{"id":183168,"date":"2024-03-18T02:34:00","date_gmt":"2024-03-18T01:34:00","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=183168"},"modified":"2024-03-14T20:33:59","modified_gmt":"2024-03-14T19:33:59","slug":"sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","title":{"rendered":"SARIMAX model: What is it? How can it be applied to time series?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"183168\" class=\"elementor elementor-183168\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-62c2338 e-flex e-con-boxed e-con\" data-id=\"62c2338\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-83a1844 elementor-widget elementor-widget-heading\" data-id=\"83a1844\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Time series analysis is a crucial methodology in many fields, such as finance, economics, meteorology and biology.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-202676d elementor-widget elementor-widget-text-editor\" data-id=\"202676d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Among the various approaches available, the SARIMAX <strong>(Seasonal Autoregressive Integrated Moving Average + exogenous variables)<\/strong> model stands out as a powerful tool for modeling and forecasting both trends and seasonal variations in temporal data, while incorporating exogenous variables into the analysis to improve prediction accuracy.<\/p><p>In this article, we&#8217;ll dive into the basics of the <strong>SARIMAX model<\/strong>, examine its key components and explore its practical application.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a244dae e-flex e-con-boxed e-con\" data-id=\"a244dae\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6c3e22a elementor-widget elementor-widget-heading\" data-id=\"6c3e22a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">The foundation: the ARIMA model<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e4e1775 elementor-widget elementor-widget-text-editor\" data-id=\"e4e1775\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>To fully grasp the essence of the SARIMAX model, let&#8217;s start by exploring the basics of the ARIMA (Autoregressive Integrated Moving Average) model. ARIMA is a powerful statistical technique for modeling and forecasting time series. It is based on three key components: autoregression (AR), moving average (MA) and integration (I).<\/p><p><strong>Autoregression (AR)<\/strong> takes into account past values of the time series to predict current values. It is characterized by an order generally noted p. Autoregression consists of performing a linear regression on the last p values of the time series in order to predict the current value:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-08a69f0 elementor-widget elementor-widget-image\" data-id=\"08a69f0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/image2.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-85d23cd elementor-widget elementor-widget-text-editor\" data-id=\"85d23cd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\">The moving average (MA), on the other hand, tackles past errors in predictions. It is characterized by an order generally noted q. The moving average consists of performing a linear regression on the last q error values in order to predict the current value:<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fbf15ce elementor-widget elementor-widget-image\" data-id=\"fbf15ce\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/image3.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9380abd elementor-widget elementor-widget-text-editor\" data-id=\"9380abd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The combination of autoregression and moving average is the ARMA model. This model is effective on stationary time series. To apply this to any time series, we use the Integration (I) component of the ARIMA model.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-beb711a elementor-widget elementor-widget-text-editor\" data-id=\"beb711a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li>Integration (I) is used to make the time series stationary, by differentiating the values to facilitate modeling. Indeed, most time series can be made stationary after a number of differentiations.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2670d81 elementor-widget elementor-widget-text-editor\" data-id=\"2670d81\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The <strong>ARIMA model<\/strong> is then characterized by three coefficients: its<a href=\"https:\/\/datascientest.com\/en\/the-var-model-from-business-approach-to-results-plotting\"> autoregression<\/a> order p. Its integration order d, which corresponds to the number of differentiations required to make the time series stationary. If the series is already stationary, the coefficient d to choose would be zero. Its moving-average order q.<\/p><p>Once these coefficients have been given to the <strong>ARIMA model,<\/strong> it will train on the data to find the optimum regression coefficients in the autoregression and moving average to make consistent predictions.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f34c0cd elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"f34c0cd\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Understanding the SARIMAX model<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-bc699aa e-flex e-con-boxed e-con\" data-id=\"bc699aa\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-73353ae elementor-widget elementor-widget-heading\" data-id=\"73353ae\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Expanding towards SARIMA: foray into seasonal variations<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3563530 elementor-widget elementor-widget-text-editor\" data-id=\"3563530\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>When temporal data show seasonal variations, the SARIMA model<\/strong> takes over the scene. The term &#8220;Seasonal&#8221; is added to ARIMA to indicate that this model can capture patterns that repeat at regular intervals.<\/p><p>Seasonal variations can occur over short periods, such as a company&#8217;s monthly sales, or over longer periods, such as climatic data. By incorporating a seasonal component (S), the<strong> SARIMA model<\/strong> can model these recurring patterns and improve forecasts. You can see an example of a non-stationary time series showing seasonality in the graph below, which represents the evolution of an airline&#8217;s annual passenger numbers.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dce3413 elementor-widget elementor-widget-image\" data-id=\"dce3413\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/image1.