regression_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pathlib import Path\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Analysis: Seasonal Effects with Sklearn Linear Regression\n",
    "In this notebook, you will build a SKLearn linear regression model to predict Yen futures (\"settle\") returns with *lagged* CAD/JPY exchange rate returns. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1982-01-05</th>\n",
       "      <td>184.65</td>\n",
       "      <td>184.65</td>\n",
       "      <td>184.65</td>\n",
       "      <td>184.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-01-06</th>\n",
       "      <td>185.06</td>\n",
       "      <td>185.06</td>\n",
       "      <td>185.06</td>\n",
       "      <td>185.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-01-07</th>\n",
       "      <td>186.88</td>\n",
       "      <td>186.88</td>\n",
       "      <td>186.88</td>\n",
       "      <td>186.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-01-08</th>\n",
       "      <td>186.58</td>\n",
       "      <td>186.58</td>\n",
       "      <td>186.58</td>\n",
       "      <td>186.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1982-01-11</th>\n",
       "      <td>187.64</td>\n",
       "      <td>187.64</td>\n",
       "      <td>187.64</td>\n",
       "      <td>187.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Price    Open    High     Low\n",
       "Date                                      \n",
       "1982-01-05  184.65  184.65  184.65  184.65\n",
       "1982-01-06  185.06  185.06  185.06  185.06\n",
       "1982-01-07  186.88  186.88  186.88  186.88\n",
       "1982-01-08  186.58  186.58  186.58  186.58\n",
       "1982-01-11  187.64  187.64  187.64  187.64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Currency pair exchange rates for CAD/JPY\n",
    "cad_jpy_df = pd.read_csv(\n",
    "    Path(\"cad_jpy.csv\"), index_col=\"Date\", infer_datetime_format=True, parse_dates=True\n",
    ")\n",
    "cad_jpy_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>126.37</td>\n",
       "      <td>126.31</td>\n",
       "      <td>126.37</td>\n",
       "      <td>126.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>125.30</td>\n",
       "      <td>125.24</td>\n",
       "      <td>125.30</td>\n",
       "      <td>125.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>123.46</td>\n",
       "      <td>123.41</td>\n",
       "      <td>123.46</td>\n",
       "      <td>123.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>124.54</td>\n",
       "      <td>124.48</td>\n",
       "      <td>124.54</td>\n",
       "      <td>124.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-08</th>\n",
       "      <td>124.27</td>\n",
       "      <td>124.21</td>\n",
       "      <td>124.27</td>\n",
       "      <td>124.21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Price    Open    High     Low\n",
       "Date                                      \n",
       "1990-01-02  126.37  126.31  126.37  126.31\n",
       "1990-01-03  125.30  125.24  125.30  125.24\n",
       "1990-01-04  123.46  123.41  123.46  123.41\n",
       "1990-01-05  124.54  124.48  124.54  124.48\n",
       "1990-01-08  124.27  124.21  124.27  124.21"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Trim the dataset to begin on January 1st, 1990\n",
    "cad_jpy_df = cad_jpy_df.loc[\"1990-01-01\":, :]\n",
    "cad_jpy_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Return</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>2020-05-29</th>\n",
       "      <td>78.29</td>\n",
       "      <td>78.21</td>\n",
       "      <td>78.41</td>\n",
       "      <td>77.75</td>\n",
       "      <td>0.076697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01</th>\n",
       "      <td>79.27</td>\n",
       "      <td>78.21</td>\n",
       "      <td>79.36</td>\n",
       "      <td>78.04</td>\n",
       "      <td>1.251756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02</th>\n",
       "      <td>80.40</td>\n",
       "      <td>79.26</td>\n",
       "      <td>80.56</td>\n",
       "      <td>79.15</td>\n",
       "      <td>1.425508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03</th>\n",
       "      <td>80.70</td>\n",
       "      <td>80.40</td>\n",
       "      <td>80.82</td>\n",
       "      <td>79.96</td>\n",
       "      <td>0.373134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-04</th>\n",
       "      <td>80.71</td>\n",
       "      <td>80.80</td>\n",
       "      <td>80.89</td>\n",
       "      <td>80.51</td>\n",
       "      <td>0.012392</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Price   Open   High    Low    Return\n",
       "Date                                            \n",
       "2020-05-29  78.29  78.21  78.41  77.75  0.076697\n",
       "2020-06-01  79.27  78.21  79.36  78.04  1.251756\n",
       "2020-06-02  80.40  79.26  80.56  79.15  1.425508\n",
       "2020-06-03  80.70  80.40  80.82  79.96  0.373134\n",
       "2020-06-04  80.71  80.80  80.89  80.51  0.012392"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a series using \"Price\" percentage returns, drop any nan\"s, and check the results:\n",
    "# (Make sure to multiply the pct_change() results by 100)\n",
    "# In this case, you may have to replace inf, -inf values with np.nan\"s\n",
    "returns = (cad_jpy_df[[\"Price\"]].pct_change() * 100)\n",
    "cad_jpy_df['Return'] = returns.replace(-np.inf, np.nan).dropna()\n",
    "cad_jpy_df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lagged Returns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Return</th>\n",
       "      <th>Lagged_Return</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",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2020-05-29</th>\n",
       "      <td>78.29</td>\n",
       "      <td>78.21</td>\n",
       "      <td>78.41</td>\n",
       "      <td>77.75</td>\n",
       "      <td>0.076697</td>\n",
       "      <td>-0.114913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01</th>\n",
       "      <td>79.27</td>\n",
       "      <td>78.21</td>\n",
       "      <td>79.36</td>\n",
       "      <td>78.04</td>\n",
       "      <td>1.251756</td>\n",
       "      <td>0.076697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02</th>\n",
       "      <td>80.40</td>\n",
       "      <td>79.26</td>\n",
       "      <td>80.56</td>\n",
       "      <td>79.15</td>\n",
       "      <td>1.425508</td>\n",
