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final draft of SARIMAX
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‎content/posts/finance/stock_prediction/SARIMAX/index.md

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In the previous articles we saw the limitations of the [ARIMA](/posts/finance/stock_prediction/arima) and [SARIMA](/posts/finance/stock_prediction/sarima). Therefore, in this article we are going to implement a SARIMAX model the can include **exogenous variables**
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## Introduction to Exogenous Variables in Time Series Models
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In the previous articles ( [ARIMA](/posts/finance/stock_prediction/arima) and [SARIMA](/posts/finance/stock_prediction/sarima)
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Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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‎content/posts/finance/stock_prediction/SARIMAX/sarimax_example.ipynb

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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"execution_count": 65,
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Performing stepwise search to minimize aic\n",
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" ARIMA(1,1,1)(1,1,1)[12] : AIC=inf, Time=1.82 sec\n",
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" ARIMA(1,1,1)(1,1,1)[12] : AIC=inf, Time=1.83 sec\n",
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" ARIMA(0,1,0)(0,1,0)[12] : AIC=3802.747, Time=0.04 sec\n",
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" ARIMA(1,1,0)(1,1,0)[12] : AIC=3597.813, Time=0.15 sec\n",
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" ARIMA(0,1,1)(0,1,1)[12] : AIC=inf, Time=0.99 sec\n",
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" ARIMA(1,1,0)(0,1,0)[12] : AIC=3804.105, Time=0.04 sec\n",
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" ARIMA(1,1,0)(2,1,0)[12] : AIC=3525.586, Time=0.34 sec\n",
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" ARIMA(1,1,0)(2,1,1)[12] : AIC=inf, Time=2.90 sec\n",
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" ARIMA(1,1,0)(1,1,1)[12] : AIC=inf, Time=1.09 sec\n",
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" ARIMA(0,1,0)(2,1,0)[12] : AIC=3523.686, Time=0.26 sec\n",
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" ARIMA(0,1,0)(1,1,0)[12] : AIC=3596.070, Time=0.08 sec\n",
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" ARIMA(0,1,0)(2,1,1)[12] : AIC=inf, Time=2.63 sec\n",
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" ARIMA(0,1,0)(1,1,1)[12] : AIC=inf, Time=0.80 sec\n",
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" ARIMA(0,1,1)(2,1,0)[12] : AIC=3525.569, Time=0.34 sec\n",
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" ARIMA(1,1,1)(2,1,0)[12] : AIC=3526.799, Time=0.70 sec\n",
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" ARIMA(0,1,0)(2,1,0)[12] intercept : AIC=3525.686, Time=0.76 sec\n",
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" ARIMA(1,1,0)(1,1,0)[12] : AIC=3597.813, Time=0.17 sec\n",
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" ARIMA(0,1,1)(0,1,1)[12] : AIC=inf, Time=1.05 sec\n",
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" ARIMA(1,1,0)(0,1,0)[12] : AIC=3804.105, Time=0.05 sec\n",
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" ARIMA(1,1,0)(2,1,0)[12] : AIC=3525.586, Time=0.35 sec\n",
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" ARIMA(1,1,0)(2,1,1)[12] : AIC=inf, Time=2.89 sec\n",
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" ARIMA(1,1,0)(1,1,1)[12] : AIC=inf, Time=1.08 sec\n",
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" ARIMA(0,1,0)(2,1,0)[12] : AIC=3523.686, Time=0.29 sec\n",
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" ARIMA(0,1,0)(1,1,0)[12] : AIC=3596.070, Time=0.12 sec\n",
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" ARIMA(0,1,0)(2,1,1)[12] : AIC=inf, Time=2.68 sec\n",
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" ARIMA(0,1,0)(1,1,1)[12] : AIC=inf, Time=0.81 sec\n",
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" ARIMA(0,1,1)(2,1,0)[12] : AIC=3525.569, Time=0.42 sec\n",
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" ARIMA(1,1,1)(2,1,0)[12] : AIC=3526.799, Time=0.73 sec\n",
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" ARIMA(0,1,0)(2,1,0)[12] intercept : AIC=3525.686, Time=0.82 sec\n",
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"\n",
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"Best model: ARIMA(0,1,0)(2,1,0)[12] \n",
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"Total fit time: 12.965 seconds\n",
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"Total fit time: 13.348 seconds\n",
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" SARIMAX Results \n",
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"==========================================================================================\n",
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"Dep. Variable: y No. Observations: 697\n",
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"Model: SARIMAX(0, 1, 0)x(2, 1, 0, 12) Log Likelihood -1758.843\n",
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"Date: Sun, 07 Jul 2024 AIC 3523.686\n",
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"Time: 00:01:08 BIC 3537.270\n",
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"Time: 00:23:29 BIC 3537.270\n",
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"Sample: 0 HQIC 3528.942\n",
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" - 697 \n",
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"Covariance Type: opg \n",
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"Dep. Variable: AAPL No. Observations: 697\n",
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"Model: SARIMAX(0, 1, 0)x(2, 1, 0, 12) Log Likelihood -1385.522\n",
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"Date: Sun, 07 Jul 2024 AIC 2779.044\n",
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"Time: 00:01:09 BIC 2797.156\n",
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"Time: 00:23:31 BIC 2797.156\n",
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"Sample: 0 HQIC 2786.053\n",
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" - 697 \n",
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"Covariance Type: opg \n",
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},
