4-analyze-pair.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4681cab6",
   "metadata": {},
   "source": [
    "This step is to analyze the pair which we have selected in the previous step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "37adeab0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:56.613383Z",
     "start_time": "2022-11-01T17:09:56.552392Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# change default plot parameters\n",
    "plt.rcParams['figure.figsize'] = [6, 4]\n",
    "plt.rcParams['figure.dpi'] = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235db422",
   "metadata": {},
   "source": [
    "### SETUP & READ FILE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13d003ed",
   "metadata": {},
   "source": [
    "#### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "25fa71b6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:56.659392Z",
     "start_time": "2022-11-01T17:09:56.624395Z"
    }
   },
   "outputs": [],
   "source": [
    "# \"0\" to use all available dates, \"1\" for custom dates\n",
    "custom_date = 0\n",
    "\n",
    "# \"1\" to add a regression coefficient α for Y*(t) = β * x*(t) + α\n",
    "enable_regression_coef = 0\n",
    "\n",
    "# number of samples for linear regression\n",
    "# \"0\" to use all datapoints\n",
    "N = 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "365cac44",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:56.911386Z",
     "start_time": "2022-11-01T17:09:56.663384Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "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>close_x</th>\n",
       "      <th>volume_x</th>\n",
       "      <th>ticker_x</th>\n",
       "      <th>close_y</th>\n",
       "      <th>volume_y</th>\n",
       "      <th>ticker_y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>datetime</th>\n",
       "      <th></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>2021-11-01 04:00:00+00:00</th>\n",
       "      <td>26.290001</td>\n",
       "      <td>3730100</td>\n",
       "      <td>CNP</td>\n",
       "      <td>20.010000</td>\n",
       "      <td>2756500</td>\n",
       "      <td>VST</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-11-02 04:00:00+00:00</th>\n",
       "      <td>26.190001</td>\n",
       "      <td>5620500</td>\n",
       "      <td>CNP</td>\n",
       "      <td>19.870001</td>\n",
       "      <td>4006000</td>\n",
       "      <td>VST</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-11-03 04:00:00+00:00</th>\n",
       "      <td>26.290001</td>\n",
       "      <td>3350900</td>\n",
       "      <td>CNP</td>\n",
       "      <td>19.680000</td>\n",
       "      <td>2460100</td>\n",
       "      <td>VST</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-11-04 04:00:00+00:00</th>\n",
       "      <td>26.500000</td>\n",
       "      <td>3364800</td>\n",
       "      <td>CNP</td>\n",
       "      <td>19.209999</td>\n",
       "      <td>6093500</td>\n",
       "      <td>VST</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-11-05 04:00:00+00:00</th>\n",
       "      <td>26.670000</td>\n",
       "      <td>3179000</td>\n",
       "      <td>CNP</td>\n",
       "      <td>20.500000</td>\n",
       "      <td>9136100</td>\n",
       "      <td>VST</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             close_x  volume_x ticker_x    close_y  volume_y  \\\n",
       "datetime                                                                       \n",
       "2021-11-01 04:00:00+00:00  26.290001   3730100      CNP  20.010000   2756500   \n",
       "2021-11-02 04:00:00+00:00  26.190001   5620500      CNP  19.870001   4006000   \n",
       "2021-11-03 04:00:00+00:00  26.290001   3350900      CNP  19.680000   2460100   \n",
       "2021-11-04 04:00:00+00:00  26.500000   3364800      CNP  19.209999   6093500   \n",
       "2021-11-05 04:00:00+00:00  26.670000   3179000      CNP  20.500000   9136100   \n",