       "      <td>1.251756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03</th>\n",
       "      <td>80.70</td>\n",
       "      <td>80.40</td>\n",
       "      <td>80.82</td>\n",
       "      <td>79.96</td>\n",
       "      <td>0.373134</td>\n",
       "      <td>1.425508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-04</th>\n",
       "      <td>80.71</td>\n",
       "      <td>80.80</td>\n",
       "      <td>80.89</td>\n",
       "      <td>80.51</td>\n",
       "      <td>0.012392</td>\n",
       "      <td>0.373134</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Price   Open   High    Low    Return  Lagged_Return\n",
       "Date                                                           \n",
       "2020-05-29  78.29  78.21  78.41  77.75  0.076697      -0.114913\n",
       "2020-06-01  79.27  78.21  79.36  78.04  1.251756       0.076697\n",
       "2020-06-02  80.40  79.26  80.56  79.15  1.425508       1.251756\n",
       "2020-06-03  80.70  80.40  80.82  79.96  0.373134       1.425508\n",
       "2020-06-04  80.71  80.80  80.89  80.51  0.012392       0.373134"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a lagged return using the shift function\n",
    "cad_jpy_df['Lagged_Return'] = cad_jpy_df['Return'].shift(1)\n",
    "cad_jpy_df.dropna(inplace = True)\n",
    "cad_jpy_df.loc[\"2020-05-29\":, :].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a train/test split for the data using 2018-2019 for testing and the rest for training\n",
    "train = cad_jpy_df[:'2017']\n",
    "test = cad_jpy_df['2018':]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create four dataframes:\n",
    "# X_train (training set using just the independent variables), X_test (test set of of just the independent variables)\n",
    "# Y_train (training set using just the \"y\" variable, i.e., \"Futures Return\"), Y_test (test set of just the \"y\" variable):\n",
    "X_train = train[\"Lagged_Return\"].to_frame()\n",
    "X_test = test[\"Lagged_Return\"].to_frame()\n",
    "y_train = train[\"Return\"]\n",
    "y_test = test[\"Return\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Lagged_Return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-10</th>\n",
       "      <td>0.667901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-11</th>\n",
       "      <td>0.567546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-12</th>\n",
       "      <td>0.031794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-15</th>\n",
       "      <td>0.119190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-16</th>\n",
       "      <td>-0.619048</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "            Lagged_Return\n",
       "Date                     \n",
       "1990-01-10       0.667901\n",
       "1990-01-11       0.567546\n",
       "1990-01-12       0.031794\n",
       "1990-01-15       0.119190\n",
       "1990-01-16      -0.619048"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Preview the X_train data\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a Linear Regression model and fit it to the training data\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Fit a SKLearn linear regression using  just the training set (X_train, Y_train):\n",
    "model = LinearRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make predictions using the Testing Data\n",
    "\n",
    "**Note:** We want to evaluate the model using data that it has never seen before, in this case: `X_test`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a prediction of \"y\" values using just the test dataset\n",
    "predictions = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assemble actual y data (Y_test) with predicted y data (from just above) into two columns in a dataframe:\n",
    "Results = y_test.to_frame()\n",
    "Results[\"Predicted Return\"] = predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Date'>"
      ]
     },
     "execution_count": 33,
     "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": [
    "# Plot the first 20 predictions vs the true values\n",
    "Results[:20].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Out-of-Sample Performance\n",
    "\n",
    "Evaluate the model using \"out-of-sample\" data (`X_test` and `y_test`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out-of-Sample Root Mean Squared Error (RMSE): 0.644584711697806\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "# Calculate the mean_squared_error (MSE) on actual versus predicted test \"y\" \n",
    "# (Hint: use the dataframe from above)\n",
    "mse = mean_squared_error(\n",
    "    Results[\"Return\"],\n",
    "    Results[\"Predicted Return\"]\n",
    ")\n",
    "\n",
    "# Using that mean-squared-error, calculate the root-mean-squared error (RMSE):\n",
    "rmse = np.sqrt(mse)\n",
    "print(f\"Out-of-Sample Root Mean Squared Error (RMSE): {rmse}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In-Sample Performance\n",
    "\n",
    "Evaluate the model using in-sample data (X_train and y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In-sample Root Mean Squared Error (RMSE): 0.8419488589455253\n"
     ]
    }
   ],
   "source": [
    "# Construct a dataframe using just the \"y\" training data:\n",
    "in_sample_results = y_train.to_frame()\n",
    "\n",
    "# Add a column of \"in-sample\" predictions to that DataFrame:  \n",
    "in_sample_results[\"In-sample Predictions\"] = model.predict(X_train)\n",
    "\n",
    "# Calculate in-sample mean_squared_error (for comparison to out-of-sample)\n",
    "in_sample_mse = mean_squared_error(\n",
    "    in_sample_results[\"Return\"],\n",
    "    in_sample_results[\"In-sample Predictions\"]\n",
    ")\n",
    "\n",
    "# Calculate in-sample root mean_squared_error (for comparison to out-of-sample)\n",
    "in_sample_rmse = np.sqrt(in_sample_mse)\n",
    "print(f\"In-sample Root Mean Squared Error (RMSE): {in_sample_rmse}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** Does this model perform better or worse on out-of-sample data as compared to in-sample data?\n",
    "\n",
    "**Answer:** RMSE of in-sample is much higher as compared to out-sample data, hence we can say for sure that this model works better on in-sample data then out-sample data. This also means that this model is over-fitted and hence need fine tunning to reduce over-fitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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