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regression and time series analysis\n", + "import statsmodels.api as sm\n", + "# numpy is for numerical computing of array and mayatrix\n", + "import numpy as np\n", + "# Matplotlib, Seaborn: plotting package\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns \n", + "# matplotlib Showing the plot right after the current code \n", + "%matplotlib inline\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "# basic statistics package\n", + "import scipy.stats as stats\n", + "from statsmodels.stats.outliers_influence import variance_inflation_factor\n", + "import datetime" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5159ee37", + "metadata": {}, + "outputs": [], + "source": [ + "# functions from last lab\n", + "def four_in_one(dataframe,model):\n", + " fitted_y = model.fittedvalues\n", + " studentized_residuals = model.get_influence().resid_studentized_internal\n", + " plt.figure(figsize=(10,10))\n", + " ax1 = plt.subplot(221)\n", + " stats.probplot(studentized_residuals, dist=\"norm\", plot=plt)\n", + " ax1.set_title('Normal Q-Q')\n", + " ax1.set_xlabel('Normal Quantiles')\n", + " ax1.set_ylabel('Studentized Residuals');\n", + "\n", + " ax2 = plt.subplot(222)\n", + " ax2.hist(studentized_residuals)\n", + " ax2.set_xlabel('Studentized Residuals')\n", + " ax2.set_ylabel('Count')\n", + " ax2.set_title('Histogram')\n", + "\n", + " ax3 = plt.subplot(223)\n", + " t = range(dataframe.shape[0])\n", + " ax3.scatter(t, studentized_residuals)\n", + " ax3.set_xlabel('Observation order')\n", + " ax3.set_ylabel('Residuals')\n", + " ax3.set_title('Time series plot of studentized residuals')\n", + "\n", + " ax4 = plt.subplot(224)\n", + " temp = pd.DataFrame({'fitted_y':fitted_y,'studentized_residuals':studentized_residuals})\n", + " ax4 = sns.residplot(data=temp,x=fitted_y, y=studentized_residuals,\n", + " lowess=True,\n", + " scatter_kws={'alpha': 0.5},\n", + " line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8})\n", + " ax4.set_title('Internally Studentized Residuals vs Fitted values')\n", + " ax4.set_xlabel('Fitted values')\n", + " ax4.set_ylabel('Studentized Residuals');\n", + " \n", + "def getvif(X):\n", + " X = sm.add_constant(X)\n", + " vif = pd.DataFrame()\n", + " vif[\"VIF\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n", + " vif[\"Predictors\"] = X.columns\n", + " return(vif.drop(index = 0).round(2)) " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "16326102", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "

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Date
1/2/2009-0.121807-0.1099310.0005-0.0695
1/3/20090.1030530.0854040.00040.0348
1/4/20090.0841980.0939250.05390.0536
1/5/2009-0.0255320.053081-0.02520.0027
1/6/2009-0.0174670.0001960.0263-0.0273
\n", + "
" + ], + "text/plain": [ + " rBH rSP SmB HmL\n", + "Date \n", + "1/2/2009 -0.121807 -0.109931 0.0005 -0.0695\n", + "1/3/2009 0.103053 0.085404 0.0004 0.0348\n", + "1/4/2009 0.084198 0.093925 0.0539 0.0536\n", + "1/5/2009 -0.025532 0.053081 -0.0252 0.0027\n", + "1/6/2009 -0.017467 0.000196 0.0263 -0.0273" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv(\"BH2009-2022.csv\",index_col=0)\n", + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7fd1d118", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(167, 4)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.shape" + ] + }, + { + "cell_type": "markdown", + "id": "09cc26c8", + "metadata": {}, + "source": [ + "# Part I: CAPM model" + ] + }, + { + "cell_type": "markdown", + "id": "ebaa4598-7164-4b6c-ac8d-7d674fa4ee4f", + "metadata": {}, + "source": [ + "### Task 1: Split the data into train (first 155 observations) and test (remaining 12 observations) set" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "095d1d13", + "metadata": {}, + "outputs": [], + "source": [ + "train = $$code here$$\n", + "test = $$code here$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0a06748", + "metadata": {}, + "outputs": [], + "source": [ + "train.shape, test.shape" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "abff4aee-07cb-4ddd-8cd2-7f909b217b41", + "metadata": {}, + "outputs": [], + "source": [ + "Y = train[\"rBH\"]\n", + "X = train[\"rSP\"]" + ] + }, + { + "cell_type": "markdown", + "id": "f84493d2-6484-4e62-a196-888c72c657f4", + "metadata": {}, + "source": [ + "### Task 2: Using training set, fit a simple regression model(SLR). Report the adjusted R-square of the model." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "76e5007b-ec3f-4271-9c25-afd7cb2bd028", + "metadata": {}, + "outputs": [], + "source": [ + "SLR = $$code here$$\n", + "print(SLR.summary())" + ] + }, + { + "cell_type": "markdown", + "id": "b9fd7ede-dabc-47d9-918f-021ee1fae9b4", + "metadata": {}, + "source": [ + "### Report the adjusted R-square of the model.