A Comparison of SARIMA and Holt-winters Models in Forecasting Motor Insurance Claims: A Case Study of Kenya
Rangita Apaka *
Department of Statistics and Actuarial Science, Maseno University, Kenya.
Kelvin Rotich
Department of Statistics and Actuarial Science, Maseno University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Most motor insurers in Kenya experience challenges in accurately forecasting future claims, leading to poor financial planning. This is why some of them have been placed under statutory management. This paper compared the two time series, the SARIMA and Holt-Winters multiplicative models, in the context of forecasting Kenya's motor insurance claims. The goal of the study is to find out the most accurate model to forecast seasonal claims, thereby enabling insurance firms to avoid insolvency and regulatory penalties. Secondary data used in the analysis was sourced from the Insurance Regulatory Authority (IRA). The time series plot showed seasonality in the data, justifying the use of the two seasonal models. The SARIMA (1, 1,0)(0,1,0)[4] model and the Holt-Winters multiplicative model with parameters α = 0.70, β = 0.10, and γ = 0.01 were selected as optimal models for forecasting. Upon fitting the models with the data, graphical results showed that both aligned closely with the actual claims, effectively capturing the seasonal and trend components present in the data. However, to supplement the visual analysis, further evaluation using RMSE, MAE, and MAPE was conducted. The results revealed that the Holt-Winters multiplicative model achieved lower values in all three metrics, indicating superior predictive performance. Motor insurance can adopt this model to anticipate future claims. However, since the SARIMA model still exhibited strong performance, it can be considered as its suitable alternative.
Keywords: SARIMA, Holt-Winters, forecasting, insurance claims