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6a85c2c e-flex e-con-boxed e-con\" data-id=\"6a85c2c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-18056e6 elementor-widget elementor-widget-heading\" data-id=\"18056e6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">The revolution: SARIMAX and covariates<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1534217 elementor-widget elementor-widget-text-editor\" data-id=\"1534217\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>While the <strong>SARIMA model<\/strong> already offers a powerful method for modeling seasonal time series, there may be external factors influencing these data. This is where the<strong> SARIMAX (Seasonal ARIMA with eXogenous variables)<\/strong> model comes in, opening the door to an <a href=\"https:\/\/datascientest.com\/en\/the-unit-test-in-data-analysis\">even richer analysis.<\/a><\/p><p>Covariates, also known as exogenous variables, are external elements that can influence the time series under study. In the context of a company&#8217;s monthly sales, covariates might include advertising expenditure, special events or vacations. The SARIMAX model makes it possible to incorporate these covariates into the analysis, thereby allowing for external factors that may affect the trends observed.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5ff2eb5 e-flex e-con-boxed e-con\" data-id=\"5ff2eb5\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-457de8a elementor-widget elementor-widget-heading\" data-id=\"457de8a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">SARIMAX model components<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-37cccc5 elementor-widget elementor-widget-text-editor\" data-id=\"37cccc5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The SARIMAX model retains the key components of the SARIMA model while introducing two major elements: the covariates (X) and the covariate component (Z).<\/p><ul><li><strong>Autoregression (AR):<\/strong> As before, autoregression examines past values of the time series to predict current values.<\/li><li><strong>Moving average (MA):<\/strong> The moving average continues to model past errors in predictions.<\/li><li><strong>Integration (I):<\/strong> Integration is always present to make the time series stationary.<\/li><li><strong>Seasonal component (S):<\/strong> The seasonal component captures variations that recur at regular intervals.<\/li><li><strong>Covariates (X):<\/strong> Covariates are external variables that can influence the time series.<\/li><li><strong>Covariate component (Z):<\/strong> The covariate component models the effect of covariates on the time series.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c240e36 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"c240e36\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-scientist-course\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Mastering the SARIMAX model<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1b2c811 e-flex e-con-boxed e-con\" data-id=\"1b2c811\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-96d2689 elementor-widget elementor-widget-heading\" data-id=\"96d2689\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Practical application of SARIMAX with covariates<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-00c9e91 elementor-widget elementor-widget-text-editor\" data-id=\"00c9e91\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Let&#8217;s take a look at a concrete application of the <strong>SARIMAX model<\/strong> to better understand its usefulness. Suppose we have monthly sales data for a company, and monthly advertising expenditure data as covariates.<\/p><ul><li><strong>Data analysis :<\/strong> Before building the model, it&#8217;s crucial to analyze trends, seasonal patterns and the potential influence of covariates on sales. This is the data mining and pre-processing stage.<\/li><li><strong>Model building:<\/strong> By choosing the ARIMA orders (p, d, q) and the seasonal period (s), we fit the SARIMAX model, taking into account the covariates (in this case, advertising expenditure).<\/li><li><strong>Validation and forecasting:<\/strong> Evaluate the model&#8217;s performance by testing it over a period distinct from the training period. Metrics such as root mean square error (RMSE) give us an insight into the quality of predictions. Once validated, the model is ready to be used for future forecasts.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d8d7c9f e-flex e-con-boxed e-con\" data-id=\"d8d7c9f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5c6deb8 elementor-widget elementor-widget-heading\" data-id=\"5c6deb8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-516d047 elementor-widget elementor-widget-text-editor\" data-id=\"516d047\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The <strong>SARIMAX model<\/strong> represents a significant advance in time-series analysis by allowing the integration of covariates. By incorporating external variables to enrich the analysis, this model enables us to better understand future trends and predictions. However, as with any methodology, it is crucial to master the model parameters and understand the results to obtain relevant and reliable predictions.<\/p><p>The <strong>SARIMAX model<\/strong> with covariates is a valuable contribution to the toolbox of time series analysts, offering a more comprehensive approach to modeling and forecasting data influenced by external factors. Whether anticipating company sales, predicting<a href=\"https:\/\/datascientest.com\/en\/optimizing-financial-insights-with-microsoft-power-bi-finance\"> financial market<\/a> fluctuations or understanding climatic variations, the SARIMAX model paves the way for more accurate analyses and informed decisions.<\/p><p>By harnessing the model&#8217;s powerful covariate integration capabilities, professionals can gain a more holistic perspective on time trends and the factors behind them. Ultimately, the <strong>SARIMAX model propels<\/strong> time series analysis to new horizons, enhancing our ability to interpret and anticipate complex temporal behaviors.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8f3a810 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"8f3a810\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Start a training course<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ae7006e elementor-widget elementor-widget-html\" data-id=\"ae7006e\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"The Foundation: ARIMA Model\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"To fully grasp the essence of the SARIMAX model, let's start by exploring the basics of the ARIMA (Autoregressive Integrated Moving Average) model. ARIMA is a powerful statistical technique for modeling and forecasting time series. It is based on three key components: autoregression (AR), moving average (MA) and integration (I).