{"id":9253,"date":"2025-07-15T13:29:07","date_gmt":"2025-07-15T10:29:07","guid":{"rendered":"https:\/\/bitimpulse.com\/?p=9253"},"modified":"2025-07-15T13:29:07","modified_gmt":"2025-07-15T10:29:07","slug":"yak-obraty-optymalnu-model-prognozuvannya-dlya-dynamichnyh-ryadiv-prodazhiv-arima-vs-regresijna-model","status":"publish","type":"post","link":"https:\/\/bitimpulse.com\/en\/yak-obraty-optymalnu-model-prognozuvannya-dlya-dynamichnyh-ryadiv-prodazhiv-arima-vs-regresijna-model\/","title":{"rendered":"How to Choose the Optimal Forecasting Model for Sales Time Series: ARIMA vs. Regression Model"},"content":{"rendered":"<p><\/p>\n<h2 data-start=\"155\" data-end=\"174\"><strong data-start=\"158\" data-end=\"174\">Introduction<\/strong><\/h2>\n<p data-start=\"176\" data-end=\"573\">Sales forecasting is a critical process for effective planning of production, procurement, logistics, and marketing. However, choosing the right model is just as important as the forecast itself. ARIMA, regression models, machine learning \u2014 each approach has its own advantages and limitations. A poor model choice can lead to misleading results and business decisions based on false expectations.<\/p>\n<p data-start=\"575\" data-end=\"768\">This article explores <strong data-start=\"597\" data-end=\"662\">how to choose the optimal model for dynamic sales time series<\/strong>, comparing ARIMA and classical regression methods, and what factors to consider in the selection process.<\/p>\n<hr data-start=\"770\" data-end=\"773\" \/>\n<h2 data-start=\"775\" data-end=\"822\"><strong data-start=\"778\" data-end=\"822\">1. What type of data are we forecasting?<\/strong><\/h2>\n<p data-start=\"824\" data-end=\"886\">Before choosing a model, assess the nature of the time series:<\/p>\n<ul data-start=\"888\" data-end=\"1119\">\n<li data-start=\"888\" data-end=\"944\">\n<p data-start=\"890\" data-end=\"944\">Is there a <strong data-start=\"901\" data-end=\"916\">clear trend<\/strong> (steady growth or decline)?<\/p>\n<\/li>\n<li data-start=\"945\" data-end=\"983\">\n<p data-start=\"947\" data-end=\"983\">Are there <strong data-start=\"957\" data-end=\"982\">seasonal fluctuations<\/strong>?<\/p>\n<\/li>\n<li data-start=\"984\" data-end=\"1069\">\n<p data-start=\"986\" data-end=\"1069\">Do sales depend on <strong data-start=\"1005\" data-end=\"1027\">external variables<\/strong> (e.g., discounts, holidays, advertising)?<\/p>\n<\/li>\n<li data-start=\"1070\" data-end=\"1119\">\n<p data-start=\"1072\" data-end=\"1119\">Are there <strong data-start=\"1082\" data-end=\"1095\">anomalies<\/strong>, such as sudden spikes?<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1121\" data-end=\"1187\">These characteristics help determine which model is more suitable.<\/p>\n<hr data-start=\"1189\" data-end=\"1192\" \/>\n<h2 data-start=\"1194\" data-end=\"1243\"><strong data-start=\"1197\" data-end=\"1243\">2. ARIMA: When it fits and its limitations<\/strong><\/h2>\n<h3 data-start=\"1245\" data-end=\"1271\"><strong data-start=\"1249\" data-end=\"1271\">2.1. What is ARIMA<\/strong><\/h3>\n<p data-start=\"1272\" data-end=\"1551\">ARIMA (AutoRegressive Integrated Moving Average) is a statistical model that works solely with the <strong data-start=\"1371\" data-end=\"1393\">time series itself<\/strong>, without incorporating external variables. It is best suited for <strong data-start=\"1459\" data-end=\"1478\">stationary data<\/strong>, or data that can be made stationary by removing trends and seasonality.