First‐order integer valued AR processes with zero inflated poisson innovations

Jazi, Mansour Aghababaei; Jones, Geoff; Lai, C. D.

doi:10.1111/j.1467-9892.2012.00809.x

Cited by 122 publications

(101 citation statements)

References 23 publications

(21 reference statements)

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“…For example, a Poisson distribution is usually used to model counts and that type of data is common in JABA reports. Alternative analytic methods based on the Poisson distribution are under development (Jazi, Jones & Lai, 2012) and represent an alternative choice for future analysis of these types of data.…”

Section: Itsa Limitationsmentioning

confidence: 99%

Comparing Visual and Statistical Analysis in Single-Case Studies Using Published Studies

Harrington

Velicer

2015

Multivariate Behavioral Research

106

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Little is known about the extent to which interrupted time-series analysis (ITSA) can be applied to short, single-case study designs and whether those applications produce results consistent with visual analysis (VA). This paper examines the extent to which ITSA can be applied to single-case study designs and compares the results based on two methods: ITSA and VA, using papers published in the Journal of Applied Behavior Analysis in 2010. The study was made possible by the development of software called UnGraph® which facilitates the recovery of raw data from the graphs. ITSA was successfully applied to 94% of the examined graphs with the number of observations ranging from 8 to 136. Moderate to high lag 1 autocorrelations (> .50) were found for 46% of the data series. Effect sizes similar to group-level Cohen’s d were identified based on the tertile distribution. Effects ranging from 0.00 to 0.99 were classified as small, those ranging from 1.00 to 2.49 as medium, and large effect sizes were defined as 2.50 or greater. Comparison of the conclusions from VA and ITSA had a low level of agreement (Kappa = .14, accounting for the agreement expected by chance). The results demonstrate that ITSA can be broadly implemented in applied behavior analysis research. These two methods should be viewed as complimentary and used concurrently.

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Section: Itsa Limitationsmentioning

confidence: 99%

Comparing Visual and Statistical Analysis in Single-Case Studies Using Published Studies

Harrington

Velicer

2015

Multivariate Behavioral Research

106

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“…An approach for dealing with an excess of zeros was considered by Jazi et al (). They introduced an INAR(1) process with zero‐inflated Poisson innovations and showed that the marginal distribution of the process is also zero‐inflated.…”

Section: Introductionmentioning

confidence: 99%

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Barreto‐Souza

2015

Journal Time Series Analysis

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In this article, we propose a first‐order integer‐valued autoregressive [INAR(1)] process for dealing with count time series with deflation or inflation of zeros. The proposed process has zero‐modified geometric marginals and contains the geometric INAR(1) process as a particular case. The proposed model is also capable of capturing underdispersion and overdispersion, which sometimes are caused by deflation or inflation of zeros. We explore several statistical and mathematical properties of the process, discuss point estimation of the parameters and find the asymptotic distribution of the proposed estimators. We also propose a test based on our model for checking if the count time series considered is deflated or inflated of zeros. Two empirical illustrations are presented in order to show the potential for practice of our zero‐modified geometric INAR(1) process. This article contains a Supporting Information.

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“…The data were used by Jazi et al. () in the context of integer‐valued time series modelling with zero‐inflated Poisson innovation. The data series has a large proportion of zeros (40.47%), with all the observations lying between 0 and 6, except for two observations, which were 8 and 9.…”

Section: Discussionmentioning

confidence: 99%

“…As an illustration, we analyse practical data, namely skin lesion data given in Jazi et al. () to see the effectiveness of our proposed process over the PINAR(1) process.…”

Section: Introductionmentioning

confidence: 99%

Time Series of Zero‐Inflated Counts and their Coherent Forecasting

Maiti

Biswas

Das

2015

Journal of Forecasting

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Poisson integer-valued auto-regressive process of order 1 (PINAR(1)) due to Al-Osh and Alzaid (Journal of Time Series Analysis 1987; 8(3): 261-275) and McKenzie (Advances in Applied Probability 1988; 20(4): 822-835) has received a significant attention in modelling low-count time series during the last two decades because of its simplicity. But in many practical scenarios, the process appears to be inadequate, especially when data are overdispersed in nature. This overdispersion occurs mainly for three reasons: presence of some extreme values, large number of zeros, and presence of both extreme values with a large number of zeros. In this article, we develop a zero-inflated Poisson INAR(1) process as an alternative to the PINAR(1) process when the number of zeros in the data is larger than the expected number of zeros by the Poisson process. We investigate some important properties such as stationarity, ergodicity, autocorrelation structure, and conditional distribution, with a detailed study on h-step-ahead coherent forecasting. A comparative study among different methods of parameter estimation is carried out using some simulated data. One real dataset is analysed for practical illustration.

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First‐order integer valued AR processes with zero inflated poisson innovations

Cited by 122 publications

References 23 publications

Comparing Visual and Statistical Analysis in Single-Case Studies Using Published Studies

Comparing Visual and Statistical Analysis in Single-Case Studies Using Published Studies

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

Time Series of Zero‐Inflated Counts and their Coherent Forecasting

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