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{
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"cell_type": "code",
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"execution_count": 66,
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"metadata": {},
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{
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"name": "stdout",
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"Mean Squared Error: 1235.4974952613672\n",
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"Mean Absolute Error: 28.192420087703255\n",
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"Root Mean Squared Error: 35.14964431201783\n",
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"Mean Squared Error: 1235.4975\n",
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"Mean Absolute Error: 28.1924\n",
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"Root Mean Squared Error: 35.1496\n",
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" SARIMAX Results \n",
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"==========================================================================================\n",
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"Dep. Variable: AAPL No. Observations: 697\n",
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"Model: SARIMAX(0, 1, 0)x(2, 1, 0, 12) Log Likelihood -1385.522\n",
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"Date: Sun, 07 Jul 2024 AIC 2779.044\n",
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"Time: 00:01:09 BIC 2797.156\n",
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"Time: 00:23:31 BIC 2797.156\n",
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"Sample: 0 HQIC 2786.053\n",
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" - 697 \n",
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"Covariance Type: opg \n",
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"mse = mean_squared_error(test['AAPL'], forecast.predicted_mean)\n",
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"mae = mean_absolute_error(test['AAPL'], forecast.predicted_mean)\n",
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"rmse = np.sqrt(mse)\n",
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"print(f'Mean Squared Error: {mse}')\n",
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"print(f'Mean Absolute Error: {mae}')\n",
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"print(f'Root Mean Squared Error: {rmse}')\n",
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"print(f'Mean Squared Error: {mse:.4f}')\n",
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"print(f'Mean Absolute Error: {mae:.4f}')\n",
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"print(f'Root Mean Squared Error: {rmse:.4f}')\n",
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"\n",
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"# Check the impact of the exogenous variable\n",
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"print(results.summary())"
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},
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"cell_type": "code",
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"execution_count": 71,
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"metadata": {},
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{
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},
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{
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"cell_type": "code",
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"metadata": {},
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"text": [
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"Mean Squared Error: 72.54815308159101\n",
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"Mean Absolute Error: 5.992999880063084\n",
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"Root Mean Squared Error: 8.517520359916436\n"
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"Mean Squared Error: 72.5482\n",
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"Mean Absolute Error: 5.9930\n",
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"Root Mean Squared Error: 8.5175\n"
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]
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}
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"mse = mean_squared_error(test['AAPL'], forecasts)\n",
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"mae = mean_absolute_error(test['AAPL'], forecasts)\n",
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"rmse = np.sqrt(mse)\n",
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"print(f'Mean Squared Error: {mse}')\n",
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"print(f'Mean Absolute Error: {mae}')\n",
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"print(f'Root Mean Squared Error: {rmse}')"
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"print(f'Mean Squared Error: {mse:.4f}')\n",
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"print(f'Mean Absolute Error: {mae:.4f}')\n",
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"print(f'Root Mean Squared Error: {rmse:.4f}')"
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‎public/index.json

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‎public/index.xml

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<pubDate>Sat, 06 Jul 2024 00:00:00 +0100</pubDate>
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<guid>http://localhost:1313/posts/finance/stock_prediction/sarimax/</guid>
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<description>Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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Market indices (e.g., S&amp;amp;P 500) Economic indicators (e.g., GDP growth, unemployment rate) Company-specific metrics (e.g., revenue, earnings per share) Sentiment indicators (e.g., social media sentiment) Mathematical Formulation of SARIMAX The SARIMAX model extends the SARIMA model by including exogenous variables.</description>
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<description>In the previous articles we saw the limitations of the ARIMA and SARIMA. Therefore, in this article we are going to implement a SARIMAX model the can include exogenous variables
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Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</description>
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‎public/posts/finance/index.html

