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

Kang, Jiwon; Lee, Sangyeol

doi:10.1111/j.1467-9892.2009.00608.x

Cited by 52 publications

(38 citation statements)

References 25 publications

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“…Among the existing change point tests, the cumulative sum (CUSUM) test has long been popular because it is easy to understand and implement in practice. The change point test for integer-valued time series has been studied by several authors; see Fokianos and Fried, [26,27] Hudecova, [28] and Fokianos et al [29] Further, Kang and Lee [30] proposed a CUSUM test for detecting change points in random coefficient integer-valued autoregressive models with Poisson innovations and used it to analyse polio data. Franke et al [31] investigated a CUSUM test based on estimated residuals from Poisson autoregressive models with intensity λ t = f (X t−1 ) for some real-valued function f. Doukhan and Kengne [32] proposed the Poisson autoregressive models with intensity λ t = f (X t−1 , X t−2 , .…”

Section: Introductionmentioning

confidence: 99%

Parameter change test for zero-inflated generalized Poisson autoregressive models

Lee

Chen

2015

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In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE-and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.

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Section: Introductionmentioning

confidence: 99%

Parameter change test for zero-inflated generalized Poisson autoregressive models

Lee

Chen

2015

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“…Zheng et al (2007) established the ergodicity of the process (1.1), and gave the conditional least-squares and quasi-likelihood estimators for the parameters of interest. Kang and Lee (2009) considered the problem of testing a parameter change in the RCINAR(1) process. Zhang et al (2011aZhang et al ( , 2011b considered the empirical likelihood inference for this kinds of process.…”

Section: Remark 11mentioning

confidence: 99%

Inference for Random Coefficient INAR(1) Process Based on Frequency Domain Analysis

Zhang

Wang

2014

Communications in Statistics - Simulation and Computation

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In this article, we present the explicit expressions for the higher-order moments and cumulants of the first-order random coefficient integer-valued autoregressive (RCINAR(1)) process. The spectral and bispectral density functions are also obtained, which can characterize the RCINAR(1) process in the frequency domain. We use a frequency domain approach which is named Whittle criterion to estimate the parameters of the process. We propose a test statistic which is based on the frequency domain approach for the hypothesis test, H 0 : α = 0 ←→ H 1 : 0 < α < 1, where α is the mean of the random coefficient in the process. The asymptotic distribution of the test statistic is obtained. We compare the proposed test statistic with other statistics that can test serial dependence in time series of count via a typically numerical simulation, which indicates that our proposed test statistic has a good power.

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“…This problem has drawn some attention in the recent past. Kang and Lee () proposed the cumulative sum procedure for detecting changes in a first‐order random coefficient integer‐valued autoregressive model. Franke et al () dealt with the residual cumulative sum procedures for parameter change in Poisson autoregressive models.…”

Section: Introductionmentioning

confidence: 99%

Testing Parameter Change in General Integer‐Valued Time Series

Diop

Kengne

2017

Journal Time Series Analysis

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We consider the structural change in a class of discrete valued time series, which the conditional distribution belongs to the one‐parameter exponential family. We propose a change point test based on the maximum likelihood estimator of the model's parameter. Under the null hypothesis (of no change), the test statistic converges to a well‐known distribution, allowing the calculation of the critical value of the test. The test statistic diverges to infinity under the alternative, meaning that the test has asymptotic power one. Some simulation results and real data applications are reported to show the effectiveness of the proposed procedure.

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

Cited by 52 publications

References 25 publications

Parameter change test for zero-inflated generalized Poisson autoregressive models

Parameter change test for zero-inflated generalized Poisson autoregressive models

Inference for Random Coefficient INAR(1) Process Based on Frequency Domain Analysis

Testing Parameter Change in General Integer‐Valued Time Series

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