3. ADP 20회 (시계열 arima).ipynb

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   "source": [
    "## Arima 모델 만들기\n",
    "\n",
    "trend : constant를 가지고 있는지, c - constant / nc - no constant\n",
    "\n",
    "disp : 수렴 정보를 나타냄(정확히 뭐를 나타내는 것인지 모르겠음, 크게 중요한 사항은 아닌듯 함)\n",
    "\n",
    "-------------------------------------------\n",
    "\n",
    "이전 포스팅에서는 정상 시계열인지 확인을 하고\n",
    "\n",
    "비정상 시계열 데이터를 차분 한 뒤, 정상 시계열이 됬는지를 확인하였습니다.\n",
    "\n",
    "이제 정상 시계열임을 확인하였으니 ARIMA로 예측 모형을 만드는 과정에 대해 포스팅 합니다.\n",
    "\n",
    "그래프 상에서는 차분 1번 이후에 추가적으로 AR, MA를 0으로 하고 진행을 하여도 되지만\n",
    "\n",
    "최적의 모형을 찾는 과정을 설명하기 위해,  일단(AR=0, 차분=1, MA=1) 파라미터로 ARIMA 모델을 학습합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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     "end_time": "2021-03-10T14:08:13.457465Z",
     "start_time": "2021-03-10T14:08:13.389098Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             ARIMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                D.price   No. Observations:                  365\n",
      "Model:                 ARIMA(0, 1, 1)   Log Likelihood               -3036.684\n",
      "Method:                       css-mle   S.D. of innovations            993.013\n",
      "Date:                Wed, 10 Mar 2021   AIC                           6079.369\n",
      "Time:                        23:08:13   BIC                           6091.068\n",
      "Sample:                    03-03-2020   HQIC                          6084.018\n",
      "                         - 03-02-2021                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "const           112.4754     50.926      2.209      0.027      12.663     212.288\n",
      "ma.L1.D.price    -0.0204      0.052     -0.391      0.696      -0.123       0.082\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "MA.1           49.1054           +0.0000j           49.1054            0.0000\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "warnings.filterwarnings(action='ignore')\n",
    "\n",
    "from statsmodels.tsa.arima_model import ARIMA\n",
    "\n",
    "model = ARIMA(series, order=(0,1,1))\n",
    "model_fit = model.fit(trend='c',full_output=True, disp=1)\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "‘P > z’ 값이 일반적으로 학습의 적정성을 위해 확인되는 t-test값이다. \n",
    "\n",
    "여기서 만약 const의  p value 0.05 이상이라면, \n",
    "\n",
    "model.fit()의 파라미터중 trend=’c’가 아니라 ‘nc’로 설정해주어야 하는게 옳다.\n",
    "\n",
    "즉 시계열 모형에 상수 값이 필요하지 않다는 것을 의미한다.\n",
    "\n",
    "여기서는 const가 아닌 그래프 상에서는 필요하지 않았지만 임의로 추가하였던 MA1이 귀무가설 채택인 상태이므로\n",
    "\n",
    "이를 제외하고 다시 모형을 만들었다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:08:13.806104Z",
     "start_time": "2021-03-10T14:08:13.792104Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             ARIMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                D.price   No. Observations:                  365\n",
      "Model:                 ARIMA(0, 1, 0)   Log Likelihood               -3036.760\n",
      "Method:                           css   S.D. of innovations            993.220\n",
      "Date:                Wed, 10 Mar 2021   AIC                           6077.520\n",
      "Time:                        23:08:13   BIC                           6085.320\n",
      "Sample:                    03-03-2020   HQIC                          6080.620\n",
      "                         - 03-02-2021                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        112.5596     51.988      2.165      0.030      10.666     214.453\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "model = ARIMA(series, order=(0,1,0))\n",
    "model_fit = model.fit(trend='c',full_output=True, disp=1)\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "확실히 MA1이 추가된 모형보다 그냥 차분만 하고 ARMIA(0,1,0)을 한 모형이 AIC, BIC 값이 더 작다.\n",
    "\n",
    "const에 대한 pvalue도 귀무가설 기각 상태이므로 해당 변수가 유의하다는 뜻이다.\n",
    "\n",
    "만약 이렇게 모형을 일일히 만들어서 하는 것이 아닌 r에서의 auto arima를 통해서 결과를 비교하고 싶다면\n",
    "\n",
    "아래와 같은 방식으로 수행을 하여야 한다.\n",
    "\n",
    "먼저 R에서의 auto arima 방식이다.\n",
    "\n",
    "---------------------------------------\n",
    "\n",
    "library(forecast)\n",
    "\n",
    "auto.arima(data)\n",
    "\n",
    "---------------------------------------\n",
    "\n",
    "이렇게 실행한 다음에, 나온 AR,차분여부,MA 값으로 모델을 만들고 예측을 하면 된다.\n",
    "\n",
    "R은 이렇게 간단하지만, python은 auto arima를 가능하게 해주는 패키지가 ADP에서는 제공이 안된다.\n",
    "\n",
    "밑에는 파이썬으로 arima를 for문을 이용해서 모든 경우의 수를 이용하여서 생성하고 AIC 값을 이용해서\n",
    "\n",
    "최적의 모형을 찾아주는 방법이다."
   ]
  },
  {
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   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:08:14.394295Z",
     "start_time": "2021-03-10T14:08:14.185068Z"
    },
    "scrolled": true
   },
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>order</th>\n",
       "      <th>AIC</th>\n",
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      "text/plain": [
       "      order          AIC\n",
       "2  p0 d1 q0  6077.520333\n",
       "5  p1 d1 q0  6079.360565\n",
       "3  p0 d1 q1  6079.368511\n",
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       "4  p1 d0 q0  6106.900505\n",
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      ]
     },
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   ],
   "source": [
    "def my_auto_arima(data, order, sort='AIC'):\n",
    "    order_list = []\n",
    "    aic_list = []\n",
    "    bic_lsit = []\n",
    "\n",
    "    for p in range(order[0]):\n",
    "        for d in range(order[1]):\n",
    "            for q in range(order[2]):\n",
    "                model = ARIMA(data, order=(p, d, q))\n",
    "\n",
    "                try:\n",
    "                    model_fit = model.fit()\n",
    "                    c_order = f'p{p} d{d} q{q}'\n",
    "                    aic = model_fit.aic\n",
    "                    bic = model_fit.bic\n",
    "                    order_list.append(c_order)\n",
    "                    aic_list.append(aic)\n",
    "                    bic_list.append(bic)\n",
    "                except:\n",
    "                    pass\n",
    "\n",
    "                result_df = pd.DataFrame(list(zip(order_list, aic_list)),\n",
    "                                         columns=['order', 'AIC'])\n",
    "                result_df.sort_values(sort, inplace=True)\n",
    "\n",
    "    return result_df\n",
    "\n",
    "\n",
    "my_auto_arima(series, [2, 2, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "차분을 1번이라도 한 게, 차분을 안 한 것보다는 AIC값이 더 낮았고,\n",
    "\n",
    "최적의 모형은 역시 차분만 하고 AR, MA는 안 한 모형으로 나온 것이 확인 되었다.\n",
    "\n",
    "그 다음은 기존 날짜의 예측값과 실제 값을 비교해서 시각화 하고\n",
    "\n",
    "forecast로 그 이후에 몇일까지를 예측할 것인지 지정을 해주면 실제 예측 값이 나오는 방식이다."