       "\n",
       "                          ticker_y  \n",
       "datetime                            \n",
       "2021-11-01 04:00:00+00:00      VST  \n",
       "2021-11-02 04:00:00+00:00      VST  \n",
       "2021-11-03 04:00:00+00:00      VST  \n",
       "2021-11-04 04:00:00+00:00      VST  \n",
       "2021-11-05 04:00:00+00:00      VST  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if custom_date:\n",
    "    df = pd.read_pickle(\"saved_custom.pkl\")\n",
    "else:\n",
    "    df = pd.read_pickle(\"saved.pkl\")  \n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f346a6aa",
   "metadata": {},
   "source": [
    "### CORRELATION & VISUAL OBSERVATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "10fd9127",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:56.959487Z",
     "start_time": "2022-11-01T17:09:56.918386Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr. Matrix:\n",
      "          CNP       VST\n",
      "CNP  1.000000  0.885624\n",
      "VST  0.885624  1.000000\n"
     ]
    }
   ],
   "source": [
    "df_corr = df[['close_x','close_y']]\n",
    "df_corr = df_corr.rename(columns={\"close_x\": df.ticker_x[0], \"close_y\": df.ticker_y[0]})\n",
    "print('Corr. Matrix:')\n",
    "print(df_corr.corr(method='pearson'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "54eb7dff",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:57.797122Z",
     "start_time": "2022-11-01T17:09:56.974496Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x144e3941a30>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# change current plot parameters. use it before defining the plot\n",
    "_ = plt.figure(figsize=(5,3))\n",
    "\n",
    "df.close_x.plot(label=df.ticker_x[0])\n",
    "df.close_y.plot(label=df.ticker_y[0])\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "afe56696",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:59.496460Z",
     "start_time": "2022-11-01T17:09:57.802123Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb\n",
    "\n",
    "# seaborn is nice to visualize a linear fit\n",
    "#sb.scatterplot(\"close_x\", \"close_y\", s=30, edgecolor=\"none\", data=df)\n",
    "scplot = sb.regplot(x=\"close_x\", y=\"close_y\", data=df, scatter_kws={\"color\": \"red\"}, line_kws={\"color\": \"black\"});\n",
    "scplot.set(xlabel=df.ticker_x[0], ylabel=df.ticker_y[0])\n",
    " \n",
    "# or you can enable to use pandas, but you should dray the regression line separately\n",
    "# plt.scatter(df.close_y,df.close_x)\n",
    "# plt.xlabel(df.ticker_x[0])\n",
    "# plt.ylabel(df.ticker_y[0])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "835f9d36",
   "metadata": {},
   "source": [
    "### ORTHOGONAL SPREAD ANALYSIS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "93678944",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:09:59.574468Z",
     "start_time": "2022-11-01T17:09:59.505462Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "β * x(t)\n",
      "COEF β: 0.7829309411807653\n",
      "\u001b[43;1mHEDGE: 0.78\u001b[0m\n",
      "EQUATION: VST=0.78*CNP\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "#  implement Ordinary Least Squares(OLS) method of linear regression\n",
    "#  Y*(t) = β * x*(t) + α\n",
    "\n",
    "if N>0: # for the recent N rows\n",
    "    Y = df.close_y.iloc[-N:]\n",
    "    X = df.close_x.iloc[-N:]\n",
    "else:\n",
    "    Y = df.close_y\n",
    "    X = df.close_x\n",
    "\n",
    "# ENABLE if you want to add a regression coefficient α\n",
    "if enable_regression_coef:\n",
    "    X = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(Y, X) # for the last N rows\n",
    "model = model.fit()\n",
    "\n",
    "# get the model coef\n",
    "if len(model.params) == 1:\n",
    "    print(\"β * x(t)\")\n",
    "    print(f\"COEF β: {model.params[0]}\")\n",
    "    hedge = round(float(model.params[0]),2)\n",