\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "3af44ff8", + "metadata": {}, + "source": [ + "# Part II: Multiple Regression Model" + ] + }, + { + "cell_type": "markdown", + "id": "3f8158d8-1c42-4226-99c3-0d04a026df5b", + "metadata": {}, + "source": [ + "### Task 3: Using training set, fit a multiple regression model with SmB and HmL explanatory variables in addition to rSP (MLR). Report the adjusted R-square of the model." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f2dfad6", + "metadata": {}, + "outputs": [], + "source": [ + "X = $$code here$$\n", + "MLR = $$code here$$\n", + "print(MLR.summary())" + ] + }, + { + "cell_type": "markdown", + "id": "18e59124-7f05-414a-9284-fde621aa94cc", + "metadata": {}, + "source": [ + "### Report the adjusted R-square of the model.\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "fcb66422-678b-4d10-9aea-e56ae1c0adfa", + "metadata": {}, + "source": [ + "### Task 4: Checking the multicollinearity problem among rSP, SmB and HmL by \n", + " i) Scatter plot matrix \n", + " ii) VIF. \n", + "#### Is the multicollinearity problem exist?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "284873a2", + "metadata": {}, + "outputs": [], + "source": [ + "$$code here$$ #<--code for scatter plot matrix" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cad9bd49-5030-4a95-a5b5-ae8677092fbe", + "metadata": {}, + "outputs": [], + "source": [ + "$$code here$$ #<--code for VIF" + ] + }, + { + "cell_type": "markdown", + "id": "aea04a9e", + "metadata": {}, + "source": [ + "### Is the multicollinearity problem exist?" + ] + }, + { + "cell_type": "markdown", + "id": "88eb43de", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "ece7bda1-23e4-47e5-84ba-d0ab6eff9f06", + "metadata": { + "tags": [] + }, + "source": [ + "### Task 5: From the fitted multiple regression model in Task 3\n", + " i) Is the model as a whole useful at 5% significant level? \n", + " ii) Which of them is not an useful explanatory variable at 5% significant level?" + ] + }, + { + "cell_type": "markdown", + "id": "413b5d9a-44c6-4f4e-91c4-3f82317b2b00", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "fe0773af-c6ee-4dce-97c6-fe33af6310b8", + "metadata": {}, + "source": [ + "### Task 6: Execute model diagnostic on the model fitted from Task3 using the “four_in_one” function. Comment on the normality, constant variance assumption.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0b372cd7", + "metadata": {}, + "outputs": [], + "source": [ + "$$code here$$ #<--code for “four_in_one” function" + ] + }, + { + "cell_type": "markdown", + "id": "919fcacf", + "metadata": {}, + "source": [ + "### Comment on the normality, constant variance assumption." + ] + }, + { + "cell_type": "markdown", + "id": "52ff227e", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "5b40b212", + "metadata": {}, + "source": [ + "# Part IV: Model Performance" + ] + }, + { + "cell_type": "markdown", + "id": "8cc559dd-6a77-4289-a451-ede8d00bbf90", + "metadata": {}, + "source": [ + "### Task 7: Compare the predictive power between SLR and MLR using the test set. Which one perform better in prediction?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6e74fa4c", + "metadata": {}, + "outputs": [], + "source": [ + "Test_X_SLR = test['rSP']\n", + "Test_X_MLR = $$code here$$\n", + "\n", + "Test_Y_SLR = SLR.predict(sm.add_constant(Test_X_SLR))\n", + "Test_Y_MLR = $$code here$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d5af214f", + "metadata": {}, + "outputs": [], + "source": [ + "Test_Y = test[\"rBH\"]\n", + "\n", + "from sklearn.metrics import mean_squared_error\n", + "rmse_SLR = np.sqrt(mean_squared_error(Test_Y, Test_Y_SLR))\n", + "rmse_MLR = $$code here$$\n", + "print(\"RMSE for test set (SLR): \", rmse_SLR)\n", + "print(\"RMSE for test set (MLR): \", rmse_MLR)" + ] + }, + { + "cell_type": "markdown", + "id": "bd0c8483", + "metadata": {}, + "source": [ + "### Which one perform better in prediction?" + ] + }, + { + "cell_type": "markdown", + "id": "36d05636", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f203f98c-2e57-4262-8fd8-5209825817af", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/BH2009-2022.csv b/BH2009-2022.csv new file mode 100644 index 0000000..0552d13 --- /dev/null +++ b/BH2009-2022.csv @@ -0,0 +1,168 @@ +Date,rBH,rSP,SmB,HmL +1/2/2009,-0.121807334,-0.109931198,0.0005,-0.0695 +1/3/2009,0.103053435,0.085404462,0.0004,0.0348 +1/4/2009,0.084198385,0.093925079,0.0539,0.0536 +1/5/2009,-0.025531915,0.053081446,-0.0252,0.0027 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