On periodic ergodicity of a general periodic mixed Poisson autoregression

Aknouche, Abdelhakim; Bentarzi, Wissam; Demouche, Nacer

doi:10.1016/j.spl.2017.10.014

Cited by 12 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To make the bivariate INAR-type models more flexible with respect to real-data applications in some cases, it may be interesting to include explanatory covariates or periodicity in the model to account for dependence through thinning operations on several factors, which will be considered in another project: see Aknouche et al [28] and Chen and Khamthong [29].…”

Section: Discussionmentioning

confidence: 99%

A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors

Chen

Zhu

Liu

2022

Stats

View full text Add to dashboard Cite

Recently, there has been a growing interest in integer-valued time series models, especially in multivariate models. Motivated by the diversity of the infinite-patch metapopulation models, we propose an extension to the popular bivariate INAR(1) model, whose innovation vector is assumed to be time-dependent in the sense that the mean of the innovation vector is linearly increased by the previous population size. We discuss the stationarity and ergodicity of the observed process and its subprocesses. We consider the conditional maximum likelihood estimate of the parameters of interest, and establish their large-sample properties. The finite sample performance of the estimator is assessed via simulations. Applications on crime data illustrate the model.

show abstract

Section: Discussionmentioning

confidence: 99%

A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors

Chen

Zhu

Liu

2022

Stats

View full text Add to dashboard Cite

show abstract

“…For more details on the Gaussian model we refer the reader to Franses and Paap (2004;Chapter 5). The univariate Poisson version of our model is discussed in Bentarzi and Bentarzi (2017); this has been extended to Poisson mixture distributions in a recent report by Aknouche et al (2017), but without addressing unconditional moments. Further related work can be found in the area of integer-valued autoregression.…”

Section: The Multivariate Periodic Autoregressive Modelmentioning

confidence: 99%

Periodically stationary multivariate autoregressive models

Bracher¹,

Held²

2017

Preprint

View full text Add to dashboard Cite

A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of the model class is an established framework for modelling multivariate time series of counts from routine surveillance of infectious diseases. We extend this model class to allow for distributed lags and apply it to a dataset on norovirus gastroenteritis in two German states. The availability of unconditional moments and auto/cross-correlations enhances model assessment and interpretation.

show abstract

“…Additional work on periodic count series is contained in (Moriña et al, 2011; Monteiro et al, 2015; Bentarzi and Bentarzi, 2017; Aknouche et al, 2018; Santos et al, 2021), and Ouzzani and Bentarzi (2019). Most of these references take one of the above approaches.…”

Section: Introductionmentioning

confidence: 99%

Seasonal count time series

Kong

Lund

2022

Journal Time Series Analysis

View full text Add to dashboard Cite

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This article uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model constructed here permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference are explored. The article first develops the modeling methods, which entail a discrete transformation of a Gaussian process having seasonal dynamics. Properties of this model class are then established and particle filtering likelihood methods of parameter estimation are developed. A simulation study demonstrating the efficacy of the methods is presented and an application to the number of rainy days in successive weeks in Seattle, Washington is given.

show abstract

On periodic ergodicity of a general periodic mixed Poisson autoregression

Cited by 12 publications

References 19 publications

A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors

A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors

Periodically stationary multivariate autoregressive models

Seasonal count time series

Contact Info

Product

Resources

About