Zero truncated Poisson integer-valued AR(1) model

Bakouch, Hassan S.; Ristić, Miroslav M.

doi:10.1007/s00184-009-0252-5

Cited by 64 publications

(38 citation statements)

References 15 publications

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“…In order to study the properties of the WE, we consider the RCINAR(1) process which was proposed by Bakouch and Ristić (2010), the definition is as follows:…”

Section: Simulation Studymentioning

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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“…In order to study the properties of the WE, we consider the RCINAR(1) process which was proposed by Bakouch and Ristić (2010), the definition is as follows:…”

Section: Simulation Studymentioning

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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“…The probability generating function is given by (6) By assigning the Poisson random variable as the innovation process, we obtain the probability generating function as…”

Section: Model Constructionmentioning

confidence: 99%

“…Brannas [4] illustrated the time series counts model with four short, annual industry series in the Swedish paper and pulp industry. Ristic et al [5] and Bakouch and Ristic [6] considered crime data, especially sex offence counts data series. Quudus [7] studied monthly car casualties within the congestion zone.…”

Section: Introductionmentioning

confidence: 99%

A new model for time series of counts

Khoo¹,

Ong²

2014

AIP Conference Proceedings

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Time series modelling is an active research area in the past few decades with much attention focused in the continuous setting. However, time series data in terms of correlated counts occur in many situations. Thus modelling of time series of count data has attracted the attention many researchers recently. A new univariate non-negative stationary time series model of count data is introduced and is referred to as the mixture of Pegram and thinning on first order integer-valued autoregressive (MPT(1)) process. It is constructed from the combination of the popular thinning and Pegram's operators. The motivation for introducing the model and important statistical properties are discussed, such as autocorrelation, regression and joint distribution. Some simulation results are presented to show the performance of the model. Finally, the advantage of this new model is illustrated with application to a real data set.

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“…Many models that have been suggested are based on the Steutel and van Harn (1979) operator. The integer-valued autoregressive (INAR) models have been discussed extensively by Al-Osh and Alzaid (1987), Latour (1997Latour ( , 1998, and Du and Li (1991). Many new results on integer-valued times series have been obtained in recent years.…”

Section: Introductionmentioning

confidence: 99%