Short-term forecasting using SARIMA models: an application to epidemiological time series data with COVID-19 in Kazakhstan as an example

Abstract

Time series forecasting is a pivotal tool across multiple disciplines, particularly in epidemiology, where precise predictions can guide resource allocation and inform public health strategies. This study explores the application of Seasonal Autoregressive Integrated Moving Average (SARIMA) models for short-term forecasting of time series data, using epidemiological data from Kazakhstan related to COVID-19 as a practical case study. The dataset encompasses total confirmed cases, daily ambulatory care patients, and daily hospitalized patients, spanning from May 30, 2022, to December 14, 2022, with forecasts extending 10 days forward to December 24, 2022. The analysis leverages SARIMA’s ability to capture both seasonal and non-stationary patterns, making it highly effective for modeling complex epidemiological dynamics. The methodology involves several key steps: data preprocessing through natural-log transformation to stabilize variance, stationarity testing using autocorrelation function (ACF) plots, and differencing to address non-stationarity. The optimal SARIMA models identified were (5,3,1)(1,1,0)_7 for total cases, (1,2,2)(0,1,1)_7 for ambulatory care patients, and (2,2,1)(2,1,1)_7 for hospitalized patients, with forecasting accuracies of 99%, 97%, and 91%, respectively. These high accuracies, measured via Mean Absolute Percentage Error (MAPE), underscore SARIMA’s robustness in short-term predictions. Residual analysis, including Shapiro-Wilk and Ljung-Box tests, confirmed that the models’ residuals were normally distributed and independent, validating their suitability for forecasting. This study highlights SARIMA’s versatility in capturing weekly seasonal patterns, as observed in the 7-day cycles within the COVID-19 data, which reflect reporting or behavioral trends. While the example focuses on epidemiological data, the methodology is broadly applicable to other domains, such as ecological monitoring or economic forecasting, where seasonal time series are prevalent. The findings demonstrate that SARIMA models provide a reliable framework for short-term forecasting, offering actionable insights for public health interventions and resource planning, with the COVID-19 dataset serving as an illustrative example of the approach’s efficacy and adaptability.