Evaluating Seasonal Patterns in Pediatric Diarrhea and Pneumonia using SARIMA: A Comparative Analysis of Simulated and Real Time Series in Rivers State, Nigeria

Abstract

This study evaluates the effectiveness of Seasonal Autoregressive Integrated Moving Average (SARIMA) models in forecasting trends of Pediatric Diarrhea and Pneumonia in Rivers State, Nigeria, with particular emphasis on handling auto-correlated errors. The objectives include analyzing seasonal patterns, assessing autocorrelation structures, comparing alternative SARIMA specifications, and identifying the most suitable model using both real and simulated datasets. The empirical data comprise monthly records of reported cases among children under five years, obtained from the Rivers State Primary Healthcare Database. Additionally, a synthetic time series was generated to replicate similar autocorrelation characteristics for robustness testing. Autocorrelation diagnostics, including the Ljung-Box test and ACF/PACF plots, revealed significant serial dependencies across all series, underscoring the limitations of models that ignore autocorrelation. Competing SARIMA models were estimated and evaluated based on Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and residual diagnostic checks. Among the models assessed, SARIMA(0,1,2)(0,0,2)[12][12][12] emerged as the best-fitting model, particularly for pediatric diarrhea, demonstrating strong predictive performance and adherence to diagnostic assumptions. Although Auto ARIMA achieved comparable results for pneumonia, SARIMA models exhibited superior residual behaviour and diagnostic reliability. By integrating actual and simulated data, this research addresses gaps in previous studies that overlooked seasonality and autocorrelation in padiatric health time series modeling. The findings affirm the usefulness of SARIMA for time series epidemiology and highlight its potential for enhancing disease investigation and informing public health interventions in resource-constrained settings such as Rivers State.