An integer‐valued time series model for multivariate surveillance

Pedeli, Xanthi; Karlis, Dimitris

doi:10.1002/sim.8453

Cited by 2 publications

(5 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As noted by Pedeli and Karlis (2020) each element α ij of A in () defines a binomial thinning operator α ij ∘ Y . For example, in the bivariate case we have

((), \begin{array}{c} Y_{1 t} \\ Y_{2 t} \end{array}) = ([], \begin{array}{c} α_{11} & α_{12} \\ α_{21} & α_{22} \end{array}) \circ ((), \begin{array}{c} Y_{1, t - 1} \\ Y_{2, t - 1} \end{array}) + ((), \begin{array}{c} ε_{1 t} \\ ε_{2 t} \end{array})

where the j th component of Y t is given by

Y_{jt} = \sum_{i = 1}^{2} α_{ij} \circ Y_{i, t - 1} + ε_{jt}

for j = 1, 2.…”

Section: Bayesian Models For Multivariate Poisson Time Seriesmentioning

confidence: 96%

“…As noted by Pedeli and Karlis (2020) each element α ij of A in (17) defines a binomial thinning operator α ij ∘ Y. For example, in the bivariate case we have…”

Section: Multivariate Inar Process Modelsmentioning

confidence: 99%

“…Elements of error vector ε t will have a joint distribution to reflect a dependence structure or they may be assumed to be independent. For example, Pedeli and Karlis (2020) assumed that ε jt 's are independent Poisson random variables with parameters λ j and showed that the conditional distribution of Y t given Y t À 1 can be obtained as the convolutions of sum of J binomials with Poissons. As shown by Pedeli and Karlis (2020), in this case, the joint distribution is the product of J generalized Poisson distributions.…”

Section: Multivariate Inar Process Modelsmentioning

confidence: 99%

“…A recent review by Karlis (2016) provides an overview of the multivariate models and discuss related statistical analysis via classical methods. For example, some of the recent observation driven models for multivariate counts include multivariate integer valued autoregressive (INAR) models of Pedeli and Karlis (2011) and Pedeli and Karlis (2020). Examples of parameter driven models include Ravishanker et al (2014) who considered a multivariate Poisson observation model with a hierarchical dynamic setup.…”

Section: Introduction and Overviewmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian modeling of multivariate time series of counts

Soyer

Zhang²

2021

WIREs Computational Stats

View full text Add to dashboard Cite

In this article, we present an overview of recent advances in Bayesian modeling and analysis of multivariate time series of counts. We discuss basic modeling strategies including integer valued autoregressive processes, multivariate Poisson time series and dynamic latent factor models. In so doing, we make a connection with univariate modeling frameworks such as dynamic generalized models, Poisson state space models with gamma evolution and present Bayesian approaches that extend these frameworks to multivariate setting. During our development, recent Bayesian approaches to the analysis of integer valued autoregressive processes and multivariate Poisson models are highlighted and concepts such as "decouple/recouple" and "common random environment" are presented. The role that these concepts play in Bayesian modeling and analysis of multivariate time series are discussed. Computational issues associated with Bayesian inference and forecasting from these models are also considered. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Time Series Models

show abstract

“…As noted by Pedeli and Karlis (2020) each element α ij of A in () defines a binomial thinning operator α ij ∘ Y . For example, in the bivariate case we have

((), \begin{array}{c} Y_{1 t} \\ Y_{2 t} \end{array}) = ([], \begin{array}{c} α_{11} & α_{12} \\ α_{21} & α_{22} \end{array}) \circ ((), \begin{array}{c} Y_{1, t - 1} \\ Y_{2, t - 1} \end{array}) + ((), \begin{array}{c} ε_{1 t} \\ ε_{2 t} \end{array})

where the j th component of Y t is given by

Y_{jt} = \sum_{i = 1}^{2} α_{ij} \circ Y_{i, t - 1} + ε_{jt}

for j = 1, 2.…”

Section: Bayesian Models For Multivariate Poisson Time Seriesmentioning

confidence: 96%

“…As noted by Pedeli and Karlis (2020) each element α ij of A in (17) defines a binomial thinning operator α ij ∘ Y. For example, in the bivariate case we have…”

Section: Multivariate Inar Process Modelsmentioning

confidence: 99%

Section: Multivariate Inar Process Modelsmentioning

confidence: 99%

Section: Introduction and Overviewmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian modeling of multivariate time series of counts

Soyer

Zhang²

2021

WIREs Computational Stats

View full text Add to dashboard Cite

show abstract

“…A detailed discussion about this is provided in Section 2.2. Applications of the MINAR model are described in the recent paper by [12].…”

Section: Multivariate Integer-valued Autoregressive Modelsmentioning

confidence: 99%

Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution

Bermúdez

Karlis

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.

show abstract

An integer‐valued time series model for multivariate surveillance

Cited by 2 publications

References 57 publications

Bayesian modeling of multivariate time series of counts

Bayesian modeling of multivariate time series of counts

Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution

Contact Info

Product

Resources

About