Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

Jiwon Kang · Sangyeol Lee

56 citations0/0 files storedJournal of Time Series Analysis

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Advanced Statistical Process Monitoring Probability and Statistical Research Time Series Analysis and Forecasting

Abstract

Abstract. In this paper, we consider the problem of testing for a parameter change in a first‐order random coefficient integer‐valued autoregressive [RCINAR(1)] model. We employ the cumulative sum (CUSUM) test based on the conditional least‐squares and modified quasi‐likelihood estimators. It is shown that under regularity conditions, the CUSUM test has the same limiting distribution as the supremum of the squares of independent Brownian bridges. The CUSUM test is then applied to the analysis of the monthly polio counts data set.

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References

1997Limit theorems in change-point analysis 1955A Test for a Change in a Parameter Occurring at an Unknown Point 2011Parametric Statistical Change Point Analysis 2000Parametric Statistical Change Point Analysis 2003The Cusum Test for Parameter Change in Time Series Models

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2018CUSUM test for general nonlinear integer-valued GARCH models: comparison study 2016Asymptotic normality and parameter change test for bivariate Poisson INGARCH models 2016On first-order integer-valued autoregressive process with Katz family innovations 2015Inference and testing for structural change in general Poisson autoregressive models 2017Tests for Structural Changes in Time Series of Counts 2021Recent progress in parameter change test for integer-valued time series models 2013Change Detection in INAR(p) Processes Against Various Alternative Hypotheses 2021Exponential family QMLE-based CUSUM test for integer-valued time series

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