Tests for Time Series of Counts Based on the Probability Generating Function

TL;DR

This paper introduces new testing procedures for count time series based on the empirical probability generating function, focusing on integer and Poisson autoregression models, with theoretical analysis, simulations, and real-data applications.

Contribution

It develops novel test statistics using the empirical probability generating function for count time series, with detailed asymptotic properties and practical evaluation.

Findings

Test statistics effectively distinguish models under null and alternative hypotheses.

Simulation studies show good power of the proposed tests.

Real-data examples demonstrate practical applicability.

Abstract

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.