   ]
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mrIqvd0xmQvs3hqZJlRnn3AbvdwHwAjAJ2Ox1HeH9LvA2Xwf0abB7PrDBa89vpH27fcwsAGQAxY3Ecb9zboJzbkJeXl5TQhcREZGWUlUIwPq61F1XZnx+CCRtvZpOFeW1OyQzn969X2HsMZkxsxQzS6u/DJwIzAdeBi7zNrsMeMm7/DIwxZuhNIDYQN9ZXldUhZlN9sbDXLrDPvXHOg943xtXIyIiIu2Vty7TmtpdnDCvXoPqTIZV7dzNVFe5X2E0pZupO/CCN6gnADzunHvTzGYDT5vZVcAa4HwA59wCM3saWAiEge875+rPX3wt8B8gCXjD+wF4CPivmS0jVpGZsl+PSkRERFpeVaybaV1dMhNT95DMVG8h6OLonVhHbWWUYDhCQsCb7Bys2K8w9pjMOOdWAOMaaS8CjtvFPjcDNzfSPgcY3Uh7LV4yJCIiIh1E6WoAClwWQ7qn7Xq7+FTq/CmsDWXQO7EOKqG8JkxeWvMkMzoDsIiIiOy1N+dvpHDJTMqT+1JBMmPzM3a9cXwK4cz+BOPS6ZEQG+y73biZlq7MiIiIiGxVWQAPHseLNd/ngLrPWZY2htzUBHqkJ+56n6N/STIwauZ9lG+Jzf3ZbtxMsHy/QlJlRkRERJpu/VwoXcM3qp+mhyvkvbLejM3PaPyEefUGHx/7ScwgIRxLXMprmq8yo2RGREREmq5wMQAn+ucCMKeuP2N676aLqaHETAJ1sWSmTMmMiIiItKZHPlnF3NUlsGXJ1rYoxgLXb/fjZRpKzMBXV44R3X5JA42ZERERkRazcR7usW/yZOnPieYM5c3UxWxOHUlWxVJqUvKpC6cyrk9m046VlIm5KCnUqptJREREWsmm+VjlJi7jFRZvLidSsIjF/iE8Fn8uGUdew/RfHkNu6i6WMthRYqyCkxuo2ZbMRMIQqt6vEJXMiIiIyK556y+d45/OKFtFIFTJV8HufNz729jka+iWtptZTDvykpleiXXbpmbX7V9VBpTMiIiIyO5UF+HMRxwR7kr9NwCflOcyuFvq3h8rMROAHnE12wYA72cXEyiZERERkd2pLqIuMY8HIqcyILQMgGXR3gzap2QmVpnpFl9LeY03AFjJjIiIiLSo6mJq4zK5NXwhVQNPxaX14kdnH86pY3ru/bGSMgHIDdQ2a2VGs5lERERk16qLqPJnEMVH6Nx/Y4EwFyfsQ1UGtlZmcvw1FJUFcc5hqsyIiIhIi3COl75YT3nxZip86fgM0pMSYF8TGYCEDPDHMyZ+IxvKanl/UcF+L2UASmZERERkR6s+purPg3jt6QeIVm2hhDSykuPx+XazZEFT+Hww/hIGbXiZQ7PK+Oubi4nWqjIjIiIizWn9XNz/vkFKXRGHBRaT7iopCKeSlRLfPMc/8heYL47bMp9l2eZSnv1k4X4fUsmMiIiIbLPiAyxcywaXzeSElfjMsbgijuzmSmbSe8LRv6THxvf4pMc/qChcu9+H1ABgERER2SZcC8D86ACOCX8FwNraZLKTmymZATj8ekjOpfvLP+Cb8auoiiQB+z52RpUZERER2SZcS9SfwArXkzhXB0Axac3XzVTvgIsgIYO0SCnlLmm/DqVkRkRERLYJB3H+BFa5HlubSlwa2SlxzXs/Pj/0PRiASiUzIiIi0mxCNUR88dslM8UuNpup2fWdDEC1L3m/DqNkRkRERLYJB4n6E1kV7b61qYTU5hsA3FDfQwDwJ6bt12E0AFhERES2CdcQ9sWzmSyi/kQiDmpJaP4xMwC9DgR/PImpWft1GCUzIiIisk04SMSXgMNHKKM/kZoyqIa81ITmv6+4RDjyF3RLHQC8sM+HUTIjIiIi24RqCPtiiUuo9ySSazZyx8njGdUrvWXu76ifs79HVjIjIiIi24SD1FmsS6n6+FtJTU/iTNvPZQxamAYAi4iIyDbhGsJeMpMQHwftPJEBJTMiIiLSUDhI0GLdTAmBjpEmdIwoRUREpHWEawlZ7AR5SmZERESk4wnVEiSehIAP6wBdTKBkRkRERBoKb0tmOoqOE6mIiIi0vHAttS6OxDh/W0fSZEpmREREJMa5WDJDHAlxHSdF6DiRioiISMsKBwGoicaTGFBlRkRERDqacC0ANS6gyoyIiIh0QA2SGVVmREREpOPxkpnqaLwqMyIiItIBheqTGb8qMyIiItIBeZWZyohmM4mIiEhH5M1mqopqzIyIiIh0ROEaACrCms0kIiIiHZFXmamMBEhQZUZEREQ6nFCsMlOuyoyIiIh0SFsrM5rNJCIiIh2RN2am1uk8MyIiItIReZWZIHEaMyMiIiI7W7ihnLXF1W0dxq55Y2ZqiSexA1VmAm0dgIiISKdXUwKv/ZTfLTmRssSevPGjI4jzt8NkwavM1KkyIyIiIttZ9h7Mf46rax5gWUElj326uq0jaly4FucLEMHfoSozTY7UzPxm9rmZvepdzzazd8xsqfc7q8G2N5jZMjNbbGYnNWg/yMy+8m67w8zMa08ws6e89plm1r8ZH6OIiEjb2vA5ACf553BG2lJuf28poUi0jYNqRLiWqD8RoNNWZn4EfN3g+q+A95xzQ4D3vOuY2UhgCjAKOBm428zqn5F7gKuBId7PyV77VUCJc24w8E/g1n16NCIiIu3R+s/YnDKMzS6Tn2VPp7Q6xMbS2raOamfhWqL+BIDOV5kxs3zgNODBBs1nAY94lx8Bzm7Q/qRzLuicWwksAyaZWU8g3Tk3wznngEd32Kf+WM8Cx9VXbURERDq0aAQ2zmOejWB13CByQhsAWFfSDgcCh2qJ+GLJTGeszNwO/AJoWBPr7pzbCOD97ua19wbWNthundfW27u8Y/t2+zjnwkAZkLNjEGZ2tZnNMbM5hYWFTQxdRESkDRUuhlAVH1TlE0nPJ6naS2ZKa9o4sEaEa4l0xsqMmZ0OFDjn5jbxmI1VVNxu2ne3z/YNzt3vnJvgnJuQl5fXxHBERETa0IbPAPi0th+JuQPw15aQarWsK2mfyUy4A1ZmmjI1+zDgTDM7FUgE0s3sf8BmM+vpnNvodSEVeNuvA/o02D8f2OC15zfS3nCfdWYWADKA4n18TCIiIu3HxnmEAymsqO1Javd4WAJjU8tZ396SmYrNrNxURKg6VkvoVJUZ59wNzrl851x/YgN733fOXQK8DFzmbXYZ8JJ3+WVgijdDaQCxgb6zvK6oCjOb7I2HuXSHfeqPdZ53HztVZkRERDqc8g1UJ/XE4SO52wAARqeU7TxmpnwDr81dznVPfN76MW76Cv4xlJ6ln1FUG6vIdKTKzP6kXX8BTjCzpcAJ3nWccwuAp4GFwJvA951zEW+fa4kNIl4GLAfe8NofAnLMbBnwE7yZUSIiIh1eVSEVgWwA0nsOBGBIQgnrG46ZcQ7uOwrfx7fx8rwNrT9te8U0ABItRNDiYpc7UGVmr84A7JybBkzzLhcBx+1iu5uBmxtpnwOMbqS9Fjh/b2IRERHpECoLKLUhxAd8pGb3An88/fxb2FhWSzgSJeD3QVUhVBWQFloJQEFFkN6ZSa0X45pPqYnLwl9XzsCeuUz2Z5Oa0HEWCeg4kYqIiHREVYVsSZ1AXmoC5vNDRh+6u0IiUcfm+qSleAUAqXWxmbqbympbL5lxDtbM4LOESbzqn8SfzzqOJ3uNb537biYdp4YkIiLS0dRVQV0lm6Lp5KbGx9oy+5BVtwmAdfWLTnrJTK6LzX3ZXN6KJ9TbshSqi3i3agDhQSdAB0tkQMmMiIhIy6mMTfRdX5dGbmpsyjOZfUn2zjWzddxMcax7qTslGFE2lbViMrNmBgAf1A5mQv+sPWzcPimZERERaSlVsW6j1cGUbclMRl8CNYUkUMem+gqMV5mJswg5VLRuZWbdLILxmaxwPTmgj5IZERERacirzKysTSE3zetmSusOQJ/4SrZU1MXaSlYS9T6SR6RWbktyWsPGeaxLHEZCwM+gvJTWu99mpGRGRESkpVTFkpnNkXTy6iszKbHVfwYnV1NYGYy1Fa9gfeJgAEalVrZaN9MLs1bgChYxP9qP4T3TYzOrOqCOGbWIiEhHUBnrZioindw0L5lJjSUz/RKq2FIRhJoSqCnhcxsJQP/48pbvZto4j+g9h/HyS09g0RAfVfZiVK/0lr3PFqRkRkREpKVUFRCKzyRMYNuYGS+Z6RNfwZbK4NbBv9ODg4ngp7e/hE3ltbToifBXf4Jv83x+6X8CgDnBPkpmREREpBGVBdQmxM7+uzWZSYktlNzDXx7rZipdA8D82hyq43PoRgm1oSjlNeGWi6tsHQDDfWupcEmsdt0Z3Suj5e6vhSmZERERaSlVhVT4Y8nM1jEzgQRIzCTXyiitDhGp2gLAlmg6tYndyIrErrfoIGAvgQJYav3x+fwM65HWcvfXwpTMiIiItJTKzZT6Mon3+0hPanDS/dRuZLlSAKrLYslLGSnUJffYehbgDWUtuKp22To2p44g6AJkD53M9ccPITGu4ywsuSMlMyIiIi2lspAiMshJjcfMtrWndCMtXAJAbdkWIoEkgsQTTe9FUtV6En0RPl1RBEA0EuX/vbqQBRvKmi+usnWsjh/MFYG/0P+cG/nBsUOa79htQMmMiIhISwjVQF0Fm6IZ28bL1EvNI7kulqyEq4oIxWcCUNf3CCxUxRW91/HW/E24r54jemt/Xpj+Bbe9vaSZ4qqFqgLWRHKoyhoBSR3zRHkNKZkRERFpCfVLGYRSt63LVC+1O/G1se6laHUxtYHYTCL/4OMgLoVvJH7GqqJqKuc8TqCujPP8HzJ1cQEbSpuh66l8PQDLghn0as2VuVuQkhkREZGW4C1lsCaYunNlJiUPX10FCdThqymh2h+bSZSRlgZDT2RQ0VSSrZbEtdMB+Fb8VCDKU7PX7n9cZbFjLKzKaL2VuVuYkhkREZGW4FVmVtQkbzthXr2t55qpJFBXSqUvFTNIT4qDEWfgq97CXTnPExet5fnI4eS7TXw3fx2PzVxDTV1k/+LypmWvCGerMiMiIiK7sXUpg4xt07LrpcbWZxqcXE1iqIwy0shIisPvMxh2KnQfzbGVr1JLPDeFLiOUlMc1/pfYUhnksZmr9y+u0rU4jM1OyYyIiIjsTmNLGdTzTpw3IKGS5Eg5JS6VzKS42G1xSXDxs5DVHzf8DG6+8HACR/6EjE0z+E7+Ou6Ztpzquv04oV7ZOoKJeYQIqJtJREREdqOqgHB8OnXENTIAONbNNDRuM36ibImkkJncYJv0nvCDuSSddy9njOuFTbgS0npyjf9FiqrqWLChfN/jKltLeUIPAHplJu77cdoRJTMiIiItoXIzNfE5ADt3M6X1BH8Co91SANYHk8hMjtt+G38AAl6CE5cIA44itSp25t7K2v2pzKyl0N+NxDgf2Snxe96+A1AyIyIi0hIqC6kM7LAuUz2fH3IG06fySwCWVATISt5DYpGQRiBUGTt0cB+TmWgUytazweXQKzNp+xP5dWBKZkRERFpCVQFlvkwCPiMjKW7n2/OGkhiMnWumOJra+DYNJaTiC1XFDr2vyUz1FogEWRHK7jTjZUDJjIiISMuoLGSLt5SBz9dIBSR32NaLpaTuuTITn4pFQ8QT2vfKTGnsHDNLajLolaFkRkRERHYlVAvBMjZH03fuYqqXN3TrxVKXuvOYmR0lxFa1TqVm35OZ+hPmVWfQO6vzJDOBPW8iIiIie8U7+++GUDq5ObtIZhpUZspIaXIykx0XbHo3UzjIIx8tZvqaIH2yU/hdzloMWO+NmekslMyIiIg0N++EeWuCKbuuzOQMBvNR60siTBMGAMenApAXH6Iy2ISzAG9egLvvKC6LhohET+ePX1/E9ZNXkRxIoZyUTjMtG9TNJCIi0vy8E+atrE0hN20XSUpcImT2I+KtmL3HadIJsWQmN66uaZWZRa9BNMziaD5npi0CoGrzKioTewCmAcAiIiKyGxUbAVgfziB/d0lDn4NJ7DmMm88Zzcie6bs/ZrzXzRQINm3MzPKpbEoeyjtuEjnVK8jw1+HK1lIS1x0z6JHReSoz6mYSERFpbqVrcBZgM1m7H2h75h34nePiuCYkFt6YmcxAHV/vKZkJVsC6WXwYdxa1eWOx4uc5JbeAlIpNrE4YRl5qAgkB/148oPZNlRkREZHmVraW6qTuRPHROzN519sFEmLdTU3hdTNl+pswAHjVxxAN81LFMHKGTQbg+KSlpEfLmF+VTt/s3cTUASmZERERaW6laymN7wnQfFOgvQHAmb7aPSczKz8k4k9gbnQoI4cMgfR8jtryOABTK/vw/WMGN09M7YSSGRERkWZUUFFLpGQ1my2PzOQ4UhOaaUSH182U5qulMhimKhhmRWFl49uWrqYyuS9B4slLS4De44kLV/FGZCLZY07imOHdmiemdkLJjIiISHOIhOCd33PTf17FKjexJprTvDOGfH6ISyaVGs6qe5XXXnmG0+6YTnVdI1Waqi1UBrIAyElJgEHHQUoeiWf+nZvPGd18MbUTSmZERESaw8oP4ON/cULBw/hwzK/MaP7pz/GppFDDT+0Jxi2/j5pQhJkrinferqqQcl86AZ+RnhSACVfATxZxzMQDSE/cw8n5OiAlMyIiIs1h8RsAnOKbBcCCmkzys5p5oG1CKpmhApItyICar0gkyIdLC7feHAzWctPLCwhXFlJCOlkp8dtWxvZ33gnMSmZERET2l3Nbk5lECwGw3uU2//pHCWlkV68EIJ4wB/sWMX3pFkqr6yh8869wa39e+WQegbpyCqNp5OzpRHydhJIZERGR/bVxHpSv59XooQBEMTa6Zh4zAxCfRkrtxq1XvxH3KWcWP8zLt15OzoxbSIjWcJBvCQCbw6l7PqtwJ9F5a04iIiKtZfn7APwl9E1OTZxFdVw2odoA+c1emUndenFptDdn+T4g4jf85qhM7kNq9VpOydkMFbA+lNJlkhlVZkRERPZX+QZC8Rmsc92o6DaB+B7Due64IYzY0xIFe8s710zY+bg9fC7FeZPYdOHbhH61gdQffgTAcLcCgDW1yV2mm0mVGRERkf1VVUBtfDYAW059gEG5KfwkJaf578c710wBmbwWncy1Z/+M0b0zYre5ZIhPpW8w1s20NpjMASm7WLG7k1FlRkREZH9VbaEqEEtmsnJ7QEskMrC1m2mjix2/Z8PFIs0gI5+UUGyqdrFLJye1a1RmlMyIiIjsr8oCynwZ+H1GZlILnsfFWzl7o8smPuDbeUxMem8Aos4oJbXLdDMpmREREdlfVYUUkUl2Sjw+n7Xc/TSozPTMSNx2Dpl6GfkAlJBKlEaSnU5KyYyIiMj+CNdBbSkF0TRyU1t4jEr9mBnLoUd6I6ttZ/QBYl1MgLqZREREpAmqtwCwIZxGbksnD95sprK4vO3Hy9TLiHUzlflig4Kzu8gAYM1mEhER2R+VBQCsq0tp+TEqmX0B47RjjyFv4KCdb/e6mWrjs/AFadnxO+2IkhkREZH9URWrzKysSWFUS3cz5U+An3zNUek9G7/dGwAcSswhK9LC43fakT12M5lZopnNMrN5ZrbAzP7gtWeb2TtmttT7ndVgnxvMbJmZLTazkxq0H2RmX3m33WHeyCUzSzCzp7z2mWbWvwUeq4iISPOrii30uCGcSk5LJzMAu0pkIJbM+BPoP2AIPzh2cMvH0k40ZcxMEDjWOTcOOAA42cwmA78C3nPODQHe865jZiOBKcAo4GTgbjPze8e6B7gaGOL9nOy1XwWUOOcGA/8Ebt3/hyYiItIKqmLdTFtcRsuPmdmTuET4zvsMOPV6rjhsQNvG0or2mMy4mErvapz344CzgEe89keAs73LZwFPOueCzrmVwDJgkpn1BNKdczOccw54dId96o/1LHCc7TTfTEREpB2qKiTqT6CKxJafzdQUPUZvnfXUVTRpNpOZ+c3sC6AAeMc5NxPo7pzbCOD97uZt3htY22D3dV5bb+/yju3b7eOcCwNlwE6nTzSzq81sjpnNKSwsbNIDFBERaVGVhQQTcgFrH8lMF9SkZMY5F3HOHQDkE6uyjN7N5o1VVNxu2ne3z45x3O+cm+Ccm5CXl7eHqEVERFpBVSHVcbFho13lvC7tzV6dZ8Y5VwpMIzbWZbPXdYT3u8DbbB3Qp8Fu+cAGrz2/kfbt9jGzAJABFO9NbCIiIm2iqoBiYud1UTLTNpoymynPzDK9y0nA8cAi4GXgMm+zy4CXvMsvA1O8GUoDiA30neV1RVWY2WRvPMylO+xTf6zzgPe9cTUiIiLtV8kqXOESZpSkcdqYniQE/HveR5pdU84z0xN4xJuR5AOeds69amYzgKfN7CpgDXA+gHNugZk9DSwEwsD3nXMR71jXAv8BkoA3vB+Ah4D/mtkyYhWZKc3x4ERERFpS9Su/wBeFf7szeOy0EW0dTpdlHbUAMmHCBDdnzpy2DkNERLqisnVUvvwLUpe/xt8jF9LnzF9zwcS+bR1Vh2Zmc51zE/ZlX50BWEREZG+983sSV77H7eFvcNo1NzMif6cJuNKKtNCkiIjI3to0n2VpE7nPLmBYr+y2jqbLUzIjIiKyN8J1ULycxdF8BndL7TLrH7VnSmZERET2RvFyiIaZW92NId1T2zoaQcmMiIjI3ilcBMDc6u4M6da1lg1or5TMiIiI7I2CRTiMZa4XQ1WZaReUzIiIiOyNwkVUJucTJF6VmXZCyYyIiMjeKFzE+rh+JMb5yM9KautoBCUzIiIiTVe6Ble0jGklORw1NE8zmdoJnTRPRESkKSJh3LPfpjoax+txJ/HQ2WPaOiLxqDIjIiLSFPMex9bN5Ia6K/nWKUeSl5bQ1hGJR8mMiIhIUyx8mZKEfF7nME4c1aOto5EGlMyIiIjswZI164mu+IB3ohOYPDCXjKS4tg5JGtCYGRERkV2pq4IXv8eK5TUMjdbxTM1YTj+me1tHJTtQMiMiIrIrG76AhS9yMlDs0lgYGMEdo5TMtDdKZkRERHaleAUAz0WOoNeoI5l5zomkJuijs73RmBkREZFdKV5B1AL8InQ1wfGXK5Fpp5TMiIiI7ErxCqqSexPBT/+clLaORnZByYyIiMiulKykMK43fp/RW0sXtFtKZkRERBrjHBSvZA096J2ZRJxfH5ntlTr/REREGlNdBMFylgTy6JeT3NbRyG4ozRQREWmMN5Ppi6osjZdp55TMiIiINMZLZhYFc1WZaeeUzIiIiDSmaBnOfKxzeQzpntbW0chuKJkRERFpzJpPKUgaQtQXz4R+WW0djeyGkhkREZEdhWph3WxmuhGMzc8gRSfLa9eUzIiIiOxo/RwI1/Ja+SAmD8xp62hkD5TMiIhI11S4hGkz53DkX6eyqawWolEKSir4ydNfULP0AxzGjMhwJTMdgJIZERHpeqJR+N83GPH2JRQUl/DbF+fjXv0x9u+TeP6zdRTNf48NSUOo8acyob/Gy7R3SmZERKTrWTsTytbSPbKRm1Jf5N2vNxP8+i3yyhdwif9depZ9zkuVIznvoHyS4zVepr3TX0hERLqeBc8T9iXwSmgCF9grvJM6mcSaTQD8v7h/U+kSedSdygvHDWnjQKUpVJkREZGuJRLGLXiBT/0TeDn9YsxFuTHhcQCmRsYB8HraeVxy7IH0zNDikh2BKjMiItK1zLgLqyrkv3WXcN4Zx8L0kfQt+Ipql8BPQ9fyxoSFfPPkX0JCaltHKk2kyoyIiHQdK6bh3r2JVyKT6X/YNzltbE8YeTYAC31DqI7LJPv0PyiR6WCUzIiISNfx+f8IJmTzi9DVfHNS31jbyLMASBh4KFcdPoA4vz4aOxp1M4mISNdRsIj1iUOJVCbTL9tbPLLbcJjyOGP6HsKY5Oy2jU/2idJPERHpGqIR2LKEJS6fgXkpBBpWYIafBkpkOiwlMyIi0jWUrIJIkM9rumsV7E5GyYyIiHQNBV8DMLOyG0O7aYBvZ6JkRkREuobCWDKz1OWrMtPJKJkREZGuoWARVUm9qCaRod1VmelMlMyIiEjXULiITfH9iPf76Fs/k0k6BSUzIiLS+UWjULSMFZZPn+yk7WcySYenv6aIiHR+VQUQrmVpKJf8LFVlOhslMyIi0vmVrAZgYXUmfbK1eGRno2RGREQ6v9I1AHxdm63KTCekZEZERDq/0lUArHe59FEy0+nsMZkxsz5mNtXMvjazBWb2I68928zeMbOl3u+sBvvcYGbLzGyxmZ3UoP0gM/vKu+0OMzOvPcHMnvLaZ5pZ/xZ4rCIi0lWVriGYkEstCeRnqZups2lKZSYM/NQ5NwKYDHzfzEYCvwLec84NAd7zruPdNgUYBZwM3G1mfu9Y9wBXA0O8n5O99quAEufcYOCfwK3N8NhERERiSlZTltATgD6alt3p7DGZcc5tdM595l2uAL4GegNnAY94mz0CnO1dPgt40jkXdM6tBJYBk8ysJ5DunJvhnHPAozvsU3+sZ4Hj6qs2IiIi+610DQX+biTH+8lKjmvraKSZ7dWYGa/7ZzwwE+junNsIsYQH6OZt1htY22C3dV5bb+/yju3b7eOcCwNlQE4j93+1mc0xszmFhYV7E7qIiHQgs1cV89IX65vnYNEIlK1jjetGflYS+q7c+TQ5mTGzVOA54MfOufLdbdpIm9tN++722b7BufudcxOccxPy8vL2FLKIiHQ0kRDcezifvvoQv3ruK+rCUQCiUUd5bWjfjlmxEaIhltVla/BvJ9WkZMbM4oglMo855573mjd7XUd4vwu89nVAnwa75wMbvPb8Rtq328fMAkAGULy3D0ZERDq44pWw6SvGF79FTSjCZ6uLqf38aW6490mO+utUqoJhiISYtWwTP3zic1YXVe3xkNEtywH4vDydfjkpLf0IpA00ZTaTAQ8