Useful models for time series of counts or simply wrong ones?

Jung, Robert C.; Tremayne, A. R.

doi:10.1007/s10182-010-0139-9

Cited by 94 publications

(53 citation statements)

References 51 publications

(75 reference statements)

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“…[4] The latter is considered by Zeger and Qaqish, [5] Li, [6] Davis et al, [7] Fahrmeir and Tutz, [8] and Jung et al [9] Further, regression models with an intensity process are considered by Ferland et al [10] and Fokianos et al [11] Sequences of counts appear in many other application fields such as statistical quality control [12] and insurance. [13] See also Winkelmann, [14] who provides a survey of statistical and econometric techniques for count data on the basis of conditional distribution models, and Jung and Tremayne, [15] who provide an overview of some recent developments in the analysis of time series of counts.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Zhu [20] studied the stationarity and ergodicity of the GP-INGARCH process and demonstrated the consistency and asymptotic normality of the conditional maximum likelihood estimator (CMLE); see also Jung and Tremayne. [15] On the other hand, the zero-inflated Poisson distribution is considered suitable for data with excess zeros; see Lambert [21] and Gupta et al [22,23] Later, Zhu [24] studied zeroinflated INGARCH models and investigated their model properties. In this study, we combine the GP-INGARCH and zero-inflated INGARCH models into one model.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

Parameter change test for zero-inflated generalized Poisson autoregressive models

Lee

Chen

2015

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“…Applications of time series with discrete marginal distributions based on thinning operators have been found in the following areas: medical science (Latour 1995), compensation claims (Freeland and McCabe 2004;Zhu and Joe 2006) and academic research with regards to abstract review counts (Zhu and Joe 2010) as well as crime count data (Ristic et al 2009). Jung and Tremayne (2011) have compared and contrast a variety of time series models for counts using two very different data sets. Recently Barczy et al (2010Barczy et al ( , 2012 and Silva and Pereira (2012) discussed the additive outliers INAR(1) model.…”

Section: Introductionmentioning

confidence: 99%

Modeling time series of counts with a new class of INAR(1) model

2015

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This paper presents a new model for a stationary non-negative first order of integer-valued random variables based on the Pegram and thinning operators. Some fundamental and regression properties of the proposed model are discussed. Maximum likelihood estimation (MLE) by the EM algorithm is applied to estimate the parameters. Numerical studies to compare the proposed model with the thinning and Pegram models and the breakdown point of MLE for the proposed model have been conducted. Finally, a real life count data set has been used to illustrate its application. Comparison with existing models by AIC showed that the proposed model is much better and illustrates its potential usefulness in empirical modeling.

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“…The data are published by the United States (US) Centers for Disease Control and consist of 168 observations with some strongly deviating data points. This data set has been previously studied by many researchers, including Zeger (1988), Davis et al (2000) and Jung and Tremayne (2011). Recently, Kang and Lee (2014) performed the CUSUM test to detect change points in this data based on Poisson autoregressive models.…”

Section: Introductionmentioning

confidence: 99%

Robust CUSUM test for time series of counts and its application to analyzing the polio incidence data

Kang¹

2015

Journal of the Korean Data and Information Science Society

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In this paper, we analyze the polio incidence data based on the Poisson autoregressive models, focusing particularly on change-point detection. Since the data include some strongly deviating observations, we employ the robust cumulative sum (CUSUM) test proposed by Kang and Song (2015) to perform the test for parameter change. Contrary to the result of Kang and Lee (2014), our data analysis indicates that there is no significant change in the case of the CUSUM test with strong robustness and the same result is obtained after ridding the polio data of outliers. We additionally consider the comparison of the forecasting performance. All the results demonstrate that the robust CUSUM test performs adequately in the presence of seemingly outliers.Keywords: Minimum density power divergence estimator, Poisson autoregressive model, robust parameter change test, the polio incidence data.

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Useful models for time series of counts or simply wrong ones?

Abstract: Count time series, Parameter-driven, Observation-driven, Autocorrelation, Overdispersion, Diagnostics,

Cited by 94 publications

References 51 publications

Parameter change test for zero-inflated generalized Poisson autoregressive models

Parameter change test for zero-inflated generalized Poisson autoregressive models

Modeling time series of counts with a new class of INAR(1) model

Robust CUSUM test for time series of counts and its application to analyzing the polio incidence data

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