<\/p>\n<h3 data-start=\"1553\" data-end=\"1583\"><strong data-start=\"1557\" data-end=\"1583\">2.2. When to use ARIMA<\/strong><\/h3>\n<ul data-start=\"1584\" data-end=\"1815\">\n<li data-start=\"1584\" data-end=\"1641\">\n<p data-start=\"1586\" data-end=\"1641\">A long history of sales data without major disruptions.<\/p>\n<\/li>\n<li data-start=\"1642\" data-end=\"1708\">\n<p data-start=\"1644\" data-end=\"1708\">No significant impact from external drivers (e.g., advertising).<\/p>\n<\/li>\n<li data-start=\"1709\" data-end=\"1778\">\n<p data-start=\"1711\" data-end=\"1778\">Data shows <strong data-start=\"1722\" data-end=\"1741\">autocorrelation<\/strong> (past values influence future ones).<\/p>\n<\/li>\n<li data-start=\"1779\" data-end=\"1815\">\n<p data-start=\"1781\" data-end=\"1815\">Short- to medium-term forecasting.<\/p>\n<\/li>\n<\/ul>\n<blockquote data-start=\"1817\" data-end=\"1892\">\n<p data-start=\"1819\" data-end=\"1892\">Example: forecasting bread sales in a supermarket without any promotions.<\/p>\n<\/blockquote>\n<h3 data-start=\"1894\" data-end=\"1926\"><strong data-start=\"1898\" data-end=\"1926\">2.3. Advantages of ARIMA<\/strong><\/h3>\n<ul data-start=\"1927\" data-end=\"2055\">\n<li data-start=\"1927\" data-end=\"1969\">\n<p data-start=\"1929\" data-end=\"1969\">High accuracy in short-term predictions.<\/p>\n<\/li>\n<li data-start=\"1970\" data-end=\"2010\">\n<p data-start=\"1972\" data-end=\"2010\">Supports seasonal series (via SARIMA).<\/p>\n<\/li>\n<li data-start=\"2011\" data-end=\"2055\">\n<p data-start=\"2013\" data-end=\"2055\">Statistically sound for well-behaved data.<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"2057\" data-end=\"2081\"><strong data-start=\"2061\" data-end=\"2081\">2.4. Limitations<\/strong><\/h3>\n<ul data-start=\"2082\" data-end=\"2265\">\n<li data-start=\"2082\" data-end=\"2126\">\n<p data-start=\"2084\" data-end=\"2126\"><strong data-start=\"2084\" data-end=\"2125\">Does not account for external factors<\/strong>.<\/p>\n<\/li>\n<li data-start=\"2127\" data-end=\"2192\">\n<p data-start=\"2129\" data-end=\"2192\">Requires <strong data-start=\"2138\" data-end=\"2165\">sufficient data history<\/strong> (usually 50+ time points).<\/p>\n<\/li>\n<li data-start=\"2193\" data-end=\"2265\">\n<p data-start=\"2195\" data-end=\"2265\">Struggles with sudden changes in market behavior or customer dynamics.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2267\" data-end=\"2270\" \/>\n<h2 data-start=\"2272\" data-end=\"2341\"><strong data-start=\"2275\" data-end=\"2341\">3. Regression Model: Flexibility through explanatory variables<\/strong><\/h2>\n<h3 data-start=\"2343\" data-end=\"2366\"><strong data-start=\"2347\" data-end=\"2366\">3.1. What it is<\/strong><\/h3>\n<p data-start=\"2367\" data-end=\"2499\">A regression model allows incorporating <strong data-start=\"2407\" data-end=\"2427\">external factors<\/strong> such as discount campaigns, ad budgets, days of the week, weather, etc.<\/p>\n<p>Sales = b0 + b1 * Advertising + b2 * Price + b3 * Day + e<\/p>\n<h3 data-start=\"2605\" data-end=\"2640\"><strong data-start=\"2609\" data-end=\"2640\">3.2. When to use regression<\/strong><\/h3>\n<ul data-start=\"2641\" data-end=\"2871\">\n<li data-start=\"2641\" data-end=\"2693\">\n<p data-start=\"2643\" data-end=\"2693\">Sales depend on <strong data-start=\"2659\" data-end=\"2692\">measurable external variables<\/strong>.