Testing Constant Serial Dynamics in Two-Step Risk Inference for Longitudinal Actuarial Data

Abstract

Forecasting Value at Risk (VaR) in non-life insurance is done by a two-step inference procedure: logistic regression for the number of claims and quantile regression for the total loss. To apply this method to longitudinal actuarial data, it is necessary to specify serial dynamics, where a constant dynamic is the simplest structure. This article diagnoses the constant serial dynamics in applying a two-step inference to each year’s actuarial data. When we do not reject this null hypothesis, we may employ panel quantile regression to improve the VaR risk forecast. The proposed test uses a two-step inference to forecast risk, constructs a test statistic by these risk forecasts, and calculates the p-value by the random weighted bootstrap method. Two simulations are performed to empirically justify the finite-sample performances. The proposed test is also applied to four datasets, revealing varying serial dynamic behaviors across different datasets and different parts of the claim distributions.