BXzvnbmtw08vAZd7ly4CXGrRP8WYoDSA20HeW1xVVYWaTvWNeusM+9cc6D3jfG1cjIiKd0JOz1jBvbenON2xZDMC4yHziCBN459ckvvQdztp4ByXVIeZ88TlVt0+kx3+PYMmXn3LGndP5orHjAISDLH79Lir+dzE1Lp64XmP47lEDW+wxSdtpSmXmMOBbwLFm9oX3cyrwF+AEM1sKnOBdxzm3AHgaWAi8CXzfORfxjnUt8CCxQcHLgTe89oeAHDNbBvwEb2aUiIh0Mhu+IPLPsTzw4pv88InPCYYj299euAiANKvhlriHmLDpKdZE85gcWMzYxELGvn0BkYoCUnxhXk/9E9185Tz40Yqd76diE+F/HciwWb9hvfXkk2Of5d5rTqV7emIrPEhpbU2ZzTTdOWfOubHOuQO8n9edc0XOueOcc0O838UN9rnZOTfIOTfMOfdGg/Y5zrnR3m0/qK++OOdqnXPnO+cGO+cmOecaeWWKiEiH98Xj+MtW81v//1hTXM0jn6za/vbCJQTjM4k443z/B8yODuVfWb/G5yI8EP8PMsLFXBS8gcIzHsUfquI73Zfy0dIthCPRbcdwDvfydUQrCrjG3UD6D6Zx3FFH4fNp4G9npTMAi4hIy6jYxPwPX+SKPz/IxJvf5YmZq2HRq9RYEsf45/GDPqu4e9pythtVULiI9UnDme9i3UG3+S7nonPOhrRedK9bw8vRQ+g2bDLDxx8OaT05wjePspoQ89aVUhvyqjzzn8OWvsUtoSkcctIU8rM1TqazUzIjIiIt49GzGP3+Zfw7+FO+lfgJT770EpSv5+bQJVQFsjgnbgal1SE2lwdj20ejsGUpy11vnkq5BE6+lcdv/B4H9c+GEWfgzMfS4d/n16eOADMYfBw9tsxgtG8VLz/zH0bf+BbPzFkL856kJKE3j7mTOPuA3ruPUTqFQFsHICIinVDxCihcxMOcxeHJa/lh1b84K6k34bCPV8IT+UXeArrVxU5Jtrywkh4ZiVC2FsI1zAv2oKTPUTD5oG3n7Tjm19i4Kfy894Hb7mPwCfg+/x8vxv+OQGWEovhf8OcXajg3YRpv+09j8qA8MnSCvC5BlRkREWl+y94D4NHgkSw79l5sxJn0zUqkcvS3eOK6U0jPH0lKxQrAsaKwMrZPYWwm06zKXIZ0S93+eEmZ0DCRARh0DPgTqMsYwOaU4dwRfzc/TXoFXzTE05XjOHFUj5Z9jNJuqDIjIiLNb9m7lCbmsybYk0NGDIAJ/8aATO+HNUPwBcvpG1/J8kLvXDELXyJscSxxffjL+CZ0DyVmwDUfkZzWk+RgOTx8CheXvUCxZfKlDeXukd1b6tFJO6NkRkREmk1tRTHvv/saxyyZyiuRoxjXJ5OslPidN8wdAsBhmSUsL6yEgkW4eY/zaPhkTp04nIF5qTvv05i8YbHfienw7Xfg+e+Q2udwXht1lKZhdyFKZkREpHl8che8ewunRmOVFv/I0/nDEaMa3zZ3KADjkwr4sLAKpt5F0JK4L3o2Lx83ZN/uP60HXPYK8cDQfTuCdFBKZkREZP9VFcHbv2GBbwzvdb+UX1x4Chdl9tn19um9IZDEkMAmKF2DW/Qq/42eyaFjh6miIntNA4BFRGT/rfoIgJtrziVnzAmwu0QGwOeD3MH0Dq/jwsD7OAf/CR7DJZP7tUKw0tkomRERkf238kNC/mS+dAM5ZGBO0/bJGUJO6Zdc5H+P9yLjyeg5iAP7ZrZomNI5KZkREZH9t/JDliaNJS05ieE90pq2z/DT8MclkJ7oJ+O4n/DAZROIrUMssnc0ZkZERPZP+QYoWsp7/kM5ZFBO09dAGnMejDmPADCpRQOUzk6VGRER2T/LpwLwZvUwjhqa18bBSFekyoyIiOyVsuo6/jtjJetKg1wyuR+jv36FsvgeLKrrzwkjddZdaX1KZkREpOne+T2BT//D+WHj2ugv+fZXK/jE/z7v+E5k8sAcshs7QZ5IC1M3k4iINE3hYvj4X3wW6kd8fALPJN/Kz/1P4osEebJyPCeP7tnWEUoXpWRGRESaZvaDRCyOH9V9j5Lzn8ef1o1zI29QGZdDqNdETh2tLiZpG+pmEhERAJxzPDFrLQUVtRw2OJeJ/bO33RiswH3xOG/boQwe0J+BQ0fDoBmw8EVSU3J5aeCRbRe4dHlKZkREBBa/Sd0bv2FScTU/CV3LC3NH8e6lPbjytQqGdE/nhrjHiaur5J7g8fz+JG9xR38gNr1apI0pmREREVjwAr7KjfSyMDf2nsPLG5cRd98jXBKZwNSVB2CBh3kqcjSjJx3DhIYVG5F2QMmMiIhAwULWpoxhYYlxatV0Uv3JbHaZHO2fx0n+OVTG5VJ60O+44ejhbR2pyE6UzIiIdHXRCGxZwtLk05mXOojTq2cwzFfEb0NXkDnxAn52SAapGb35bmJGW0cq0ijNZhIR6epKVkG4lrk1PSjpfRQEEon44nk1eghnTB4N3UeCEhlpx1SZERHp6goWAvBpZXdO6tUdun8Pn/l4cdzp9M9NaePgRPZMyYyISFdX8DUAS11vftAtFUbdiAH92zQokaZTN5OISFdX8DUVSb2pIZFhPdLaOhqRvaZkRkSkKytYRMXS6cyq6k6vjET6ZCW3dUQie03dTCIiXYhzjjfnb8IMDvUvIu3pc3HReBbnn8+LUw7D57O2DlFkrymZERHppJYXVvLFmlLOPSgfALfwZda8/ndKS7N5NHIifRPuJ8tyuCz+Vl66/CyS4v1tHLHIvlEyIyLS2UQj8PgFTN88gBsLjyYl4Mhf8yIj5v4eXzSHc+KXMcV9gLko1wW/z1WnTlAiIx2akhkRkc5m6Tuw7B0udj42xNUw+vnryLctfOkfyZITH+bcsTnYyz8kGg5y0WHXc/DA3LaOWGS/mHOurWPYJxMmTHBz5sxp6zBERNoF5xwvfL6eNcXVXLnyp0Q3LaAmDD2tiJXWlwUjruPkcy4nEBfX1qGKNMrM5jrnJuzLvqrMiIh0UHVlm3nio4WsWzSL71Q/SM9QLpWuN+mBD/lb6JtkjjmF7/RZx4BJVzMgLrGtwxVpMUpmREQ6Gudgxl3wzh+5zNUBsNzXnxGplRwc/oTCrEM48fgbGDN4AGh2knQBSmZERDqaVR/B27/lw8iB1A06kVNH5jLowEshkADOkWdGXlvHKNKKlMyIiHQ0S98hanFcF/oBjx59DPTP3nabqRIjXY/OACwizat4Jc9MX8A5d39MaXVdW0fTOa2YyqrkUfgTUhnXJ7OtoxFpc0pmRKT5lKwmes+hjHlnCgvXFPDTp+cRjXbMGZPtVmUhbPqKd4MjmTwohzi//o2L6F0g0oWV1YRYuaWq0ducc+x46oYNJVX87sX5bCit2doWjkSpqYswc/E6ljz0bUKhMMNtDc/2fY73Fm3mj68uZOGGch6evpJQJLpPcdYVr+MXz87jgQ9X7NP+ncrKDwB4tWoERw7R+WFEQGNmRLom5+DDv3HH1914ZlNPZv3meBLj/BCNUrPkfe57YxZPbBlEXk4W1w8r5qGvA/yg7kHy61byTO2fqQqGue2Mvix8/zFenbuMYyOfMNGW4jPHQ2nf47g+jjEL7+Gl3lFKZ6/li1k5/DH8bUqr6zh8SB6fr9hAr4r53Lm8O8eM6MENp45oNMZpSwqp/eCfnLzhburqvsfffUdyzoG9yU1NaP3nrB1wy96j4uVfEnTp+HqN44xxvdo6JJF2QcmMSFe0/D2YejOHR8bxUOiXTF+6heNHdodpfybpw7/yY+DbSVkUVyTSd/ZGjgOiGD4cf8qfw2Pz1lG67C5GhjYzEihN6ceSvtcwcNxRXDXi5Nh9vO1n3Iy7CMUlEhetpXu37mRM/4yE6XWcZ0XkWAWLfVfwfx+dwBnjeuH3GQNyU1hTVMlr70/j0tW/ZlRtBXlWRtj5+HX667xcdiiPfLKKn544rO2euxbyxZoSnpy9liOG5DFxQBYbS2v5fE0Jx4/sTn5WMnVfPE3gxe+yOdqTaSP/xjPnH6EuJhGPzgAs0tU4h3vgWGzDZ4QIcAwPMGnkQP5x9hD45yg+rRvIK2kXcEvi/4jWlPHF4O8xNrmIwMAj4IO/Et34FeHaSgrI5KUBN3HVmceSmNVr51k0zsGaGdB9FDz1LVj5AVv8eZSmDqZv91yo2Ehc8VL+X90F5EU283ToCG5L+g9Do0uJOqOSJJanHsSkkYOJdhtFwms/5O4ef+LeTcO2VZI6gVkzptH9g1+QUbOO56JHURRNY5xvOelU86fwJRTF9+aP3aZxXOEjzI0O5cOJ9/Cz08djmrUkncz+nAFYyYxIF7KlMkjp1DsZPPdPPB4+hosCU3mm58/4dEOEA+PXcHHoOc4L/p7LL7yQ08f0jCUkvgbf/ld+BI+cTmG3Q5lz0N84edKopn2oVm2B+c/DuCmQmB5rK/ga7jkMXGTrZnUEeMd/FEcPTMN3wo0kdRsYuyEShjsOoCB5MJNWfocXvnco4/tmNeMzE1NRGyIlPoCvNU40t/oTtjx9HblVSykig8KMMQwr/wRzUaoSe+B3YRLqinHO4cMxI+lo/GffwaRh/Vo+NpE2oOUMRKRxZev5cFkx93y4ih8lvkpw0xKOss94J3IgwRP/CnO/wXkb/8H55iAE65KGM2jU8Zw8qkes0rJjojLgCLjuc/Iy+3GKby8qIym5cPDV27d1GwHnPQQY5A6FD27FN/4yjut/1M5VF38A+h9BztJ3AMf89WX7ncxEoo53Fm6mui5MVt1Gokve4qdLRtGvRx5/O38cQ7un7dfxd6fo81dJe/lKKiKZfNT9e5x+6U/JScuFUC24KClxSVBdDDPuxOKSYeAxHNJnYovFI9LRqTIj0pn9axyRkrVUugQSqaMw0Av/4GMIH/8n+uRlwEe34T57lIWjf86gntkk9hoFmX3bOurGzbwf3vg5J/vuY8yIEfzt/HH7dpxolHXv3k3x7KcproUQfo7wfUWihSgM9OCH0Z+yxAbw4S+OITVh2/e9gvJakuL9+MxYVlDJii2V9MtKIFhZygNzSumbncw543vvdN6X2lCEV7/cyPAeaYzO9VHx9DWkLX+Vxa4v0w5+gG+ffDB+LTkgosqMiDSibB2UrGKhDSOSkkf/82+hV9+x23ehHPET7IifMKrtomy6XuMBOCVnE2+s34dZPM4RWfI2K1/4I4Nr51NLH/JzMkj1BanJOZ2yIWfQ/cMbeCjpcUat/RmPfLKK7x09CEpWUfLp//jHJ5Vku1KG+NaRSxmr3RDG+mYwyLeR7uRzx4pzOXvGJKZM7Muhg3LpkxIiNON+Ele8xUvBc7nZhvBsxr/oVz2fe30XcMJV/4/v9u7WzE+SSNekZEaks1o7C4Bf136Ls449jQP6D2zjgPZTj9Fgfg5OWM0d6wbx1Ow1VAYjXHX4ACDWbVQbipDSoJpSVBlkwYZyFmwoZ9ym