <td>1.846e-02</td> <td>    2.188</td> <td>2.870e-02</td>  <td>[4.203e-03,7.658e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[8]</th>  <td>    0.0654</td> <td>1.833e-02</td> <td>    3.565</td> <td>3.633e-04</td>   <td>[2.943e-02,  0.101]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[9]</th>  <td>    0.0292</td> <td>1.603e-02</td> <td>    1.820</td> <td>6.877e-02</td> <td>[-2.244e-03,6.058e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[10]</th> <td>    0.0335</td> <td>1.605e-02</td> <td>    2.089</td> <td>3.670e-02</td>  <td>[2.072e-03,6.498e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[11]</th> <td>    0.0775</td> <td>1.760e-02</td> <td>    4.403</td> <td>1.067e-05</td>   <td>[4.300e-02,  0.112]</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[12]</th> <td>    0.0473</td> <td>1.873e-02</td> <td>    2.526</td> <td>1.153e-02</td>  <td>[1.060e-02,8.402e-02]</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>alpha[13]</th> <td>    0.0372</td> <td>1.431e-02</td> <td>    2.600</td> <td>9.317e-03</td>  <td>[9.162e-03,6.526e-02]</td>\n",
       "</tr>\n",
       "</table><br/><br/>Covariance estimator: robust"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                      Constant Mean - ARCH Model Results                      \n",
       "==============================================================================\n",
       "Dep. Variable:                returns   R-squared:                      -0.001\n",
       "Mean Model:             Constant Mean   Adj. R-squared:                 -0.001\n",
       "Vol Model:                       ARCH   Log-Likelihood:               -6984.18\n",
       "Distribution:                  Normal   AIC:                           13998.4\n",
       "Method:            Maximum Likelihood   BIC:                           14096.2\n",
       "                                        No. Observations:                 5020\n",
       "Date:                Mon, Sep 16 2019   Df Residuals:                     5005\n",
       "Time:                        17:02:36   Df Model:                           15\n",
       "                                 Mean Model                                 \n",
       "============================================================================\n",
       "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
       "----------------------------------------------------------------------------\n",
       "mu             0.0492  1.206e-02      4.077  4.566e-05 [2.553e-02,7.281e-02]\n",
       "                               Volatility Model                              \n",
       "=============================================================================\n",
       "                 coef    std err          t      P>|t|       95.0% Conf. Int.\n",
       "-----------------------------------------------------------------------------\n",
       "omega          0.1871  2.210e-02      8.466  2.538e-17      [  0.144,  0.230]\n",
       "alpha[1]       0.0568  1.729e-02      3.282  1.029e-03  [2.287e-02,9.065e-02]\n",
       "alpha[2]       0.1156  2.017e-02      5.733  9.841e-09    [7.610e-02,  0.155]\n",
       "alpha[3]       0.1265  2.625e-02      4.820  1.433e-06    [7.509e-02,  0.178]\n",
       "alpha[4]       0.0884  2.159e-02      4.093  4.265e-05    [4.605e-02,  0.131]\n",
       "alpha[5]       0.0695  1.750e-02      3.970  7.189e-05    [3.518e-02,  0.104]\n",
       "alpha[6]       0.0865  1.926e-02      4.491  7.092e-06    [4.874e-02,  0.124]\n",
       "alpha[7]       0.0404  1.846e-02      2.188  2.870e-02  [4.203e-03,7.658e-02]\n",
       "alpha[8]       0.0654  1.833e-02      3.565  3.633e-04    [2.943e-02,  0.101]\n",
       "alpha[9]       0.0292  1.603e-02      1.820  6.877e-02 [-2.244e-03,6.058e-02]\n",
       "alpha[10]      0.0335  1.605e-02      2.089  3.670e-02  [2.072e-03,6.498e-02]\n",
       "alpha[11]      0.0775  1.760e-02      4.403  1.067e-05    [4.300e-02,  0.112]\n",
       "alpha[12]      0.0473  1.873e-02      2.526  1.153e-02  [1.060e-02,8.402e-02]\n",
       "alpha[13]      0.0372  1.431e-02      2.600  9.317e-03  [9.162e-03,6.526e-02]\n",
       "=============================================================================\n",
       "\n",
       "Covariance estimator: robust\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_arch_13 = arch_model(df.returns[1:], mean = \"Constant\", vol = \"ARCH\", p = 13)\n",
    "results_arch_13 = model_arch_13.fit(update_freq = 5)\n",
    "results_arch_13.summary()"
   ]
  }
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