<\/p>\n<\/li>\n<li data-start=\"2694\" data-end=\"2751\">\n<p data-start=\"2696\" data-end=\"2751\">Data on marketing, pricing, and campaigns is available.<\/p>\n<\/li>\n<li data-start=\"2752\" data-end=\"2806\">\n<p data-start=\"2754\" data-end=\"2806\">You need to estimate <strong data-start=\"2775\" data-end=\"2805\">impact of specific changes<\/strong>.<\/p>\n<\/li>\n<li data-start=\"2807\" data-end=\"2871\">\n<p data-start=\"2809\" data-end=\"2871\">Scenario modeling is required (\u201cwhat if we lower the price?\u201d).<\/p>\n<\/li>\n<\/ul>\n<blockquote data-start=\"2873\" data-end=\"2981\">\n<p data-start=\"2875\" data-end=\"2981\">Example: predicting electronics sales during seasonal promotions based on ad spending and discount levels.<\/p>\n<\/blockquote>\n<h3 data-start=\"2983\" data-end=\"3006\"><strong data-start=\"2987\" data-end=\"3006\">3.3. Advantages<\/strong><\/h3>\n<ul data-start=\"3007\" data-end=\"3194\">\n<li data-start=\"3007\" data-end=\"3064\">\n<p data-start=\"3009\" data-end=\"3064\">Accounts for <strong data-start=\"3022\" data-end=\"3044\">management actions<\/strong> and market effects.<\/p>\n<\/li>\n<li data-start=\"3065\" data-end=\"3130\">\n<p data-start=\"3067\" data-end=\"3130\">Useful for <strong data-start=\"3078\" data-end=\"3099\">scenario modeling<\/strong> and <strong data-start=\"3104\" data-end=\"3129\">cause-effect analysis<\/strong>.<\/p>\n<\/li>\n<li data-start=\"3131\" data-end=\"3194\">\n<p data-start=\"3133\" data-end=\"3194\">Flexible in handling <strong data-start=\"3154\" data-end=\"3193\">complex multi-variable environments<\/strong>.<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"3196\" data-end=\"3220\"><strong data-start=\"3200\" data-end=\"3220\">3.4. Limitations<\/strong><\/h3>\n<ul data-start=\"3221\" data-end=\"3387\">\n<li data-start=\"3221\" data-end=\"3286\">\n<p data-start=\"3223\" data-end=\"3286\">Requires quality input data and careful <strong data-start=\"3263\" data-end=\"3285\">variable selection<\/strong>.<\/p>\n<\/li>\n<li data-start=\"3287\" data-end=\"3335\">\n<p data-start=\"3289\" data-end=\"3335\">Sensitive to multicollinearity and data noise.<\/p>\n<\/li>\n<li data-start=\"3336\" data-end=\"3387\">\n<p data-start=\"3338\" data-end=\"3387\">Needs expertise to build and interpret correctly.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3389\" data-end=\"3392\" \/>\n<h2 data-start=\"3394\" data-end=\"3439\"><strong data-start=\"3397\" data-end=\"3439\">4. ARIMA vs. Regression: How to choose<\/strong><\/h2>\n<div class=\"_tableContainer_80l1q_1\">\n<div class=\"_tableWrapper_80l1q_14 group flex w-fit flex-col-reverse\" tabindex=\"-1\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"3441\" data-end=\"3874\">\n<thead data-start=\"3441\" data-end=\"3495\">\n<tr data-start=\"3441\" data-end=\"3495\">\n<th data-start=\"3441\" data-end=\"3473\" data-col-size=\"sm\">Criterion<\/th>\n<th data-start=\"3473\" data-end=\"3481\" data-col-size=\"sm\">ARIMA<\/th>\n<th data-start=\"3481\" data-end=\"3495\" data-col-size=\"sm\">Regression<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"3550\" data-end=\"3874\">\n<tr data-start=\"3550\" data-end=\"3610\">\n<td data-start=\"3550\" data-end=\"3581\" data-col-size=\"sm\">Seasonality supported<\/td>\n<td data-start=\"3581\" data-end=\"3589\" data-col-size=\"sm\">\u2714<\/td>\n<td data-start=\"3589\" data-end=\"3610\" data-col-size=\"sm\">\u2714 (via variables)<\/td>\n<\/tr>\n<tr data-start=\"3611\" data-end=\"3664\">\n<td data-start=\"3611\" data-end=\"3642\" data-col-size=\"sm\">External variable sensitivity<\/td>\n<td data-start=\"3642\" data-end=\"3650\" data-col-size=\"sm\">\u2716<\/td>\n<td data-start=\"3650\" data-end=\"3664\" data-col-size=\"sm\">\u2714<\/td>\n<\/tr>\n<tr data-start=\"3665\" data-end=\"3718\">\n<td data-start=\"3665\" data-end=\"3696\" data-col-size=\"sm\">Short-term forecasting<\/td>\n<td data-start=\"3696\" data-end=\"3704\" data-col-size=\"sm\">\u2714<\/td>\n<td data-start=\"3704\" data-end=\"3718\" data-col-size=\"sm\">\u2714<\/td>\n<\/tr>\n<tr data-start=\"3719\" data-end=\"3766\">\n<td data-start=\"3719\" data-end=\"3757\" data-col-size=\"sm\">Analyzing advertising\/price effects<\/td>\n<td data-start=\"3757\" data-end=\"3761\" data-col-size=\"sm\">\u2716<\/td>\n<td data-start=\"3761\" data-end=\"3766\" data-col-size=\"sm\">\u2714<\/td>\n<\/tr>\n<tr data-start=\"3767\" data-end=\"3820\">\n<td data-start=\"3767\" data-end=\"3798\" data-col-size=\"sm\">Stable data (no major shifts)<\/td>\n<td data-start=\"3798\" data-end=\"3806\" data-col-size=\"sm\">\u2714<\/td>\n<td data-start=\"3806\" data-end=\"3820\" data-col-size=\"sm\">\u2716<\/td>\n<\/tr>\n<tr data-start=\"3821\" data-end=\"3874\">\n<td data-start=\"3821\" data-end=\"3852\" data-col-size=\"sm\">Need for flexibility<\/td>\n<td data-start=\"3852\" data-end=\"3860\" data-col-size=\"sm\">\u2716<\/td>\n<td data-start=\"3860\" data-end=\"3874\" data-col-size=\"sm\">\u2714<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr data-start=\"3876\" data-end=\"3879\" \/>\n<h2 data-start=\"3881\" data-end=\"3908\"><strong data-start=\"3884\" data-end=\"3908\">5. Hybrid Approaches<\/strong><\/h2>\n<p data-start=\"3910\" data-end=\"3962\">In complex cases, <strong data-start=\"3928\" data-end=\"3945\">hybrid models<\/strong> often work best:<\/p>\n<ul data-start=\"3963\" data-end=\"4147\">\n<li data-start=\"3963\" data-end=\"4001\">\n<p data-start=\"3965\" data-end=\"4001\">ARIMAX (ARIMA + external variables),<\/p>\n<\/li>\n<li data-start=\"4002\" data-end=\"4071\">\n<p data-start=\"4004\" data-end=\"4071\">Regression with lags (previous values of the series as predictors),<\/p>\n<\/li>\n<li data-start=\"4072\" data-end=\"4147\">\n<p data-start=\"4074\" data-end=\"4147\">Machine learning models (XGBoost, Random Forest) for nonlinear scenarios.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"4149\" data-end=\"4152\" \/>\n<h2 data-start=\"4154\" data-end=\"4212\"><strong data-start=\"4157\" data-end=\"4212\">6. How BAT helps test and select forecasting models<\/strong><\/h2>\n<p data-start=\"4214\" data-end=\"4261\"><strong data-start=\"4214\" data-end=\"4246\">Business Analysis Tool (BAT)<\/strong> allows you to:<\/p>\n<ul data-start=\"4263\" data-end=\"4572\">\n<li data-start=\"4263\" data-end=\"4326\">\n<p data-start=\"4265\" data-end=\"4326\">Import and clean sales time series data from CRM, ERP, Excel;<\/p>\n<\/li>\n<li data-start=\"4327\" data-end=\"4385\">\n<p data-start=\"4329\" data-end=\"4385\">Automatically test ARIMA, regression, and hybrid models;<\/p>\n<\/li>\n<li data-start=\"4386\" data-end=\"4443\">\n<p data-start=\"4388\" data-end=\"4443\">Compare accuracy using metrics such as MAE, RMSE, MAPE;<\/p>\n<\/li>\n<li data-start=\"4444\" data-end=\"4509\">\n<p data-start=\"4446\" data-end=\"4509\">Simulate scenarios (e.g., change price, campaign, seasonality);<\/p>\n<\/li>\n<li data-start=\"4510\" data-end=\"4572\">\n<p data-start=\"4512\" data-end=\"4572\">Visualize factor impact and build <strong data-start=\"4546\" data-end=\"4571\">data-driven forecasts<\/strong>.