\n      Autoregression (AR) takes into account past values of the time series to predict current values. It is characterized by an order generally noted p. Autoregression consists of performing a linear regression on the last p values of the time series in order to predict the current value:\n      The moving average (MA), on the other hand, tackles past errors in predictions. It is characterized by an order generally noted q. The moving average consists of performing a linear regression on the last q error values to predict the current value:\n      The combination of autoregression and the moving average constitutes the ARMA model. This model is effective on stationary time series. To apply this to any time series, we use the Integration (I) component of the ARIMA model.\n      Integration (I) is used to make the time series stationary, by differentiating the values to facilitate modeling. Indeed, most time series can be made stationary after a certain number of differentiations.\n      The ARIMA model is then characterized by three coefficients: its autoregression order p. Its integration order d, which corresponds to the number of differentiations required to make the time series stationary. If the series is already stationary, the coefficient d to choose would be zero. Its moving-average order q.\n      Once the ARIMA model has been given these coefficients, it will train on the data to find the optimal regression coefficients in the autoregression and moving average to make consistent predictions.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"SARIMAX model components\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The SARIMAX model retains the key components of the SARIMA model while introducing two major elements: the covariates (X) and the covariate component (Z).\n      Autoregression (AR): As before, autoregression examines past values of the time series to predict current values.\n      Moving average (MA): The moving average continues to model past errors in predictions.\n      Integration (I): Integration is always present to make the time series stationary.\n      Seasonal component (S): The seasonal component captures variations that recur at regular intervals.\n      Covariates (X): Covariates are external variables that can influence the time series.\n      Covariate component (Z): The covariate component models the effect of covariates on the time series.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Practical Application of SARIMAX with Covariables\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's take a look at a concrete application of the SARIMAX model to better understand its usefulness. Suppose we have monthly sales data for a company, as well as monthly advertising expenditure data as covariates.\n      Data analysis : Before building the model, it is crucial to analyze trends, seasonal patterns and the potential influence of covariates on sales. This is the data mining and pre-processing stage.\n      Model building: By choosing the ARIMA orders (p, d, q) and the seasonal period (s), we fit the SARIMAX model, taking into account the covariates (in this case, advertising expenditure).\n      Validation and Forecasting: Evaluate the model's performance by testing it over a period distinct from the training period. Metrics such as root mean square error (RMSE) give us an insight into the quality of predictions. Once validated, the model is ready to be used for future forecasts.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Advantages of SARIMAX with Covariables\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Incorporating covariates gives the SARIMAX model a significant advantage. By incorporating exogenous variables, forecasts take into account not only internal and seasonal trends, but also external factors that may influence the time series. This enables decision-makers to take more informed action.\"\n    }\n  }]\n}\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Time series analysis is a crucial methodology in many fields, such as finance, economics, meteorology and biology. Among the various approaches available, the SARIMAX (Seasonal Autoregressive Integrated Moving Average + exogenous variables) model stands out as a powerful tool for modeling and forecasting both trends and seasonal variations in temporal data, while incorporating exogenous variables [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":183169,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>SARIMAX model: What is it? How can it be applied to time series?<\/title>\n<meta name=\"description\" content=\"SARIMAX is a versatile and powerful model for time series forecasting that incorporates seasonal patterns and external factors to improve forecasting accuracy.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SARIMAX model: What is it? How can it be applied to time series?\" \/>\n<meta property=\"og:description\" content=\"Time series analysis is a crucial methodology in many fields, such as finance, economics, meteorology and biology. Among the various approaches available,\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\" \/>\n<meta property=\"og:site_name\" content=\"Data Science Courses | DataScientest\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/DataScientestEN\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-18T01:34:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-14T19:33:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/en\/files\/2024\/03\/sarimax.png\" \/>\n\t<meta property=\"og:image:width\" content=\"768\" \/>\n\t<meta property=\"og:image:height\" content=\"422\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Melanie\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@DataScientest__\" \/>\n<meta name=\"twitter:site\" content=\"@DataScientest__\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Melanie\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series#article\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\"},\"author\":{\"name\":\"Melanie\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d\"},\"headline\":\"SARIMAX model: What is it? How can it be applied to time series?