Checking Model Adequacy for Count Time Series by Using Pearson Residuals

Abstract

Abstract After having fitted a model to a given count time series, one has to check the adequacy of this model fit. The (standardized) Pearson residuals, being easy to compute and interpret, are a popular diagnostic approach for this purpose. But which types of model inadequacy might be uncovered by which statistics based on the Pearson residuals? In view of being able to apply such statistics in practice, it is also crucial to ask for the properties of these statistics under model adequacy. We look for answers to these questions by means of a comprehensive simulation study, which considers diverse types of count time series models and inadequacy scenarios. We illustrate our findings with two real-data examples about strikes in the U.S., and about corporate insolvencies in the districts of Rhineland–Palatinate. We conclude with a theoretical discussion of Pearson residuals.