5zh00c0kuRzeHvJbDj3vx6QmxgEQD2QA+MpIefV6fp0/nyXTZnPIRwdzX+IdjKuewa3eYSviu0NiBkeWP09lch/m9bqWMRXTuX3zv7ghYwCzPu9BxWeJDPTPJN2qKfNl8Gj8rUTwY1UR7s79NSd981oGtWA3lkhXs8dkxsweBk4HCpxzo722bOApoD+wCvimc67Eu+0G4CogAlznnHvLaz8I+A+QBLwO/Mg558wsAXgUOAgoAi5wzq1qtkconUpFbQiANO9DSHZj3Wwi/kS+dn35Q7/mHyzb6uKSoNtIRpd/yKfxz/LvF0/h7shZxIWr6LPxLR5amc2Xdb3475WTiFv3Mcs+fYX0kq8Z7FtPRXQgB/o+58PoGJ4b8U9uv3BC4wOXD7gEPrqNq7f8GQy+DIxjbPU8/hX+BoEDpvD90yeTlpgR27aykNTEDMYF4mMDlOc8TPdl73B64RKiVUUUdT+czROuY8jIg2D6bQQiIdyIM/lh/kGt+7yJdAF7HDNjZkcClcCjDZKZvwLFzrm/mNmvgCzn3C/NbCTwBDAJ6AW8Cwx1zkXMbBbwI+BTYsnMHc65N8zse8BY59w1ZjYFOMc5d8GeAteYmdblnGvbqaDRCHx6N9+dN4RiS+eZaw5tu1g6igeOY015mOOLf8VXfziRhEAnmMr80g/g8/8ScYbfHJ8kHc2Y6pmkWQ2VlsqDgSkcF3yPMb6VhPFTkjwQX+4gsjd+RMSfyMNj/seU4yaSvrtkeMU0WP5+LEH59P+o9adyfPQunr/+FLqlJ7baQxXpalp0zIxz7kMz679D81nA0d7lR4BpwC+99iedc0FgpZktAyaZ2Sog3Tk3wwv4UeBs4A1vn5u8Yz0L3GVm5jrqyOTOpnQNa5Yv5JSX4NJD+/OTE4a2zYm6VkyDt3/L+PDp/CV8EcsLKxmUl7rH3daX1jB3dQmnj+nZOtNt24tQLW7jPGbFn8no3umdI5EBGHICLH2H+Yffw6gv/sAhBR+ztPvxlB34TfI/vZEflz5IQUJvZgz5PeNP/y55yd5rpLacQKSOq1OacPr/gUfHfpyD+GQS84bz7vAzO815bUQ6o30dM9PdObcRwDm30czqR7H1JlZ5qbfOawt5l3dsr99nrXessJmVATnAlh3v1MyuBq4G6Nu3nc646Gxe+xl9l77F76NH87tpV7B0cyX3feugnWdflK7lqYU1TF1ewd0XH4jPZ0SijhlLN7N4yULe25jEgLxU/nDmKAJ7mQyVVYeom/0MecDZ/o/5a3gKL32+nin9q7htdg1rKn38v7NHEyDKjHlfsXTlGioqKzi59k2+rs3ittC5JAR8nDSqxz49BWuLqymprmN0r4wOkxDVfXo/8dEQb5X347xj+rR1OM1n5Fkw4kzGmcGBkyESZGiS14U26lDY+CXdBh9Htx2njdef22ZvmMGxv43tvp9hi0jLau4BwI39p3e7ad/dPjs3Onc/cD/Eupn2JUDZC3XVsPID1vryuSAwjYP6pHL81xfy1zcXbb+WTmUB7v8OJiE0kTdrr+atBZs42X3Esrfu44DK+RxutQwKHM4VK64hFIly67lj99hlVVQZ5L5pS7ii9n88viKRy6peo8gy6GEl/L7nTPp+fDu9PpnDj10eT/hO44s7V3Kifw4X2/aLJh7n9/N24ik8PnMNJ43qQXVdmFDYkZEc62aoqYvw4dJC+mQlM6Jn2vZxBSsIvfFrXv4qwqNVhxDI7M3T1xxC78ykZnuKm8vGgkLe/PBjXluXyBWR5zit4mnejhzEoSdfyEUHd7LEv/5vFJ8MJG9rT+sR+xGRLmdfk5nNZtbTq8r0BAq89nVAw6+B+cAGrz2/kfaG+6wzswCxSQXF+xiXNKeVH0K4lhvqvsV1w0qZtPIe7hg4iOs+NC47tD+96j/Up9+Ohao4w33A/1LP5fPXH+CUmn8QiPZkac/TGZWfxdFzH+Dpgf05f86pHDW0G6eN7bnLu3WvXE/oy3c4oLYnPf2z+CmAwfV11/KXpEe5vOROKkhiWt7FHF43nZ+X/YdgQiobexxDZOiR5HTrFesiSO+F78Hj+HXPOdy9bDmP/vN5Zhf6eS06mQuGx3FC7dvYpnl8GhrBn6IH4TL6ccLI7hw3ohvBUJS+c25h6IpH+T7wrYz3OaH6Fq5/6gue+M7kfT4vSElVHTNXFnFQ0kZu+TREecjH384fR1pigIDPMDMqakOkJgSaNkapbB3Ln/gZfTa+wxUW5gqv+Y2Ek8n95h2cOKj7PsUpItKR7Gsy8zJwGfAX7/dLDdofN7PbiA0AHgLM8gYAV5jZZGAmcClw5w7HmgGcB7y/r+NlnHMs2lRBelJcu/z23OEseZOQP5lZ0eFknXQsvD6Pk8tfBQ7m7QWbuPywAVCxCTfnIT7gQA7xLeCR+L8SV7WBWW44bx14L78964BY6c3VMeHz/3JC7iH87a1FDO2eytzVJYSijm+M771tOu3Xr2JzHybBpXKqfy2ze1xIP9tEXtlXTD7hcqL+wVC+iviDf8jRGd0hHITKzSSk59Pf10j31cCjOWT1wxwaXwdlcGk8/L/450hduQm/OYoC3TmGOdzIf1kXGcBHcwbhn72BIKkM9M3hicgxlA07j2tWXMdzvR7j2lVHc/gtZYzqk8MZ43px2phYUvb52lK+WldG7zQfa4pr+GJDNVcc1p8J/bOJRB3riirInfH/+GT+asqrg+QFpnJ5dBB3uvP459+eY1GoB33jy+kRqOLDynyykwO4lDw2WzcO7JfF5IHZ9M5MYkNZLRtLqtlYHqRfySdctPp39I6E+SD9DA489ARyqpfDgKM4ZeBRrfUqERFpc02ZzfQEscG+ucBm4EbgReBpoC+wBjjfOVfsbf8b4EogDPzYOfeG1z6BbVOz3wB+6E3NTgT+C4wnVpGZ4pxbsafAt5vNFK6j+LPnmf3us/yt4gRKkgfy1HcnM7ibzuPQVM455q8vp3dWEtkp8ZSvnofvv2fzcd0gbsv6PW/++Ahs9oPw+s+4MuX/qMkYzBNXT4Y3fkV05v0cE/wbTx+2gW6LH2djz2OJP/535HZrUPKvKoI7DqAkfRgfbIqjrxWw1nXj+tD3uOqIQfzmtJFQVUTk/yaxpDqVP3b7J/87PQ1//kGxboW6KkjY84DfnSx9F568iDWjriUy4SoGlM+GOf+mtscE6sZeTHqvIVC0HJa8CYtex62fS0X6YBKrN+Iz46XDnuPECSNJm30HvPdHACr9GbzE0dxWdTKXZc/noOAs0kJbWOO6caTvS4LEcw/fZEFdDw5K3kxyuJQ+0XWc5f+EoIsjwUIsyD2Z4aUf4g9X7zb8Qn8PPokMJRKJ0tu20JMielgxJaSTbeUsjvbhrVF/5/rzj+8w43lERBrTJReaHDVimOt21X1cfkhfpqy8gYRlbwJQHZ/LxZEb2ejvzXs/PWq7E2jJ9rZUBslNiafg0yf4fPobvFLSj/Xkcknyp5wdfpMKl8wzQ/7Kued8k+yUeCjfALeN4KM+13D58qOY86PRZN4/gZcih/DGoN9x37f28Br86B/w3h+p8adTktyPXhVf8XivG/jX6gF8e1IuwxfcxuS6Tzk3cgv/+tElDMhNaZ4HGo3A3qwjBBCNQjQEgYRtbYVLYPN8+Ppl3IIXMW9o13pfT+Jz+pFds5qybhNJrlpL4ubPdzrkzD5X4T/8R0zoBmT1g5LVULQUMvvBliWQkhdbw2jTV+CPh9I1sOoj3JqZhCye6qQe+DLzSczOJ76mEOcLUH7Un8jIytmPJ0dEpH3oksnMhF4B9+OrziHeBflm4AP+HLqQo067iEM/uoyS9GGMX/1D7v/WQZy4jzNYOrX1n7F8wSymvJ/GQ5kPM7Z2DiH8xBFbvTiKj4+zzqL7mX9g6IAdVuh98Hhqaqo5YP3P+Xf2oxxcPY3j627j/35wLiN77WHGSCQcO39H/8MgkAQPHkukZA211ZWkWBCAe/0XkXnSDUyZ1M4Hra7/DL58CoafBv2P2H5BxmgUNn0JNSWQ1R9Su0NNMWTk7/JwIiJdXZdMZgb2zHQrvhuLfXHvc9ly9K0cNiQP3r0J98mdHBx+gOPHD+GWc8a0caTt0L9Pg9XTCTk/UXw8nHwlp19xA31CK6CyAHIGQ+6Qxved/SC89lPq/CnER6q4j/MYc8mtHDq4Cefv2NGq6fCf0ynqNpkNvU5kdFYEO/z62ArJIiLSpXTJZKbXkFFuw/yZgIOEBmNjVn0M/zmVe7rfxP/KxjH9l8e07Zlr25tQLfylL1/5hhO0eIZfeDOJfSc2/dwvzsGi12DG/1E96kKCo6eQlRK/7/GUb4xVLhobvCsiIl1Gl1w1u1dGUuMDQvtMgoR0Toj7iltLh7KsoJIhWtBtmw2fQSTIXcHj6X/Y+UwYMGLP+zRkBiNOhxGns8NZPvZN+q6naIuIiDRF5/s67I+DQccwoPQTkqjl+qe/4IlZa/h0RRFPzV7Dqi1Vez5GZ7b6YwA+DQ9j8gANHBURkY6vw1Zmdmv0ufgXvsS8tB8zo3QkJa/4MCvmr3U/4qjxI7ntggPaOsJW55xj1ooicma/TVygP+WWykH9O8FKyiIi0uV1zmRm5Flw5dvEz3mYI9fNIlpdgr+2hJOzN7K2anBbR9dqnHMUVQYpmv004U/vZ3xwIQGiPMWJHD00b/crB4uIiHQQnTOZAeh7MPQ9GAP8xSvgjvH0T6plXlWwrSPbqqYuQkLAhxks2VxJv5zk5lmZt2Q1H099la++nMuB0flM8i1mNT1Z3v9CBmcHuPDQ73Fh3rD9vx8REZF2oPMmMw0lx8aGdAtUUlIWauNggJoSqj9/jhPfyeH05IUMszU8VjSU+YGR/PLk4Vxx2IA9H8M55q4p5ZV5G7js0P7bTjC3ZRmRe4/gsHA1h+CjIqU3i0fdRI+jr6Vfqtb+FRGRzqdrJDMJ6eCLI9cqKa6qa+toYNqtJM+8h3ddHIlVseTqnAS4M+sG/vwGHDe8O31zGpknFKplc8EG/vDSfH5XdiOJtVFWhC7g+E8P4M/fGMM3x/cg/OxVVIX9XBf4G//60UVkpqWS0coPT0REpDV1jWTGDJJzyKScmlCEmroISfHN0J3TRNGoozoUISXez4fzV3DY3Ef53DeOaHwqBx11JjUjziftqW/wvYr/8IjvL/zoiTkc0M3P+pp4UhPjGNkrnahzXLzuT3Rf8gL/cPGE8WP+DB61W/lX9m/59fOO8Z//liGbvuA34Z/wg8vPIzNtH9YyEhER6WC6RjIDkJxDhisHoKS6jqT4fVhVOxqhYuUcvvduDanU0DPVx6dbkvnzN8Ywrk9mo9uvnf44T8xaw+bici5J+IC4sBHwV/Gn4Hn84NxvEhjVgzSAU/6K/+ET+STuewQKq/FtcZRYBptcDpULAjwUPpVvx7/IB9FxZOT0YNR5vyGt2zB49Eyu2/h3jk0ayJD1