garch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from arch import arch_model\n",
    "from fredapi import Fred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>RPI</th>\n",
       "      <th>W875RX1</th>\n",
       "      <th>DPCERA3M086SBEA</th>\n",
       "      <th>CMRMTSPL</th>\n",
       "      <th>RSXFS</th>\n",
       "      <th>INDPRO</th>\n",
       "      <th>IPFPNSS</th>\n",
       "      <th>IPFINAL</th>\n",
       "      <th>IPCONGD</th>\n",
       "      <th>...</th>\n",
       "      <th>CES2000000008</th>\n",
       "      <th>CES3000000008</th>\n",
       "      <th>UMCSENT</th>\n",
       "      <th>MZMSL</th>\n",
       "      <th>DTCOLNVHFNM</th>\n",
       "      <th>DTCTHFNM</th>\n",
       "      <th>INVEST</th>\n",
       "      <th>S&amp;P: indust</th>\n",
       "      <th>S&amp;P div yield</th>\n",
       "      <th>S&amp;P PE ratio</th>\n",
       "    </tr>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.013423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1871-02-28</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>-0.08</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13664 rows × 125 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Unnamed: 0  RPI  W875RX1  DPCERA3M086SBEA  CMRMTSPL  RSXFS  INDPRO  \\\n",
       "0      1871-01-01  NaN      NaN              NaN       NaN    NaN     NaN   \n",
       "1      1871-01-31  NaN      NaN              NaN       NaN    NaN     NaN   \n",
       "2      1871-02-01  NaN      NaN              NaN       NaN    NaN     NaN   \n",
       "3      1871-02-28  NaN      NaN              NaN       NaN    NaN     NaN   \n",
       "4      1871-03-01  NaN      NaN              NaN       NaN    NaN     NaN   \n",
       "...           ...  ...      ...              ...       ...    ...     ...   \n",
       "13659  2023-04-01  0.0      0.0              0.0       0.0    0.0     0.0   \n",
       "13660  2023-04-03  0.0      0.0              0.0       0.0    0.0     0.0   \n",
       "13661  2023-04-04  0.0      0.0              0.0       0.0    0.0     0.0   \n",
       "13662  2023-04-05  0.0      0.0              0.0       0.0    0.0     0.0   \n",
       "13663  2023-04-30  0.0      0.0              0.0       0.0    0.0     0.0   \n",
       "\n",
       "       IPFPNSS  IPFINAL  IPCONGD  ...  CES2000000008  CES3000000008  UMCSENT  \\\n",
       "0          NaN      NaN      NaN  ...            NaN            NaN      NaN   \n",
       "1          NaN      NaN      NaN  ...            NaN            NaN      NaN   \n",
       "2          NaN      NaN      NaN  ...            NaN            NaN      NaN   \n",
       "3          NaN      NaN      NaN  ...            NaN            NaN      NaN   \n",
       "4          NaN      NaN      NaN  ...            NaN            NaN      NaN   \n",
       "...        ...      ...      ...  ...            ...            ...      ...   \n",
       "13659      0.0      0.0      0.0  ...            0.0            0.0      0.0   \n",
       "13660      0.0      0.0      0.0  ...            0.0            0.0      0.0   \n",
       "13661      0.0      0.0      0.0  ...            0.0            0.0      0.0   \n",
       "13662      0.0      0.0      0.0  ...            0.0            0.0      0.0   \n",
       "13663      0.0      0.0      0.0  ...            0.0            0.0      0.0   \n",
       "\n",
       "       MZMSL  DTCOLNVHFNM  DTCTHFNM  INVEST  S&P: indust  S&P div yield  \\\n",
       "0        NaN          NaN       NaN     NaN          NaN            NaN   \n",
       "1        NaN          NaN       NaN     NaN          NaN            NaN   \n",
       "2        NaN          NaN       NaN     NaN          NaN           0.00   \n",
       "3        NaN          NaN       NaN     NaN          NaN          -0.08   \n",
       "4        NaN          NaN       NaN     NaN          NaN           0.00   \n",
