05_volatility_volume_relationship.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "bAM_eZzd2eN-"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotly.graph_objects as go\n",
    "import seaborn as sns\n",
    "import yfinance as yf\n",
    "from statsmodels.regression.linear_model import OLS\n",
    "from statsmodels.tools.tools import add_constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 467
    },
    "id": "tGMsKcxZ2lYq",
    "outputId": "8361763f-9218-40e6-8dcd-e07a0beee27e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-01-02</th>\n",
       "      <td>14.50</td>\n",
       "      <td>14.84</td>\n",
       "      <td>14.48</td>\n",
       "      <td>14.83</td>\n",
       "      <td>109370878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-03</th>\n",
       "      <td>14.67</td>\n",
       "      <td>14.73</td>\n",
       "      <td>14.09</td>\n",
       "      <td>14.27</td>\n",
       "      <td>153873531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-06</th>\n",
       "      <td>14.03</td>\n",
       "      <td>14.08</td>\n",
       "      <td>13.50</td>\n",
       "      <td>13.57</td>\n",
       "      <td>136423179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-07</th>\n",
       "      <td>13.79</td>\n",
       "      <td>13.86</td>\n",
       "      <td>13.52</td>\n",
       "      <td>13.54</td>\n",
       "      <td>154729229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-08</th>\n",
       "      <td>13.05</td>\n",
       "      <td>13.62</td>\n",
       "      <td>13.03</td>\n",
       "      <td>13.50</td>\n",
       "      <td>197012716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-08-27</th>\n",
       "      <td>12.75</td>\n",
       "      <td>12.75</td>\n",
       "      <td>12.53</td>\n",
       "      <td>12.68</td>\n",
       "      <td>64421920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-08-31</th>\n",
       "      <td>12.72</td>\n",
       "      <td>12.78</td>\n",
       "      <td>12.64</td>\n",
       "      <td>12.68</td>\n",
       "      <td>53636208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-09-01</th>\n",
       "      <td>12.73</td>\n",
       "      <td>12.98</td>\n",
       "      <td>12.73</td>\n",
       "      <td>12.90</td>\n",
       "      <td>89007860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-09-02</th>\n",
       "      <td>12.92</td>\n",
       "      <td>12.93</td>\n",
       "      <td>12.80</td>\n",
       "      <td>12.90</td>\n",
       "      <td>54512227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-09-03</th>\n",
       "      <td>12.95</td>\n",
       "      <td>13.09</td>\n",
       "      <td>12.82</td>\n",
       "      <td>12.88</td>\n",
       "      <td>92161781</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>417 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Open   High    Low  Close     Volume\n",
       "Date                                             \n",
       "2020-01-02  14.50  14.84  14.48  14.83  109370878\n",
       "2020-01-03  14.67  14.73  14.09  14.27  153873531\n",
       "2020-01-06  14.03  14.08  13.50  13.57  136423179\n",
       "2020-01-07  13.79  13.86  13.52  13.54  154729229\n",
       "2020-01-08  13.05  13.62  13.03  13.50  197012716\n",
       "...           ...    ...    ...    ...        ...\n",
       "2021-08-27  12.75  12.75  12.53  12.68   64421920\n",
       "2021-08-31  12.72  12.78  12.64  12.68   53636208\n",
       "2021-09-01  12.73  12.98  12.73  12.90   89007860\n",
       "2021-09-02  12.92  12.93  12.80  12.90   54512227\n",
       "2021-09-03  12.95  13.09  12.82  12.88   92161781\n",
       "\n",
       "[417 rows x 5 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thyao = yf.download(\"THYAO.IS\", period=\"max\", start=\"2020-01-02\")\n",
    "thyao.drop([\"Close\"], axis=1, inplace=True)\n",
    "thyao.rename(columns={\"Adj Close\": \"Close\"}, inplace=True)\n",
    "thyao"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "alPe-gr52sw4"
   },
   "outputs": [],
   "source": [
    "# True Range as Volatility proxy\n",
    "thyao[\"TR\"] = thyao.Close - thyao.Open"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "U_B_jcHM3FCz"
   },
   "outputs": [],
   "source": [
    "# Normalize volume and tr for each day by\n",
    "# subtracting the mean of the last 20 days\n",
    "# and dividing by the last 20 days’ standard\n",
    "# deviation for each\n",
    "thyao[\"TR_norm\"] = np.nan\n",
    "thyao[\"Vol_norm\"] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "-D3ksEBa54fg"
