GLARMA time series modeling of counts

Abstract

This thesis investigates the potential of using GLARMA (Generalised Linear Autoregressive Moving Average) models in insurance. Traditional time series analysis assumes a Gaussian distribution for the dependent variable, which may not be suitable for discrete variables like the number of accidents. GLARMA models provide an alternative by incorporating autoregressive or moving average models for variables that follow Poisson or negative binomial distributions, making them an appealing choice for insurance applications. The objective of this thesis is to explain the GLARMA modeling framework, apply it to predict the number of accidents in Finland and assess the limitations and benefits of this approach. The study employs the Glama package to implement the GLARMA model on car accident datasets. Through a comparative study with two other ARMAX models, it is found that the GLARMA model provides a comparatively better framework for forecasting car accidents in Finland. The forecasted data reveals that accident incidence typically peaks during the summer months (June to August) and decreases during the winter months (December to February). The observed pattern is primarily attributed to the increase in traffic volume. This study introduces the promising possibilities of utilizing the GLARMA model in insurance, particularly in scenarios where count data is prevalent.