Modeling Insurance Claim Count Dynamics using Regime-Switching INGARCH Model

Abstract This paper analyzes insurance claim count data using a Regime-Switching Integer-Valued Generalized Autoregressive Conditional Heteroscedasticity (RS-INGARCH) model. Weekly claim counts from a Ugandan insurance company, spanning 2020–2024 and covering Motor Private and Motor Commercial lines of business, are used. The study examines both the COVID-19 period (March 2020–January 2022) and the post-COVID-19 period, which saw major structural shifts in claims. The RS-INGARCH model outperforms benchmark models such as the Integer-Valued Autoregressive (INAR) and single-regime INGARCH models, based on Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Mean Squared Error (MSE), and out-of-sample forecasting accuracy. Performance gains were especially notable when the COVID-19 period was included, suggesting the RS-INGARCH(1,1) model better captures abrupt changes in claim dynamics. The Autocorrelation Function (ACF) plots and Ljung–Box test confirms reduced residual autocorrelation under RS-INGARCH(1,1), and the INGARCH(1,1) specification performed best among alternative lag choices. A two-regime specification was preferred over three regimes, as the latter introduced instability and overfitting due to limited data in infrequent regimes. The study recommends RS-INGARCH(1,1) models for forecasting and risk evaluation during periods of structural change, especially in emerging insurance markets.