Abstract
This paper considers the problem of testing for parameter change in random coefficient integer-valued autoregressive models. To overcome some size distortions of the existing estimate-based cumulative sum (CUSUM) test, we suggest estimating function-based test and residual-based CUSUM test. More specifically, we employ the estimating function of the conditional least squares estimator. Under the regularity conditions and the null hypothesis, we derive their limiting distributions, respectively. Simulation results demonstrate the validity of the proposed tests. A real data analysis is performed on the polio incidence data.
Highlights
In recent years, time series of counts are widely observed in real-world applications, for instance, the monthly number of people with a certain disease, the number of transactions per minute of some stock, the number of accidents per a day and so on
Among the existing models for analyzing those data sets, autoregressive moving average (ARMA)-type models based on a thinning operator, referred to as integer-valued ARMA models, are still popular since ARMA-type models provide a convenient way to transfer the classical ARMA recursion to discrete-valued time series
We propose an estimating function (EF)-based test and residual-based cumulative sum (CUSUM) test
Summary
Time series of counts are widely observed in real-world applications, for instance, the monthly number of people with a certain disease, the number of transactions per minute of some stock, the number of accidents per a day and so on. Kang and Lee [5,9] constructed the estimate-based cumulative sum (CUSUM) tests for parameter change in random coefficient integer-valued autoregressive (RCINAR). Hudecová et al [12,13,14,15] studied methods for detecting structural changes in INAR and Poisson AR models incorporating the empirical probability generating function and Kang and Song [16] constructed the score test in Poisson AR models. Kang and Lee [9] developed the estimate-based CUSUM test in RCINAR models They constructed the test statistics based on the differences θk − θn to detect a change in parameter θ, where θk denotes the estimator based on { X1 , · · · , Xk }.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
