On causality test for time series of counts based on poisson ingarch models with application to crime and temperature data

In this study, we consider the causality test for the integer-valued time series. Using the mean equation of Poisson INGARCH models, we construct a regression that includes exogenous variables. The test is then constructed based on the least squares estimator and is shown to follow a chi-square distribution under the null of no causal relationships. A simulation study and real data analysis using the crime and temperature data in Chicago are provided for illustration.