Novel goodness-of-fit tests for binomial count time series

Abstract

For testing the null hypothesis of a marginal binomial distribution of bounded count data, we derive novel and flexible goodness-of-fit (GoF) tests. We propose two general approaches to construct moment-based test statistics. The first one relies on properties of higher-order factorial moments, while the second one uses a so-called Stein identity being satisfied under the null. For a broad class of stationary time series processes of bounded counts with joint bivariate binomial distributions of lagged time series values, we derive the limiting distributions of the proposed GoF-test statistics. Among others, our setup covers the binomial autoregressive model, but includes also other binomial time series obtained, e. g. by superpositioning independent binary time series. The test performance under the null and under different alternatives is investigated in simulations. Two data examples are used to illustrate the application of the novel GoF-tests in practice.