       "...      ...          ...       ...     ...          ...            ...   \n",
       "13659    0.0          0.0       0.0     0.0     0.000000           0.00   \n",
       "13660    0.0          0.0       0.0     0.0     0.001889           0.00   \n",
       "13661    0.0          0.0       0.0     0.0    -0.022781           0.00   \n",
       "13662    0.0          0.0       0.0     0.0    -0.013091           0.00   \n",
       "13663    0.0          0.0       0.0     0.0     0.000000          -0.07   \n",
       "\n",
       "       S&P PE ratio  \n",
       "0               NaN  \n",
       "1          0.000000  \n",
       "2          0.013423  \n",
       "3          0.000000  \n",
       "4          0.023717  \n",
       "...             ...  \n",
       "13659      0.003635  \n",
       "13660      0.000000  \n",
       "13661      0.000000  \n",
       "13662      0.000000  \n",
       "13663      0.000000  \n",
       "\n",
       "[13664 rows x 125 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fred = Fred(api_key='6cc00d6dd7a79e8de471491dc74cc1fe')\n",
    "df=pd.read_csv('Data\\Transformed HistoricalVariables.csv')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "y must be squeezable to 1 dimension",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[6], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m model \u001b[39m=\u001b[39m arch_model(df, vol\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mGARCH\u001b[39;49m\u001b[39m\"\u001b[39;49m, p\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m, q\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m)\n",
      "File \u001b[1;32mc:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\univariate\\mean.py:1970\u001b[0m, in \u001b[0;36march_model\u001b[1;34m(y, x, mean, lags, vol, p, o, q, power, dist, hold_back, rescale)\u001b[0m\n\u001b[0;32m   1968\u001b[0m     am \u001b[39m=\u001b[39m LS(y, x, hold_back\u001b[39m=\u001b[39mhold_back, rescale\u001b[39m=\u001b[39mrescale)\n\u001b[0;32m   1969\u001b[0m \u001b[39melif\u001b[39;00m mean_model \u001b[39m==\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mconstant\u001b[39m\u001b[39m\"\u001b[39m:\n\u001b[1;32m-> 1970\u001b[0m     am \u001b[39m=\u001b[39m ConstantMean(y, hold_back\u001b[39m=\u001b[39;49mhold_back, rescale\u001b[39m=\u001b[39;49mrescale)\n\u001b[0;32m   1971\u001b[0m \u001b[39melse\u001b[39;00m:  \u001b[39m# mean == \"zero\"\u001b[39;00m\n\u001b[0;32m   1972\u001b[0m     am \u001b[39m=\u001b[39m ZeroMean(y, hold_back\u001b[39m=\u001b[39mhold_back, rescale\u001b[39m=\u001b[39mrescale)\n",
      "File \u001b[1;32mc:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\univariate\\mean.py:1107\u001b[0m, in \u001b[0;36mConstantMean.__init__\u001b[1;34m(self, y, hold_back, volatility, distribution, rescale)\u001b[0m\n\u001b[0;32m   1099\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m__init__\u001b[39m(\n\u001b[0;32m   1100\u001b[0m     \u001b[39mself\u001b[39m,\n\u001b[0;32m   1101\u001b[0m     y: ArrayLike \u001b[39m|\u001b[39m \u001b[39mNone\u001b[39;00m \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m,\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m   1105\u001b[0m     rescale: \u001b[39mbool\u001b[39m \u001b[39m|\u001b[39m \u001b[39mNone\u001b[39;00m \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m,\n\u001b[0;32m   1106\u001b[0m ) \u001b[39m-\u001b[39m\u001b[39m>\u001b[39m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m-> 1107\u001b[0m     \u001b[39msuper\u001b[39;49m()\u001b[39m.\u001b[39;49m\u001b[39m__init__\u001b[39;49m(\n\u001b[0;32m   1108\u001b[0m         y,\n\u001b[0;32m   1109\u001b[0m         hold_back\u001b[39m=\u001b[39;49mhold_back,\n\u001b[0;32m   1110\u001b[0m         volatility\u001b[39m=\u001b[39;49mvolatility,\n\u001b[0;32m   1111\u001b[0m         distribution\u001b[39m=\u001b[39;49mdistribution,\n\u001b[0;32m   1112\u001b[0m         rescale\u001b[39m=\u001b[39;49mrescale,\n\u001b[0;32m   1113\u001b[0m     )\n\u001b[0;32m   1114\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_name \u001b[39m=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mConstant Mean\u001b[39m\u001b[39m\"\u001b[39m\n",
