Testing for parameter change in general integer-valued time series

TL;DR

This paper introduces a statistical test for detecting parameter changes in integer-valued time series modeled with exponential family distributions, demonstrating its effectiveness through simulations and real data.

Contribution

It proposes a novel change-point test based on maximum likelihood estimation for discrete time series with exponential family distributions, with proven asymptotic properties.

Findings

Test statistic converges to a known distribution under null hypothesis.

Test statistic diverges under the alternative, ensuring power.

Simulation and real data show the test's practical applicability.

Abstract

We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the parameter of the model. Under the null hypothesis (of no change), the test statistics converges to a well known distribution, allowing for the calculation of the critical values of the test. The test statistic diverges to infinity under the alternative, that is, the test asymptotically has power one. Some simulation results and real data applications are reported to show the applicability of the test procedure.