   },
   "outputs": [],
   "source": [
    "for i in range(22, len(thyao)):\n",
    "    data = thyao.iloc[i - 22 : i, [4, 5]]\n",
    "\n",
    "    Vol_mean = np.mean(data.Volume)\n",
    "    Vol_stdd = np.std(data.Volume)\n",
    "    TR_mean = np.mean(data.TR)\n",
    "    TR_stdd = np.std(data.TR)\n",
    "\n",
    "    thyao.loc[thyao.index[i], \"Vol_norm\"] = (\n",
    "        thyao.loc[thyao.index[i], \"Volume\"] - Vol_mean\n",
    "    ) / Vol_stdd\n",
    "    thyao.loc[thyao.index[i], \"TR_norm\"] = (\n",
    "        thyao.loc[thyao.index[i], \"TR\"] - TR_mean\n",
    "    ) / TR_stdd\n",
    "\n",
    "thyao.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "wE5ZWz4f6BU5",
    "outputId": "5473c5d4-69d7-41a9-a729-ab72d3c1c1c6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Vol_norm', ylabel='TR_norm'>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Scatter plot with regression line\n",
    "sns.regplot(\n",
    "    data=thyao,\n",
    "    x=\"Vol_norm\",\n",
    "    y=\"TR_norm\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 444
    },
    "id": "wILPdrGSCkrC",
    "outputId": "f92e00d8-801f-4940-aa6b-87606a43d2f7"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\murat\\AppData\\Roaming\\Python\\Python39\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>TR_norm</td>     <th>  R-squared:         </th> <td>   0.150</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.148</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   69.30</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 04 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>1.41e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>09:33:22</td>     <th>  Log-Likelihood:    </th> <td> -607.84</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   395</td>      <th>  AIC:               </th> <td>   1220.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   393</td>      <th>  BIC:               </th> <td>   1228.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</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>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>    <td>   -0.0211</td> <td>    0.057</td> <td>   -0.371</td> <td> 0.711</td> <td>   -0.133</td> <td>    0.091</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Vol_norm</th> <td>    0.3271</td> <td>    0.039</td> <td>    8.325</td> <td> 0.000</td> <td>    0.250</td> <td>    0.404</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>50.548</td> <th>  Durbin-Watson:     </th> <td>   1.979</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 385.946</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.097</td> <th>  Prob(JB):          </th> <td>1.56e-84</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 7.839</td> <th>  Cond. No.          </th> <td>    1.45</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                TR_norm   R-squared:                       0.150\n",
       "Model:                            OLS   Adj. R-squared:                  0.148\n",
       "Method:                 Least Squares   F-statistic:                     69.30\n",
       "Date:                Sat, 04 Sep 2021   Prob (F-statistic):           1.41e-15\n",
       "Time:                        09:33:22   Log-Likelihood:                -607.84\n",
       "No. Observations:                 395   AIC:                             1220.\n",
       "Df Residuals:                     393   BIC:                             1228.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.0211      0.057     -0.371      0.711      -0.133       0.091\n",
       "Vol_norm       0.3271      0.039      8.325      0.000       0.250       0.404\n",
       "==============================================================================\n",
       "Omnibus:                       50.548   Durbin-Watson:                   1.979\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              385.946\n",
       "Skew:                           0.097   Prob(JB):                     1.56e-84\n",
       "Kurtosis:                       7.839   Cond. No.                         1.45\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# OLS\n",
    "lm = OLS(thyao.TR_norm, add_constant(thyao.Vol_norm))\n",
    "res = lm.fit()\n",
    "res.summary()"
   ]
  }
 ],
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   "authorship_tag": "ABX9TyNCJab2p8AImGJhCdeSzZoD",
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   "name": "05_volatility_volume_relationship.ipynb",
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