Tests for Changes in Count Time Series Models With Exogenous Covariates

ABSTRACT We deal with a parametric change in models for count time series with exogenous covariates specified via the conditional distribution, i.e., with integer generalized autoregressive conditional heteroscedastic models with covariates (INGARCH‐X). CUSUM‐type methods for the change point detection are proposed, and their asymptotic distributions are derived. The finite‐sample behavior of the proposed tests is illustrated through a Monte Carlo simulation study and on a real‐time series of daily traffic accident counts.