\",\"datePublished\":\"2024-03-18T01:34:00+00:00\",\"dateModified\":\"2024-03-14T19:33:59+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\"},\"wordCount\":1021,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/datascientest.com\/en\/#organization\"},\"articleSection\":[\"Data Science\"],\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series#respond\"]}],\"copyrightYear\":\"2024\",\"copyrightHolder\":{\"@id\":\"https:\/\/datascientest.com\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\",\"url\":\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\",\"name\":\"SARIMAX model: What is it? How can it be applied to time series?\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/en\/#website\"},\"datePublished\":\"2024-03-18T01:34:00+00:00\",\"dateModified\":\"2024-03-14T19:33:59+00:00\",\"description\":\"SARIMAX is a versatile and powerful model for time series forecasting that incorporates seasonal patterns and external factors to improve forecasting accuracy.\",\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/en\/#website\",\"url\":\"https:\/\/datascientest.com\/en\/\",\"name\":\"Data Science Courses | DataScientest\",\"description\":\"Leader in Data Science Courses\",\"publisher\":{\"@id\":\"https:\/\/datascientest.com\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/datascientest.com\/en\/#organization\",\"name\":\"DataScientest\",\"url\":\"https:\/\/datascientest.com\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png\",\"contentUrl\":\"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png\",\"width\":301,\"height\":301,\"caption\":\"DataScientest\"},\"image\":{\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/DataScientestEN\",\"https:\/\/twitter.com\/DataScientest__\",\"https:\/\/www.linkedin.com\/school\/datascientest\/mycompany\/\",\"https:\/\/www.tiktok.com\/@datascientest\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d\",\"name\":\"Melanie\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g\",\"caption\":\"Melanie\"},\"url\":\"https:\/\/datascientest.com\/en\/author\/melaniekrause\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"SARIMAX model: What is it? How can it be applied to time series?","description":"SARIMAX is a versatile and powerful model for time series forecasting that incorporates seasonal patterns and external factors to improve forecasting accuracy.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","og_locale":"en_GB","og_type":"article","og_title":"SARIMAX model: What is it? How can it be applied to time series?","og_description":"Time series analysis is a crucial methodology in many fields, such as finance, economics, meteorology and biology. Among the various approaches available,","og_url":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","og_site_name":"Data Science Courses | DataScientest","article_publisher":"https:\/\/www.facebook.com\/DataScientestEN","article_published_time":"2024-03-18T01:34:00+00:00","article_modified_time":"2024-03-14T19:33:59+00:00","og_image":[{"width":768,"height":422,"url":"https:\/\/datascientest.com\/en\/files\/2024\/03\/sarimax.png","type":"image\/png"}],"author":"Melanie","twitter_card":"summary_large_image","twitter_creator":"@DataScientest__","twitter_site":"@DataScientest__","twitter_misc":{"Written by":"Melanie","Estimated reading time":"6 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series#article","isPartOf":{"@id":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series"},"author":{"name":"Melanie","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d"},"headline":"SARIMAX model: What is it? How can it be applied to time series?","datePublished":"2024-03-18T01:34:00+00:00","dateModified":"2024-03-14T19:33:59+00:00","mainEntityOfPage":{"@id":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series"},"wordCount":1021,"commentCount":0,"publisher":{"@id":"https:\/\/datascientest.com\/en\/#organization"},"articleSection":["Data Science"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series#respond"]}],"copyrightYear":"2024","copyrightHolder":{"@id":"https:\/\/datascientest.com\/#organization"}},{"@type":"WebPage","@id":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","url":"https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series","name":"SARIMAX model: What is it? How can it be applied to time series?","isPartOf":{"@id":"https:\/\/datascientest.com\/en\/#website"},"datePublished":"2024-03-18T01:34:00+00:00","dateModified":"2024-03-14T19:33:59+00:00","description":"SARIMAX is a versatile and powerful model for time series forecasting that incorporates seasonal patterns and external factors to improve forecasting accuracy.","inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/datascientest.com\/en\/sarimax-model-what-is-it-how-can-it-be-applied-to-time-series"]}]},{"@type":"WebSite","@id":"https:\/\/datascientest.com\/en\/#website","url":"https:\/\/datascientest.com\/en\/","name":"Data Science Courses | DataScientest","description":"Leader in Data Science Courses","publisher":{"@id":"https:\/\/datascientest.com\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/datascientest.com\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/datascientest.com\/en\/#organization","name":"DataScientest","url":"https:\/\/datascientest.com\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/","url":"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png","contentUrl":"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png","width":301,"height":301,"caption":"DataScientest"},"image":{"@id":"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/DataScientestEN","https:\/\/twitter.com\/DataScientest__","https:\/\/www.linkedin.com\/school\/datascientest\/mycompany\/","https:\/\/www.tiktok.com\/@datascientest"]},{"@type":"Person","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d","name":"Melanie","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g","caption":"Melanie"},"url":"https:\/\/datascientest.com\/en\/author\/melaniekrause"}]}},"_links":{"self":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts\/183168"}],"collection":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/users\/67"}],"replies":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/comments?post=183168"}],"version-history":[{"count":0,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts\/183168\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/media\/183169"}],"wp:attachment":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/media?parent=183168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/categories?post=183168"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/tags?post=183168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}