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<div class="card-body">
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<a href="/posts/finance/stock_prediction/sarimax/" class="post-card-link">
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<h5 class="card-title">SARIMAX Model Analysis of Apple Stock with Exogenous Variables</h5>
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<p class="card-text post-summary">Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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Market indices (e.g., S&amp;P 500) Economic indicators (e.g., GDP growth, unemployment rate) Company-specific metrics (e.g., revenue, earnings per share) Sentiment indicators (e.g., social media sentiment) Mathematical Formulation of SARIMAX The SARIMAX model extends the SARIMA model by including exogenous variables.</p>
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<p class="card-text post-summary">In the previous articles we saw the limitations of the ARIMA and SARIMA. Therefore, in this article we are going to implement a SARIMAX model the can include exogenous variables
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Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</p>
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‎public/posts/finance/index.xml

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<pubDate>Sat, 06 Jul 2024 00:00:00 +0100</pubDate>
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<guid>http://localhost:1313/posts/finance/stock_prediction/sarimax/</guid>
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<description>Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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Market indices (e.g., S&amp;amp;P 500) Economic indicators (e.g., GDP growth, unemployment rate) Company-specific metrics (e.g., revenue, earnings per share) Sentiment indicators (e.g., social media sentiment) Mathematical Formulation of SARIMAX The SARIMAX model extends the SARIMA model by including exogenous variables.</description>
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<description>In the previous articles we saw the limitations of the ARIMA and SARIMA. Therefore, in this article we are going to implement a SARIMAX model the can include exogenous variables
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Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</description>
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‎public/posts/finance/stock_prediction/sarimax/index.html

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<div class="post-content" id="post-content">
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<h2 id="introduction-to-exogenous-variables-in-time-series-models">Introduction to Exogenous Variables in Time Series Models</h2>
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<p>In the previous articles we saw the limitations of the <a href="/posts/finance/stock_prediction/arima">ARIMA</a> and <a href="/posts/finance/stock_prediction/sarima">SARIMA</a>. Therefore, in this article we are going to implement a SARIMAX model the can include <strong>exogenous variables</strong></p>
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<h2 id="introduction-to-exogenous-variables-in-time-series-models">Introduction to Exogenous Variables in Time Series Models</h2>
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<p>Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</p>
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<li>Market indices (e.g., S&amp;P 500)</li>

‎public/posts/index.html

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<div class="card-body">
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<a href="/posts/finance/stock_prediction/sarimax/" class="post-card-link">
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<h5 class="card-title">SARIMAX Model Analysis of Apple Stock with Exogenous Variables</h5>
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<p class="card-text post-summary">Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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Market indices (e.g., S&amp;P 500) Economic indicators (e.g., GDP growth, unemployment rate) Company-specific metrics (e.g., revenue, earnings per share) Sentiment indicators (e.g., social media sentiment) Mathematical Formulation of SARIMAX The SARIMAX model extends the SARIMA model by including exogenous variables.</p>
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<p class="card-text post-summary">In the previous articles we saw the limitations of the ARIMA and SARIMA. Therefore, in this article we are going to implement a SARIMAX model the can include exogenous variables
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Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</p>
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‎public/posts/index.xml

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<pubDate>Sat, 06 Jul 2024 00:00:00 +0100</pubDate>
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<guid>http://localhost:1313/posts/finance/stock_prediction/sarimax/</guid>
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<description>Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:
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Market indices (e.g., S&amp;amp;P 500) Economic indicators (e.g., GDP growth, unemployment rate) Company-specific metrics (e.g., revenue, earnings per share) Sentiment indicators (e.g., social media sentiment) Mathematical Formulation of SARIMAX The SARIMAX model extends the SARIMA model by including exogenous variables.</description>
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<description>In the previous articles we saw the limitations of the ARIMA and SARIMA. Therefore, in this article we are going to implement a SARIMAX model the can include exogenous variables
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Introduction to Exogenous Variables in Time Series Models Exogenous variables, also known as external regressors, are independent variables that are not part of the main time series but can influence it. In the context of stock price prediction, exogenous variables might include:</description>
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