      "File \u001b[1;32mc:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\univariate\\mean.py:264\u001b[0m, in \u001b[0;36mHARX.__init__\u001b[1;34m(self, y, x, lags, constant, use_rotated, hold_back, volatility, distribution, rescale)\u001b[0m\n\u001b[0;32m    245\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m__init__\u001b[39m(\n\u001b[0;32m    246\u001b[0m     \u001b[39mself\u001b[39m,\n\u001b[0;32m    247\u001b[0m     y: ArrayLike \u001b[39m|\u001b[39m \u001b[39mNone\u001b[39;00m \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m,\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m    262\u001b[0m     rescale: \u001b[39mbool\u001b[39m \u001b[39m|\u001b[39m \u001b[39mNone\u001b[39;00m \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m,\n\u001b[0;32m    263\u001b[0m ) \u001b[39m-\u001b[39m\u001b[39m>\u001b[39m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m--> 264\u001b[0m     \u001b[39msuper\u001b[39;49m()\u001b[39m.\u001b[39;49m\u001b[39m__init__\u001b[39;49m(\n\u001b[0;32m    265\u001b[0m         y,\n\u001b[0;32m    266\u001b[0m         hold_back\u001b[39m=\u001b[39;49mhold_back,\n\u001b[0;32m    267\u001b[0m         volatility\u001b[39m=\u001b[39;49mvolatility,\n\u001b[0;32m    268\u001b[0m         distribution\u001b[39m=\u001b[39;49mdistribution,\n\u001b[0;32m    269\u001b[0m         rescale\u001b[39m=\u001b[39;49mrescale,\n\u001b[0;32m    270\u001b[0m     )\n\u001b[0;32m    271\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_x \u001b[39m=\u001b[39m x\n\u001b[0;32m    272\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_x_names: \u001b[39mlist\u001b[39m[\u001b[39mstr\u001b[39m] \u001b[39m=\u001b[39m []\n",
      "File \u001b[1;32mc:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\univariate\\base.py:192\u001b[0m, in \u001b[0;36mARCHModel.__init__\u001b[1;34m(self, y, volatility, distribution, hold_back, rescale)\u001b[0m\n\u001b[0;32m    190\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_is_pandas \u001b[39m=\u001b[39m \u001b[39misinstance\u001b[39m(y, (pd\u001b[39m.\u001b[39mDataFrame, pd\u001b[39m.\u001b[39mSeries))\n\u001b[0;32m    191\u001b[0m \u001b[39mif\u001b[39;00m y \u001b[39mis\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m--> 192\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_y_series \u001b[39m=\u001b[39m cast(pd\u001b[39m.\u001b[39mSeries, ensure1d(y, \u001b[39m\"\u001b[39;49m\u001b[39my\u001b[39;49m\u001b[39m\"\u001b[39;49m, series\u001b[39m=\u001b[39;49m\u001b[39mTrue\u001b[39;49;00m))\n\u001b[0;32m    193\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m    194\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_y_series \u001b[39m=\u001b[39m cast(pd\u001b[39m.\u001b[39mSeries, ensure1d(np\u001b[39m.\u001b[39mempty((\u001b[39m0\u001b[39m,)), \u001b[39m\"\u001b[39m\u001b[39my\u001b[39m\u001b[39m\"\u001b[39m, series\u001b[39m=\u001b[39m\u001b[39mTrue\u001b[39;00m))\n",
      "File \u001b[1;32mc:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\utility\\array.py:67\u001b[0m, in \u001b[0;36mensure1d\u001b[1;34m(x, name, series)\u001b[0m\n\u001b[0;32m     65\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39misinstance\u001b[39m(x, DataFrame):\n\u001b[0;32m     66\u001b[0m     \u001b[39mif\u001b[39;00m x\u001b[39m.\u001b[39mshape[\u001b[39m1\u001b[39m] \u001b[39m!=\u001b[39m \u001b[39m1\u001b[39m:\n\u001b[1;32m---> 67\u001b[0m         \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m{\u001b[39;00mname\u001b[39m}\u001b[39;00m\u001b[39m must be squeezable to 1 dimension\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[0;32m     68\u001b[0m     \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m series:\n\u001b[0;32m     69\u001b[0m         \u001b[39mreturn\u001b[39;00m np\u001b[39m.\u001b[39masarray(x\u001b[39m.\u001b[39miloc[:, \u001b[39m0\u001b[39m])\n",