    "    print(f\"\\u001b[43;1mHEDGE: {hedge}\\u001b[0m\")\n",
    "    alfa = 0\n",
    "else:\n",
    "# get the model coef with regression coefficient α\n",
    "    print(\"β * x(t) + α\")\n",
    "    print(f\"COEF β: {model.params[1]}\")\n",
    "    hedge = round(float(model.params[1]),2)\n",
    "    print(f\"COEF α: {model.params[0]}\")\n",
    "    alfa = round(float(model.params[0]),2)\n",
    "    print(f\"\\u001b[43;1mHEDGE: {hedge}\\u001b[0m\")\n",
    "    \n",
    "if hedge<0:\n",
    "    print(\"\\u001b[41;1mAvoid pairs with negative β\\u001b[0m\")\n",
    "     \n",
    "# print pair equation\n",
    "print(f\"EQUATION: {df.ticker_y[0]}={hedge}*{df.ticker_x[0]}{'+' + str(round(alfa,1)) if alfa>0 else ''}\")\n",
    "# enable to see the model summary\n",
    "# model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3c90d74",
   "metadata": {},
   "source": [
    "### ORTHOGONAL RESIDUALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a2c389b6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:10:00.223536Z",
     "start_time": "2022-11-01T17:09:59.579460Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean : 0.2091174274020717 | std dev : 0.8416336092378484\n",
      "min : -1.4600009155273455 | max : 2.650601196289063\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# spread y(t) - β * x(t) - α\n",
    "spread = df['spread'] = df.close_y - hedge * df.close_x - alfa\n",
    "df['mean_spread'] = spread.mean()\n",
    "\n",
    "# lower and upper bounds\n",
    "std_spread = spread.std()\n",
    "df['std_upper'] = df['mean_spread'] + std_spread\n",
    "df['std_lower'] = df['mean_spread'] - std_spread\n",
    "\n",
    "print(f\"mean : {spread.mean()} | std dev : {std_spread}\")\n",
    "print(f\"min : {spread.min()} | max : {spread.max()}\")\n",
    "\n",
    "\n",
    "# plot\n",
    "# change current plot parameters. use it before defining the plot\n",
    "_ = plt.figure(figsize=(5,3))\n",
    "\n",
    "# df[['spread','mean_spread','std_lower','std_upper']].plot()\n",
    "df.spread.plot(label='spread', color='red')\n",
    "df.mean_spread.plot(label='mean', color='black')\n",
    "plt.fill_between(df.index, df.std_lower, df.std_upper, facecolor='green', alpha=0.3);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fc03c70",
   "metadata": {},
   "source": [
    "### UNIT ROOT TEST"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1911e114",
   "metadata": {},
   "source": [
    "#### Augmented Dickey-Fuller Unit Root Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3447e012",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:10:00.349287Z",
     "start_time": "2022-11-01T17:10:00.228530Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test stat. : -4.096918425479465\n",
      "p-value: 0.0009799463998137034\n",
      "critical values: {'1%': -3.4566744514553016, '5%': -2.8731248767783426, '10%': -2.5729436702592023}\n",
      "90% CONFIDENCE: \u001b[42;1mPASSED\u001b[0m\n",
      "95% CONFIDENCE: \u001b[42;1mPASSED (H0 rejected, the time series is stationary)\u001b[0m\n",
      "99% CONFIDENCE: \u001b[42;1mPASSED (H0 rejected, the time series is stationary)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# The Augmented Dickey-Fuller test can be used to test for a unit root\n",
    "# The ADF test expands the Dickey-Fuller test equation to include high order regressive process in the model.\n",
    "\n",
    "# Null Hypothesis: No cointegration\n",
    "# Decision Rule:Reject the null hypothesis if the  test statistic is less than the critical value\n",
    "\n",
    "# The presence of a unit root is one cause for non-stationarity\n",
    "# An ideal time series has stationarity.\n",
    "# That means that a shift in time doesn’t cause a change in the shape of the distribution. \n",
    "# Data points are often non-stationary or have means, variances, and covariances that change over time.\n",