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"4574\" data-end=\"4577\" \/>\n<h2 data-start=\"4579\" data-end=\"4596\"><strong data-start=\"4582\" data-end=\"4596\">Conclusion<\/strong><\/h2>\n<p data-start=\"4598\" data-end=\"4636\">The best forecasting model depends on:<\/p>\n<ul data-start=\"4637\" data-end=\"4843\">\n<li data-start=\"4637\" data-end=\"4717\">\n<p data-start=\"4639\" data-end=\"4717\">The <strong data-start=\"4643\" data-end=\"4675\">characteristics of your data<\/strong> (trend, seasonality, external influence),<\/p>\n<\/li>\n<li data-start=\"4718\" data-end=\"4777\">\n<p data-start=\"4720\" data-end=\"4777\">The <strong data-start=\"4724\" data-end=\"4747\">goal of forecasting<\/strong> (explanation vs. prediction),<\/p>\n<\/li>\n<li data-start=\"4778\" data-end=\"4843\">\n<p data-start=\"4780\" data-end=\"4843\"><strong data-start=\"4780\" data-end=\"4801\">Data availability<\/strong> (historical series + explanatory inputs).<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"4845\" data-end=\"5259\" data-is-last-node=\"\" data-is-only-node=\"\">If your data is stable and self-contained, <strong data-start=\"4888\" data-end=\"4897\">ARIMA<\/strong> will likely offer strong results.<br data-start=\"4931\" data-end=\"4934\" \/>If you need to model external factors like promotions, pricing, or media campaigns \u2014 <strong data-start=\"5019\" data-end=\"5033\">regression<\/strong> gives better flexibility and insight.<br data-start=\"5071\" data-end=\"5074\" \/>Tools like <strong data-start=\"5085\" data-end=\"5092\">BAT<\/strong> help turn this decision into <strong data-start=\"5122\" data-end=\"5150\">an evidence-based choice<\/strong>, by testing accuracy directly on your data and supporting strategic forecasting with transparency and speed.<\/p>\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>Introduction Sales forecasting is a critical process for effective planning of production, procurement, logistics, and marketing. However, choosing the right model is just as important as the forecast itself. ARIMA, regression models, machine learning \u2014 each approach has its own advantages and limitations. A poor model choice can lead to misleading results and business decisions [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"inline_featured_image":false,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-9253","post","type-post","status-publish","format-standard","hentry","category-pytannya-vidpovidi"],"_links":{"self":[{"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/posts\/9253","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/comments?post=9253"}],"version-history":[{"count":1,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/posts\/9253\/revisions"}],"predecessor-version":[{"id":9254,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/posts\/9253\/revisions\/9254"}],"wp:attachment":[{"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/media?parent=9253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/categories?post=9253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bitimpulse.com\/en\/wp-json\/wp\/v2\/tags?post=9253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}