A robust approach for testing parameter change in Poisson autoregressive models

TL;DR

This paper introduces a robust statistical test for detecting parameter changes in Poisson autoregressive models, effectively handling outliers in time series data.

Contribution

It develops a new density power divergence-based test specifically designed for integer-valued time series with outliers, with proven robustness and validity.

Findings

The proposed test maintains accuracy in the presence of outliers.

Simulation results confirm the test's robustness and effectiveness.

The method extends existing change point detection techniques to more contaminated data.

Abstract

Parameter change test has been an important issue in time series analysis. The problem has also been actively explored in the field of integer-valued time series, but the testing in the presence of outliers has not yet been extensively investigated. This study considers the problem of testing for parameter change in Poisson autoregressive models particularly when observations are contaminated by outliers. To lessen the impact of outliers on testing procedure, we propose a test based on the density power divergence, which is introduced by Basu et al. (Biometrika, 1998), and derive its limiting null distribution. Monte Carlo simulation results demonstrate validity and strong robustness of the proposed test.