C7kz8g1OOv87TOyfvT/PloiISIfRhZKZbFIqywAorqqjV+ZeJjPOEX7pOtLm/Y+HXIB4C1NFIudwG798zvHKDw8nruFZdEvXUvrfb9Gn6HN+ARAPBf5e5FJAad5Ezh57BseN6L5t+74Hw8m3Er9lMS45FxLTydq8gMzqItz6z5hYfTuVJPHzyA948bIziKuP/4LHsBevYVRVMVt6/IALj/0duWkaGyMiIl1HF0pmckgsXg+wb+NmPvoHgXn/43/h4zh0RF8G9u5ByvTb+W+35zh4xVX84ZUF/OSEYWTXbWTq1LcY+eWfSXK13J7+U6448wQyfDV0G3A0BMvJ9MdxZXwjK0JPvgaAhosvGGAFi+Cx84iOuYz7hp6wfSKWmgeXPIcP2IfVkURERDq8rpPMpOQSX1cCxLqZditYyfNTP2HqsjKWh3IZkJvMHevvYm7cJB7P/DGXXHxkbLtAIt3fvZHXutXxk5mncfEXn/Oa/2ccEwlS7Mvi9fEP850TTyAlocHTnJS597F3Gw4//op0M8bv/d4iIiKdWtdJZpJz8NWW4iO6+8pMwde4e4/gG9EQ3wCK/bncVXYOfkq4t+5Izjkif9u2h3wfQtWMmnkfr2Yv5a3KwYTDES6p+x23fP8SpuT3aL74tVimiIhIozrf2ky7kpyD4ciySkp2l8zMfx6iEX5U9z2WH/Jnsq2K3/EgRS6N6W4sZx7Qa9u2/jg45tfwreeJqy7gdJvOs5EjyBxxNIObM5ERERGRXepSyQxA/6Raiqrq+GhpIbWhyM7bLXqN5clj+DDxGPodfw0cfyOGY3m3kzhv0kC6pzcyuLb3QXDYj3GBJFKP/Rl/PGt0Cz8YERERqdelupkATg3MIXfBG1w281tcdthAbjxj1LZtildAwQKe51KOG9WdgN8Hk74L5mPSiDOZlN5z18c/7vfYYddxZpIWbxQREWlNXS6ZuTj0DIkuyMf+vrz9aRl5rphXV8KDx0Ypm/ovRgCvBMfzp7Fe4uLzwcHf3fPxzUCJjIiISKvrcslMoostNPmb+KcIRP9L5dxEFoYvo/tzd9LNwcyMk7j93HM4qJ8SExERkY6gC42Z2XZG3FtDU0h3FYRzhpLrr+GuuH+xKtqdS3OfZPx1TyqRERER6UC6TjITlwRxKdQEMrg/chqbr5xFxven4j/rDkjrRfDsB7n7qmOID3Sdp0RERKQz6DrdTAB5w3DdD+SewZPo0debOj1uCoy9gJE6j4uIiEiH1LWSmaveJtl8nOjbYcVsJTIiIiIdVtdKZvxxbR2BiIiINDMNEBEREZEOTcmMiIiIdGhKZkRERKRDUzIjIiIiHZqSGREREenQlMyIiIhIh6ZkRkRERDo0JTMiIiLSoSmZERERkQ5NyYyIiIh0aEpmREREpENTMiMiIiIdmjnn2jqGfWJmFcDi3WySAZQ14VDNuV3DbXKBLa18n3u7XWMxtvR97ut2u3s+W+o+9+VY+/t3b63ntmGcbf2c7Wm7OHb/t2/r93q9fX0/7c997st29XG2p9djY9vs6T3fXp5b/R9tnmPlAjnOubQmbLsz51yH/AHm7OH2+5t4nGbbruE2u4uvpe5zb7drLMaWvs/9eJy7/Xu3l+d2f//urfXcNoyzrZ+zPW3X3t/ru/vbt8fntj7O9vR6bGyb1vy76/9ou3hu5zQ1vsZ+OnM30yttsJ3us2W3a+377CrPbXs9lu5T96n77Dr/R/dLR+5mmuOcm9DWcexKe48POkaM9TpKrIqz+XWUWBVn81Kcza89x2pmcwD2Nb5A84bTqu5v6wD2oL3HBx0jxnodJVbF2fw6SqyKs3kpzubXnmPdr9g6bGVGREREBDQ1W0RERDo4JTMiIiLSoSmZ2U9mdo6ZOTMb3taxNOTF9N8G1wNmVmhmr7ZlXHtiZpVtHUNT7SlWM5tmZm022K69vjZ3ZGa/MbMFZvalmX1hZge3dUy7Ymb5ZvaSmS01s+Vm9i8zi9/N9j82s+RWjtGZ2T8aXP+Zmd3UmjHsiZlFvL/1AjObZ2Y/MbN2/XnUEf43NXhe63/672bbVvv/1BqfR+36xdNBXAhMB6bszU5m5m+ZcLaqAkabWZJ3/QRgfQvfp7Qv+/TabE1mdghwOnCgc24scDywtm2japyZGfA88KJzbggwFEgFbt7Nbj8GWjWZAYLAN8wst5Xvd2/UOOcOcM6NIva/6VTgxjaOqTOof17rf1a1dUCe/f48MrPdTlhSMrMfzCwVOAy4Cu8Dw8yONrMPzewFM1toZvfWf+Mws0oz+6OZzQQOaYUQ3wBO8y5fCDzRIPZJZvaJmX3u/R7mtX9kZgc02O5jMxvbCrFu5T2Hrza4fpeZXe5dXmVmfzCzz8zsq7auOuwu1ra0m9fmrp7XU81skZlNN7M7WrGC1xPY4pwLAjjntjjnNpjZQWb2gZnNNbO3zKynF+c0M7vde83ON7NJrRQnwLFArXPu316sEeB64EozSzGzv3uvyS/N7Idmdh3QC5hqZlNbMc4wsZkh1+94g5n1M7P3vBjfM7O+Zpbhva/q/08lm9laM4trjWCdcwXA1cAPLMZvZn8zs9lenN9tEP8vvOd4npn9pTXia8jMUr3nrf7/z1lee38z+9rMHvCqTW83+OBuU7t6L3kuacX30r58Hl1uZs+Y2SvA27s7uJKZ/XM28KZzbglQbGYHeu2TgJ8CY4BBwDe89hRgvnPuYOfc9FaI70lgipklAmOBmQ1uWwQc6ZwbD/weuMVrfxC4HMDMhgIJzrkvWyHWvbHFOXcgcA/ws7YOpp06m8ZfmzvxXh/3Aac45w4H8lonRCD2D6qPmS0xs7vN7CjvQ/RO4Dzn3EHAw2xf/Uhxzh0KfM+7rbWMAuY2bHDOlQNrgG8DA4DxXoXpMefcHcAG4Bjn3DGtGCfA/wEXm1nGDu13AY/Wxwjc4ZwrA+YBR3nbnAG85ZwLtVawzrkVxD6PuhFLwMuccxOBicB3zGyAmZ1C7HV9sHNuHPDX1oqvgVrgHO//zzHAP8zMvNuGAP/nVZtKgXPbIL4k29bF9EI7ey/ty+cRxL74X+acO3Z3B+/I55lpDy4EbvcuP+ldfw2Y5b05MbMngMOBZ4EI8FxrBeec+9JifaYXAq/vcHMG8IiZDQEcsfVvAJ4BfmdmPweuBP7TOtHulee933PZlijK9nb12mzMcGCFc26ld/0JYt+UW5xzrtLMDgKOIPbh8BTw/4DRwDve54Qf2Nhgtye8fT80s3Qzy3TOlbZCuEbsvdJY+5HAvc65sBdbcSvEs0vOuXIzexS4DqhpcNMhbHvP/JdtCcFTwAXAVGKVvLtbKdSG6pOCE4GxZnaedz2DWKJwPPBv51w1tNlzbMAtZnYkEAV6A92921Y6577wLs8F+rd6dF43U/0VMxtNO3kv7ePnEcA7TflbK5nZR2aWQ6zsPNrMHLEXiSP2R9rxH1799VqvNN2aXgb+DhwN5DRo/xMw1Tl3jvcCmwbgnKs2s3eAs4BvAm0xgDXM9lXDxB1uD3q/I7T9a3hPsba63bw2X6bxWI025L0npgHTzOwr4PvAAufcrrpid/X+amkL2OHbtpmlA32AFa0YR1PdDnwG/Hs329TH/DLwZzPLBg4C3m/Z0LZnZgOJvZ8LiL0ef+ice2uHbU6m7Z/ji4lVLg9yzoXMbBXb3kfBBttFgPbQzWS0r/fSXn0eeaqacmB1M+2784iVa/s55/o75/oAK4lVYSZ5ZVEfsW87rdGltCsPA390zn21Q3sG2wZgXb7DbQ8CdwCz2+jbz2pgpJkleGXy49oghqZqj7Hu6rUJjce6CBho22Y+XNBagZrZMO/bWL0DgK+BPIsNDsbM4sxsVINtLvDaDyfWHdGUFXmbw3tAspld6t2/H/gHserl28A15g1S9JICgApg31YB3k/ee/dpYt029T5h24Dwi/H+NznnKoFZwL+AV1vzS5eZ5QH3Ane52Flc3wKurR+zY2ZDzSyF2HN8pXmzwxo8x60pAyjwEpljgH5tEMPeWEz7ei/ty+dRk7T1t9qO7EJgxwFozwHXAjO828YAHwIvtG5o2zjn1hH7B7WjvxIr6/2EHb6FOefmmlk5u/9G1+y8D4Kgc26tmT0NfAksBT5vzTiaop3HuqvX5kXEPty2i9U5V2Nm3wPeNLMtxD7UWksqcKeZZRKrci0j1sV1P3CHl3QFiFUZFnj7lJjZJ0A6sa7QVuGcc2Z2DnC3mf2O2JfB14FfE/smPhT40sxCwAPExqfcD7xhZhvbYNwMxJKtHzS4fh3wsNeNXAhc0eC2p4h1Mx/dCnElmdkXxLoTwsS6vG7zbnuQWBfNZ954lELgbOfcmxabnDDHzOrY9ty3uPr3O7FxRq9YbB2hL4h9EWi3nHN1Xnddu3gv7cvnUVNpOYNmZmZHAz9zzp3exqHsMzPrRazMN9w5F23F+x0HPOCca80ZKvukI8XaFGaW6o1fMWKDR5c65/7Z1nHtyMymEXt/zWnrWKTr6Gzv985I3UyyHa+EPhP4TSsnMtcQG4z229a6z33VkWLdC9/xvikvIFbyva9twxFpHzrp+73TUWVGREREOjRVZkRERKRDUzIjIiLiMbM+ZjbVYmf0XWBmP/Las83sHYuty/WOmWV57SdY7Oy6X3m/j21wrJstdjbldr+uU0enbiYRERGPxU7339M595mZpRE7Ad7ZxKYMFzvn/mJmvwKynHO/NLPxwGZvGY7RxM6e3Ns71mRip29Y6pxLbYvH01UomREREdkFM3uJ2DT7u4CjnXMbvYRnmnNu2A7bGrAF6FW/3pjXXqlkpmWpm0lERKQR3okkxxOb4dndObcRwPvdrZFdzgU+b5jISOvQSfNERER2YLGV558DfuytdbWn7UcBtxJbW0pamSozIiIiDXhLKTxHbPXz+oVtN3vdS/XjagoabJ9P7Ezvlzrnlrd2vKJkRkREZCtv3MtDwNfOudsa3PQycJl3+TLgJW/7TGIr0t/gnPu4FUOVBjQAWERExOMtuvgR8BVQfxb0XxMbN/M00BdYA5zvnCs2s98CNxBb76zeic65AjP7K7E10XoBG4AHnXM3tcoD6WKUzIiIiEiHpm4mERER6dCUzIiIiEiHpmRGREREOjQlMyIiItKhKZkRERGRDk3JjIiIiHRoSmZERESkQ/v/hZ5A83/I5+MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([49730.98961644, 49843.54923288, 49956.10884932, 50068.66846575,\n",
      "       50181.22808219]), array([ 993.22014229, 1404.62539564, 1720.30774954, 1986.44028457,\n",
      "       2220.90775477]), array([[47784.31390884, 51677.66532404],\n",