      "\u001b[1;31mValueError\u001b[0m: y must be squeezable to 1 dimension"
     ]
    }
   ],
   "source": [
    "model = arch_model(df, vol=\"GARCH\", p=1, q=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 21426350720303.88\n",
      "Iteration:      2,   Func. Count:     19,   Neg. LLF: 271512.14996703813\n",
      "Iteration:      3,   Func. Count:     29,   Neg. LLF: 12462.278561662893\n",
      "Iteration:      4,   Func. Count:     35,   Neg. LLF: 227.76766320978254\n",
      "Iteration:      5,   Func. Count:     40,   Neg. LLF: 282.43102070439414\n",
      "Iteration:      6,   Func. Count:     46,   Neg. LLF: 9028.844704082114\n",
      "Iteration:      7,   Func. Count:     52,   Neg. LLF: 118.71872894144434\n",
      "Iteration:      8,   Func. Count:     57,   Neg. LLF: 118.70581929297947\n",
      "Iteration:      9,   Func. Count:     62,   Neg. LLF: 118.70097377527054\n",
      "Iteration:     10,   Func. Count:     67,   Neg. LLF: 118.68322289603122\n",
      "Iteration:     11,   Func. Count:     72,   Neg. LLF: 118.67511080160858\n",
      "Iteration:     12,   Func. Count:     77,   Neg. LLF: 118.67275088680759\n",
      "Iteration:     13,   Func. Count:     82,   Neg. LLF: 118.67260951625275\n",
      "Iteration:     14,   Func. Count:     87,   Neg. LLF: 2865.6012080825103\n",
      "Iteration:     15,   Func. Count:     98,   Neg. LLF: 1652.5905898089495\n",
      "Iteration:     16,   Func. Count:    108,   Neg. LLF: 118.74194115837503\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 118.6726067250429\n",
      "            Iterations: 17\n",
      "            Function evaluations: 111\n",
      "            Gradient evaluations: 16\n"
     ]
    }
   ],
   "source": [
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                     Constant Mean - GARCH Model Results                      \n",
      "==============================================================================\n",
      "Dep. Variable:                   None   R-squared:                       0.000\n",
      "Mean Model:             Constant Mean   Adj. R-squared:                  0.000\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -118.673\n",
      "Distribution:                  Normal   AIC:                           245.345\n",
      "Method:            Maximum Likelihood   BIC:                           267.789\n",
      "                                        No. Observations:                 2020\n",
      "Date:                Wed, Apr 19 2023   Df Residuals:                     2019\n",
      "Time:                        01:06:16   Df Model:                            1\n",
      "                                 Mean Model                                 \n",
      "============================================================================\n",
      "                 coef    std err          t      P>|t|      95.0% Conf. Int.\n",
      "----------------------------------------------------------------------------\n",
      "mu             0.0333  5.365e-03      6.208  5.380e-10 [2.279e-02,4.382e-02]\n",
      "                               Volatility Model                              \n",
      "=============================================================================\n",
      "                 coef    std err          t      P>|t|       95.0% Conf. Int.\n",
      "-----------------------------------------------------------------------------\n",
      "omega          0.0221  3.520e-03      6.287  3.234e-10  [1.523e-02,2.903e-02]\n",
      "alpha[1]       0.9228  2.098e-02     43.980      0.000      [  0.882,  0.964]\n",
      "beta[1]    3.3841e-10  7.040e-03  4.807e-08      1.000 [-1.380e-02,1.380e-02]\n",
      "=============================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\__future__\\_utility.py:11: FutureWarning: \n",