    "# Non-stationary behaviors can be trends, cycles, random walks, or combinations of the three.\n",
    "# Non-stationary data, as a rule, are unpredictable and cannot be modeled or forecasted.\n",
    "\n",
    "\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "\n",
    "# By default, lag value is 12*(nobs/100)^{1/4}, where nobs is the number of observations in the series.\n",
    "# But, optionally you can specify either the maximum number of lags with maxlags parameter\n",
    "# or let the algorithm compute the optimal number iteratively. This can be done by setting the autolag='AIC'\n",
    "#adf = adfuller(df.spread, maxlag = 1)\n",
    "adf = adfuller(df.spread, autolag='AIC')\n",
    "\n",
    "# show test statistic\n",
    "print(f\"test stat. : {adf[0]}\")\n",
    "stat = adf[0]\n",
    "\n",
    "# show pvalue\n",
    "# The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis.\n",
    "# If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.\n",
    "print(f\"p-value: {adf[1]}\")\n",
    "\n",
    "# show critical values\n",
    "print(f\"critical values: {adf[4]}\")\n",
    "critical_values = adf[4]\n",
    "\n",
    "# print pair equation\n",
    "import sys\n",
    "green_bg = '\\u001b[42;1m'\n",
    "red_bg = '\\u001b[41;1m'\n",
    "reset_bg = '\\u001b[0m' \n",
    "print(f\"90% CONFIDENCE: {green_bg + 'PASSED' if critical_values['10%']>stat else red_bg + ' FAILED'}{reset_bg}\")\n",
    "print(f\"95% CONFIDENCE: {green_bg + 'PASSED (H0 rejected, the time series is stationary)' if critical_values['5%']>stat else red_bg + ' FAILED (residuals seem to contain a unit root, the time series is non-stationary)'}{reset_bg}\")\n",
    "print(f\"99% CONFIDENCE: {green_bg + 'PASSED (H0 rejected, the time series is stationary)' if critical_values['1%']>stat else red_bg + ' FAILED (residuals seem to contain a unit root, the time series is non-stationary)'}{reset_bg}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ecc95a1",
   "metadata": {},
   "source": [
    "#### Phillips-Perron Unit Root Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "3eff5ab0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:10:00.396305Z",
     "start_time": "2022-11-01T17:10:00.354309Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test stat. : -33.23932302593357\n",
      "p-value: 0.004148306000452942\n",
      "critical values: {'1%': -28.44956269586627, '5%': -21.200229467423238, '10%': -17.878007111330238}\n",
      "90% CONFIDENCE: \u001b[42;1mPASSED\u001b[0m\n",
      "95% CONFIDENCE: \u001b[42;1mPASSED (H0 rejected, the time series is stationary)\u001b[0m\n",
      "99% CONFIDENCE: \u001b[42;1mPASSED (H0 rejected, the time series is stationary)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# Phillips-Perron unit root test\n",
    "# https://arch.readthedocs.io/en/latest/unitroot/generated/arch.unitroot.PhillipsPerron.html\n",
    "\n",
    "#A great advantage of Philips-Perron test is that it is non-parametric,\n",
    "#i.e. it does not require to select the level of serial correlation as in ADF.\n",
    "#It rather takes the same estimation scheme as in DF test, but corrects the statistic\n",
    "#to conduct for autocorrelations and heteroscedasticity (HAC type corrections).\n",
    "\n",
    "#The main disadvantage of the PP test is that it is based on asymptotic theory.\n",
    "#Therefore it works well only in large samples that are indeed luxury if not it\n",
    "# comes for financial time series data. And it also shares\n",
    "# disadvantages of ADF tests: sensitivity to structural breaks, poor small sample power\n",
    "# too often resulting in unit root conclusions.\n",
    "\n",
    "\n",
    "# Parameters\n",
    "# y{ndarray, Series}: The data to test for a unit root\n",
    "\n",
    "# lagsint, optional\n",
    "# The number of lags to use in the Newey-West estimator of the long-run covariance. If omitted or None, the lag length is set automatically to 12 * (nobs/100) ** (1/4)\n",