      "       [47090.53404565, 52596.56442011],\n",
      "       [46584.36761789, 53327.85008074],\n",
      "       [46175.31705055, 53962.01988095],\n",
      "       [45828.32886985, 54534.12729453]]))\n"
     ]
    }
   ],
   "source": [
    "model_fit.plot_predict()\n",
    "plt.show()\n",
    "\n",
    "fore = model_fit.forecast(steps=5)\n",
    "print(fore)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 잔차 분석\n",
    "\n",
    "최적의 모델에서 나온 잔차를 그래프로 그려보고 acf, pacf를 분석을 통해 잔차가 정상성을 가지는지 확인해보고\n",
    "\n",
    "qqplot과 shapiro test, normaltest로 정규분포 형태를 가지는지 확인 해보고\n",
    "\n",
    "마지막으로 durbin_watson 검증을 통해서 잔차의 자기상관 관계 여부를 확인해보았다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:22:39.620334Z",
     "start_time": "2021-03-10T14:22:39.604310Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_rolling(data, interval):\n",
    "    \n",
    "    rolmean = data.rolling(interval).mean()\n",
    "    rolstd = data.rolling(interval).std()\n",
    "    \n",
    "    #Plot rolling statistics:\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    plt.xlabel('Date')\n",
    "    orig = plt.plot(data, color='blue',label='Original')\n",
    "    mean = plt.plot(rolmean, color='red', label='Rolling Mean')\n",
    "    std = plt.plot(rolstd, color='black', label = 'Rolling Std')\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:22:40.251784Z",
     "start_time": "2021-03-10T14:22:39.887010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [9, 6]\n",
    "plot_rolling(model_fit.resid, 30)\n",
    "plot_acf(model_fit.resid)\n",
    "plot_pacf(model_fit.resid)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "잔차의 그래프만 확인해보면, 1차 차분을 한 것과 모양이 굉장히 흡사하다.\n",
    "\n",
    "평균을 일정해 보이는 것이 확인이 되었고, 분산의 경우, 마지막 부분에 왔다갔다 하는 값이 크기 때문에 분산이 일정하다고는 말 할 수 없을 것으로 보인다.\n",
    "\n",
    "정상성을 추가로 확인하기 위해서, ACF, PACF 표를 확인해본 결과, 두 그래프에서 모두 절단점이 발견되지 않아\n",
    "\n",
    "정상 시계열일 것으로 추측할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:08:15.688657Z",
     "start_time": "2021-03-10T14:08:15.674656Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "원 데이터 ADF Statistic: -5.660\n",
      "원 데이터 p-value: 0.000\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller\n",
    "result = adfuller(model_fit.resid)\n",
    "print(f'원 데이터 ADF Statistic: {result[0]:.3f}')\n",
    "print(f'원 데이터 p-value: {result[1]:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ADF 검증을 통해서 확인해본 결과, pvalue가 매우 작으므로, 귀무가설인 비정상 시계열임을 기각하고\n",
    "\n",
    "정상 시계열임을 채택할 수 있다.\n",
    "\n",
    "그리고 잔차가 정규분포인지를 확인해보는 것의 경우, 아래와 같은 결과가 나왔는데\n",
    "\n",
    "시각화를 해서 봤을 때는, 어느 정도는 정규분포를 따르는 모습으로 보이기는 하지만\n",
    "\n",
    "shapiro wilk test와 normaltest를 통해서 수행한 결과에서는 모두 pvalue가 매우 작아서\n",
    "\n",
    "귀무가설인 해당 잔차가 정규분포를 따른다는 가설을 기각하게 된 모습을 확인할 수 있었다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:25:27.827419Z",
     "start_time": "2021-03-10T14:25:27.727386Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics=0.730, p=0.000\n",
      "Sample does not look Gaussian (reject H0)\n",
      "----------------\n",
      "Statistics=126.455, p=0.000\n",
      "Sample does not look Gaussian (reject H0)\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot\n",
    "from scipy.stats import shapiro, normaltest\n",
    "\n",
    "qqplot(model_fit.resid, line='s')\n",
    "plt.show()\n",
    "\n",
    "stat1, p1 = shapiro(model_fit.resid)\n",
    "print('Statistics=%.3f, p=%.3f' % (stat1, p1))\n",
    "# interpret\n",
    "alpha = 0.05\n",
    "if p1 > alpha:\n",
    " print('Sample looks Gaussian (fail to reject H0)')\n",
    "else:\n",
    " print('Sample does not look Gaussian (reject H0)')\n",
    "\n",
    "print(\"----------------\")\n",
    "\n",
    "stat2, p2 = normaltest(model_fit.resid)\n",
    "print('Statistics=%.3f, p=%.3f' % (stat2, p2))\n",
    "# interpret\n",
    "alpha = 0.05\n",
    "if p2 > alpha:\n",
    " print('Sample looks Gaussian (fail to reject H0)')\n",
    "else:\n",
    " print('Sample does not look Gaussian (reject H0)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "마지막으로 잔차가 자기상관관계를 가지고 있는지 확인하기 위해서 durbin watson 검증을 수행한 결과\n",
    "\n",
    "2에 가까운 값을 가진 것으로 확인 하였다.\n",
    "\n",
    "2에 가까울수록 auto correlation을 가지고 있지 않다는 가설을 채택할 수 있다.\n",
    "\n",
    "pvalue는 R 처럼 나오지 않기에, 값이 2에 얼마나 가까운지를 통해서 결론을 도출하여야 한다.\n",
    "\n",
    "0에 가까우면 양의 auto correlation, 4에 가까우면 음의 auto correlation을 가진다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:08:16.747636Z",
     "start_time": "2021-03-10T14:08:16.740630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9869860884341106"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#자기상관\n",
    "from statsmodels.stats.stattools import durbin_watson\n",
    "\n",
    "durbin_watson(model_fit.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## cf1) SARIMA 사용시\n",
    "\n",
    "19회 ADP 실기 시험에서 SARIMA가 나왔다는 이야기가 있어서\n",
    "\n",
    "일단은 추가로 포스팅을 해본다.\n",
    "\n",
    "딱히 나올 가능성이 크지는 않을 것으로 보인다.\n",
    "\n",
    "나와도 어차피 공식 문서를 활용해서 충분히 구현 가능할 것으로 보인다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-03-10T14:08:48.012554Z",