      "The default for reindex is True. After September 2021 this will change to\n",
      "False. Set reindex to True or False to silence this message. Alternatively,\n",
      "you can use the import comment\n",
      "\n",
      "from arch.__future__ import reindexing\n",
      "\n",
      "to globally set reindex to True and silence this warning.\n",
      "\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "forecasts = results.forecast(horizon=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next-period forecast:  h.1    0.033303\n",
      "Name: 2023-03-01 00:00:00, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"Next-period forecast: \", forecasts.mean.iloc[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.arima.model import ARIMA\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = df.iloc[:1500]\n",
    "test_data = df.iloc[1500:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  self._init_dates(dates, freq)\n",
      "c:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  self._init_dates(dates, freq)\n",
      "c:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  self._init_dates(dates, freq)\n"
     ]
    }
   ],
   "source": [
    "model1 = ARIMA(train_data, order=(1,1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "results1 = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                 2008\n",
      "Model:                 ARIMA(1, 1, 1)   Log Likelihood                 534.276\n",
      "Date:                Wed, 19 Apr 2023   AIC                          -1062.552\n",
      "Time:                        01:51:26   BIC                          -1045.739\n",
      "Sample:                    12-01-1854   HQIC                         -1056.380\n",
      "                         - 03-01-2022                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "ar.L1       1.074e-07   2.31e-14   4.65e+06      0.000    1.07e-07    1.07e-07\n",
      "ma.L1      -1.044e-07    2.4e-14  -4.35e+06      0.000   -1.04e-07   -1.04e-07\n",
      "sigma2         0.0344      0.000    118.712      0.000       0.034       0.035\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.00   Jarque-Bera (JB):             56909.26\n",
      "Prob(Q):                              1.00   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               0.57   Skew:                            -0.07\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                        29.09\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "[2] Covariance matrix is singular or near-singular, with condition number    inf. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "print(results1.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\admin\\Documents\\GitHub\\projet-de-fin-d-annee\\.venv\\lib\\site-packages\\arch\\__future__\\_utility.py:11: FutureWarning: \n",
      "The default for reindex is True. After September 2021 this will change to\n",
      "False. Set reindex to True or False to silence this message. Alternatively,\n",
      "you can use the import comment\n",
      "\n",
      "from arch.__future__ import reindexing\n",
      "\n",
      "to globally set reindex to True and silence this warning.\n",
      "\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "forecast = results.forecast()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forecast for next 12 months:                   h.1\n",
      "1854-12-01       NaN\n",
      "1855-01-01       NaN\n",
      "1855-02-01       NaN\n",
      "1855-03-01       NaN\n",
      "1855-04-01       NaN\n",
      "...              ...\n",
      "2022-11-01       NaN\n",
      "2022-12-01       NaN\n",
      "2023-01-01       NaN\n",
      "2023-02-01       NaN\n",
      "2023-03-01  0.033303\n",
      "\n",
      "[2020 rows x 1 columns]\n"
     ]
    }
   ],
   "source": [
    "# Print forecast\n",
    "print(\"Forecast for next 12 months: \", forecast.mean)"
   ]
  }
 ],
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