Research Article Open Access

Poisson Quasi-Maximum Likelihood Estimator-based CUSUM Test for Integer-Valued Time Series

Sangyeol Lee1
  • 1 Seoul National University, Korea

Abstract

This study considers the parameter change test for integer-valued time series models based on the Poisson quasi-maximum likelihood estimates. As a change point test, we consider the score vector-based CUSUM test and show that its limiting null distribution takes the form of a function of Brownian bridges. Moreover, the residual-based CUSUM tests are considered as alternatives. For evaluation, we conduct a Monte Carlo simulation study with Poisson, zero-inflated Poisson, negative binomial and Conway-Maxwell integer-valued generalized autoregressive conditional heteroscedastic models andPoisson integer-valued autoregressive models, and compare the performance of the proposed CUSUM tests. Our findings confirm that the proposed test is a functional tool for detecting a change point when the underlying distribution is unspecified.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 250-258

DOI: https://doi.org/10.3844/jmssp.2019.250.258

Submitted On: 21 June 2019 Published On: 1 October 2019

How to Cite: Lee, S. (2019). Poisson Quasi-Maximum Likelihood Estimator-based CUSUM Test for Integer-Valued Time Series. Journal of Mathematics and Statistics, 15(1), 250-258. https://doi.org/10.3844/jmssp.2019.250.258

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Keywords

  • Time Series of Counts
  • INGARCH Model
  • INAR Model
  • Poisson QMLE
  • CUSUM Test