     "start_time": "2021-03-10T14:08:33.459432Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████████████████████████████████████████████████| 8/8 [00:13<00:00,  1.66s/it]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>                <td>price</td>             <th>  No. Observations:  </th>    <td>366</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>           <td>SARIMAX(1, 1, 1)x(0, 1, 1, 12)</td> <th>  Log Likelihood     </th> <td>-2841.303</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>                   <td>Wed, 10 Mar 2021</td>        <th>  AIC                </th> <td>5690.606</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                       <td>23:08:48</td>            <th>  BIC                </th> <td>5705.910</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>                    <td>03-02-2020</td>           <th>  HQIC               </th> <td>5696.705</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                          <td>- 03-02-2021</td>          <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>               <td>opg</td>              <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ar.L1</th>    <td>   -0.8834</td> <td>    0.085</td> <td>  -10.434</td> <td> 0.000</td> <td>   -1.049</td> <td>   -0.717</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>    <td>    0.9155</td> <td>    0.074</td> <td>   12.310</td> <td> 0.000</td> <td>    0.770</td> <td>    1.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.S.L12</th> <td>   -0.9451</td> <td>    0.038</td> <td>  -25.004</td> <td> 0.000</td> <td>   -1.019</td> <td>   -0.871</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th>   <td> 1.053e+06</td> <td> 3.83e+04</td> <td>   27.462</td> <td> 0.000</td> <td> 9.78e+05</td> <td> 1.13e+06</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>     <td>0.81</td>  <th>  Jarque-Bera (JB):  </th> <td>2460.19</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                <td>0.37</td>  <th>  Prob(JB):          </th>  <td>0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>22.13</td> <th>  Skew:              </th>  <td>0.75</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>    <td>0.00</td>  <th>  Kurtosis:          </th>  <td>16.11</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                     SARIMAX Results                                      \n",
       "==========================================================================================\n",
       "Dep. Variable:                              price   No. Observations:                  366\n",
       "Model:             SARIMAX(1, 1, 1)x(0, 1, 1, 12)   Log Likelihood               -2841.303\n",
       "Date:                            Wed, 10 Mar 2021   AIC                           5690.606\n",
       "Time:                                    23:08:48   BIC                           5705.910\n",
       "Sample:                                03-02-2020   HQIC                          5696.705\n",
       "                                     - 03-02-2021                                         \n",
       "Covariance Type:                              opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "ar.L1         -0.8834      0.085    -10.434      0.000      -1.049      -0.717\n",
       "ma.L1          0.9155      0.074     12.310      0.000       0.770       1.061\n",
       "ma.S.L12      -0.9451      0.038    -25.004      0.000      -1.019      -0.871\n",
       "sigma2      1.053e+06   3.83e+04     27.462      0.000    9.78e+05    1.13e+06\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                   0.81   Jarque-Bera (JB):              2460.19\n",
       "Prob(Q):                              0.37   Prob(JB):                         0.00\n",
       "Heteroskedasticity (H):              22.13   Skew:                             0.75\n",
       "Prob(H) (two-sided):                  0.00   Kurtosis:                        16.11\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from tqdm import tqdm\n",
    "import itertools\n",
    "# Grid Search\n",
    "p = d = q = range(0,2) # p, d, and q can be either 0, 1, or 2\n",
    "pdq = list(itertools.product(p,d,q)) # gets all possible combinations of p, d, and q \n",
    "p2 = d2 = q2 = range(0, 2) # second set of p's, d's, and q's\n",
    "pdq2 = list(itertools.product(p2,d2,q2)) # simular too code above but for seasonal parameters\n",
    "s = 12 # here I use twelve but the number here is representative of the periodicty of the seasonal cycle\n",
    "pdqs2 = [(c[0], c[1], c[2], s) for c in pdq2]\n",
    "combs = {}\n",
    "aics = []\n",
    "# Grid Search Continued\n",
    "for combination in tqdm(pdq):\n",
    "    for seasonal_combination in pdqs2:\n",
    "        try:\n",
    "            model = sm.tsa.statespace.SARIMAX(series, order=combination, seasonal_order=seasonal_combination,\n",
    "                                             enforce_stationarity=False,\n",
    "                                             enforce_invertibility=False)\n",
    "            model = model.fit()\n",
    "            combs.update({model.aic : [combination, seasonal_combination]})\n",
    "            aics.append(model.aic)\n",
    "            \n",
    "        except:\n",
    "            continue\n",
    "            \n",
    "best_aic = min(aics)\n",
    "# Modeling and forcasting\n",
    "model = sm.tsa.statespace.SARIMAX(series, order=combs[best_aic][0], seasonal_order=combs[best_aic][1],\n",
    "                                             enforce_stationarity=False,\n",
    "                                             enforce_invertibility=False)\n",
    "model = model.fit()\n",
    "model.summary()"
   ]
  }
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