    "\n",
    "# trend{“n”, “c”, “ct”}, optional\n",
    "# The trend component to include in the test\n",
    "\n",
    "# “n” - No trend components\n",
    "# “c” - Include a constant (Default)\n",
    "# “ct” - Include a constant and linear time trend\n",
    "\n",
    "# test_type{“tau”, “rho”}\n",
    "# The test to use when computing the test statistic. “tau” is based on the t-stat and “rho” uses a test based on nobs times the re-centered regression coefficien\n",
    "\n",
    "import arch.unitroot as at\n",
    "pp = at.PhillipsPerron(df.spread, trend='ct', test_type='rho')\n",
    "stat = pp.stat\n",
    "print(f\"test stat. : {pp.stat}\")\n",
    "print(f\"p-value: {pp.pvalue}\")\n",
    "print(f\"critical values: {pp.critical_values}\")\n",
    "critical_values = pp.critical_values\n",
    "\n",
    "\n",
    "# print pair equation\n",
    "import sys\n",
    "green_bg = '\\u001b[42;1m'\n",
    "red_bg = '\\u001b[41;1m'\n",
    "reset_bg = '\\u001b[0m' \n",
    "print(f\"90% CONFIDENCE: {green_bg + 'PASSED' if critical_values['10%']>stat else red_bg + ' FAILED'}{reset_bg}\")\n",
    "print(f\"95% CONFIDENCE: {green_bg + 'PASSED (H0 rejected, the time series is stationary)' if critical_values['5%']>stat else red_bg + ' FAILED (residuals seem to contain a unit root, the time series is non-stationary)'}{reset_bg}\")\n",
    "print(f\"99% CONFIDENCE: {green_bg + 'PASSED (H0 rejected, the time series is stationary)' if critical_values['1%']>stat else red_bg + ' FAILED (residuals seem to contain a unit root, the time series is non-stationary)'}{reset_bg}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71e593c2",
   "metadata": {},
   "source": [
    "#### Engle-Granger Two-Step Cointegration Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "0803a04a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-01T17:10:00.537292Z",
     "start_time": "2022-11-01T17:10:00.433290Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-stat. : -3.708762037061511\n",
      "p-value: 0.0178554964790457\n",
      "critical values: [-3.94060523 -3.36058133 -3.06139039]\n",
      "90% CONFIDENCE: \u001b[42;1mPASSED\u001b[0m\n",
      "95% CONFIDENCE: \u001b[42;1mPASSED (there is cointegrating relationship)\u001b[0m\n",
      "99% CONFIDENCE: \u001b[41;1m FAILED (there is no cointegration)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# This uses the augmented Engle-Granger two-step cointegration test.\n",
    "# Constant or trend is included in 1st stage regression, i.e. in cointegrating equation.\n",
    "# The Null hypothesis is that there is no cointegration, the alternative hypothesis is that\n",
    "# there is cointegrating relationship. If the pvalue is small, below a critical size, then\n",
    "#we can reject the hypothesis that there is no cointegrating relationship.\n",
    "\n",
    "from statsmodels.tsa.stattools import coint\n",
    "# coint,p,_= coint(df.close_x,df.close_y)\n",
    "coint = coint(df.close_x,df.close_y)\n",
    "\n",
    "stat = coint[0]\n",
    "critical_values = coint[2]\n",
    "\n",
    "print(f\"t-stat. : {stat}\")\n",
    "print(f\"p-value: {coint[1]}\")\n",
    "print(f\"critical values: {critical_values}\")\n",
    "\n",
    "# print pair equation\n",
    "import sys\n",
    "green_bg = '\\u001b[42;1m'\n",
    "red_bg = '\\u001b[41;1m'\n",
    "reset_bg = '\\u001b[0m' \n",
    "print(f\"90% CONFIDENCE: {green_bg + 'PASSED' if critical_values[2]>stat else red_bg + ' FAILED'}{reset_bg}\")\n",
    "print(f\"95% CONFIDENCE: {green_bg + 'PASSED (there is cointegrating relationship)' if critical_values[1]>stat else red_bg + ' FAILED (there is no cointegration)'}{reset_bg}\")\n",
    "print(f\"99% CONFIDENCE: {green_bg + 'PASSED (there is cointegrating relationship)' if critical_values[0]>stat else red_bg + ' FAILED (there is no cointegration)'}{reset_bg}\")\n"
   ]
  }
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