INARMA Modeling of Count Time Series

Weiß, Christian; Feld, Martin; Khan, Naushad Mamode; Sunecher, Yuvraj

doi:10.3390/stats2020022

Cited by 11 publications

(6 citation statements)

References 23 publications

(53 reference statements)

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“…Furthermore, a new INMA(1) model based on the negative binomial thinning op-eration was proposed in [36]. Additionally, likelihood-based inference was efficiently implemented by [42,43] and diagnostic tests regarding the marginal distribution and the autocorrelation structure of INMA(1) models were proposed in [1].…”

Section: Introductionmentioning

confidence: 99%

Inference for bivariate integer-valued moving average models based on binomial thinning operation

Silva

Torres

2020

Journal of Applied Statistics

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Time series of (small) counts are common in practice and appear in a wide variety of fields. In the last three decades, several models that explicitly account for the discreteness of the data have been proposed in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so detailed. This work considers Bivariate INteger-valued Moving Average, BINMA, models based on the binomial thinning operation. The main probabilistic and statistical properties of BINMA models are studied. Two parametric cases are analysed, one with the cross-correlation generated through a Bivariate Poisson innovation process and another with a Bivariate Negative Binomial innovation process. Moreover, parameter estimation is carried out by the Generalized Method of Moments. The performance of the model is illustrated with synthetic data as well as with real datasets. KEYWORDS Bivariate discrete distributions, bivariate models, generalized method of moments, moving average, time series of counts *

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Section: Introductionmentioning

confidence: 99%

Inference for bivariate integer-valued moving average models based on binomial thinning operation

Silva

Torres

2020

Journal of Applied Statistics

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“…However, little is known about such an ability in nonnested and nonlinear time series models for counts (Jung et al 2016). Two recent studies, Weiß and Feld (2020) and Weiß et al (2019), partially follow the direction outlined by Jung et al (2016), but concentrate on the case of unbounded counts. Diop and Kenge (2020) propose a penalized criterion relying on a Poisson quasi-likelihood approach for some INGARCH-type processes of counts, and they prove its consistency under certain regularity conditions.…”

Section: Using Information Criteria For Model Selectionmentioning

confidence: 99%

Models for autoregressive processes of bounded counts: How different are they?

2020

Self Cite

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We focus on purely autoregressive (AR)-type models defined on the bounded range {0, 1, . . . , n} with a fixed upper limit n ∈ N. These include the binomial AR model, binomial AR conditional heteroscedasticity (ARCH) model, binomial-variation AR model with their linear conditional mean, nonlinear max-binomial AR model, and binomial logit-ARCH model. We consider the key problem of identifying which of these AR-type models is the true data-generating process. Despite the volume of the literature on model selection, little is known about this procedure in the context of nonnested and nonlinear time series models for counts. We consider the most popular approaches used for model identification, Akaike's information criterion and the Bayesian information criterion, and compare them using extensive Monte Carlo simulations. Furthermore, we investigate the properties of the fitted models (both the correct and wrong models) obtained using maximum likelihood estimation. A real-data example demonstrates our findings.

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“…The thinning operator "•" is defined for a constant α ∈ [0, 1] and a non-negative, integer random variable X as α • X = ∑ X i=1 Z i for X > 0, where Z i iid ∼ Bern(α) and zero if X = 0. In line with the notation of Weiß et al [5], a non-negative and integer-valued process {Y t } follows INARMA(p, q) process if…”

Section: Inarma Frameworkmentioning

confidence: 99%

“…Further, it also does not incorporate zero inflation, a model property frequently used in count data analysis. The thinning-based INARMA model can be formulated as Hidden Markov model, as for example discussed by Weiß et al [5], so that the R packages Hidden-Markov (Harte [6]), and HMM (Himmelmann [7]) can be used to estimate its parameters. Both packages have been developed for general HMMs, thus the CountTimeSeries package offers the advantage of a more convenient usage and similar notation for both frameworks making it easy to switch between frameworks or compare results between those.…”

Section: Introductionmentioning

confidence: 99%

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Stapper

2021

Entropy

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A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

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INARMA Modeling of Count Time Series

Cited by 11 publications

References 23 publications

Inference for bivariate integer-valued moving average models based on binomial thinning operation

Inference for bivariate integer-valued moving average models based on binomial thinning operation

Models for autoregressive processes of bounded counts: How different are they?

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

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