Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts

Livsey, James; Lund, Robert; Kechagias, Stefanos; Pipiras, Vladas

doi:10.1214/17-aoas1098

Cited by 38 publications

(43 citation statements)

References 57 publications

(49 reference statements)

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“…Modeling and inference of multivariate count time series is an important research topic; see [45] for a medical application, [47] for a financial application and more recently [49] for a marketing application and [39] for an environmental study. The interested reader is referred to the review paper by [33], for further details.…”

Section: Introductionmentioning

confidence: 99%

Multivariate count autoregression

Fokianos¹,

Støve²,

Tjøstheim³

et al. 2020

Bernoulli

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We are studying linear and log-linear models for multivariate count time series data with Poisson marginals. For studying the properties of such processes we develop a novel conceptual framework which is based on copulas. Earlier contributions impose the copula on the joint distribution of the vector of counts by employing a continuous extension methodology. Instead we introduce a copula function on a vector of associated continuous random variables. This construction avoids conceptual difficulties related to the joint distribution of counts yet it keeps the properties of the Poisson process marginally. Furthermore, this construction can be employed for modeling multivariate count time series with other marginal count distributions. We employ Markov chain theory and the notion of weak dependence to study ergodicity and stationarity of the models we consider. Suitable estimating equations are suggested for estimating unknown model parameters. The large sample properties of the resulting estimators are studied in detail. The work concludes with some simulations and a real data example.

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Section: Introductionmentioning

confidence: 99%

Multivariate count autoregression

Fokianos¹,

Støve²,

Tjøstheim³

et al. 2020

Bernoulli

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“…Pedeli and Karlis () introduce a bivariate version of INAR(1), called BINAR(1):

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

but its contemporaneous dependence structure is quite restrictive, since the thinning operators α i , j ∘, i , j = 1,2 are required to be independent from each other given X t . Heinen and Rengifo (), Doukhan et al (), Livsey et al (), Cui and Zhu () propose non‐thinning‐based processes. None of them allow for tractable multi‐step‐ahead nonlinear forecasting formulae beyond the point predictions based on conditional expectation…”

Section: Introductionmentioning

confidence: 99%

“…In the model of Heinen and Rengifo (), Doukhan et al (), only the conditional expectation is known; in the model of Cui and Zhu (), forecasting formulae are only known at horizon 1; the model of Livsey et al () is parameter‐driven. While it is more flexible than its competitors, its downside is that neither linear, nor nonlinear forecasting formula is available at any horizon.…”

mentioning

confidence: 99%

“…The extension to models with negative conditional correlation is out of the scope of the article. Other bivariate, unbounded count process model allowing for negative correlation include Doukhan et al (), Cui and Zhu () and Livsey et al (). However the prediction formulae are somewhat cumbersome in these models (see the discussions in the Introduction).…”

mentioning

confidence: 99%

“…This parametrization relies on the interpretation of the NB distribution as a Poisson distribution with gamma stochastic intensity, with the degree of freedom of the gamma distribution, and the scale of 2 See also Latour (1998). 3 In the model of Heinen and Rengifo (2007), Doukhan et al (2017), only the conditional expectation is known; in the model of Cui and Zhu (2018), forecasting formulae are only known at horizon 1; the model of Livsey et al (2018) is parameter-driven. While it is more flexible than its competitors, its downside is that neither linear, nor nonlinear forecasting formula is available at any horizon.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Negative Binomial Autoregressive Process with Stochastic Intensity

Gouriéroux

2018

Journal Time Series Analysis

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We introduce negative binomial‐60 autoregressive (NBAR) processes with stochastic intensity for (univariate and bivariate) count processes. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial conditional and marginal distributions. The process is then extended to the bivariate case with a Wishart autoregressive matrix intensity process. The NBAR processes are compound autoregressive, which allows for simple stationarity condition and quasi‐closed form nonlinear forecasting formulae at any horizon, as well as a computationally tractable generalized method of moment estimator. The model is applied to a pairwise analysis of weekly occurrence counts of a contagious disease between the greater Paris region and other French regions.

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A bivariate autoregressive Poisson model and its application to asthma‐related emergency room visits

Al-Wahsh

Hussein

2020

Statistics in Medicine

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There are no gold standard methods that perform well in every situation when it comes to the analysis of multiple time series of counts. In this paper, we consider a positively correlated bivariate time series of counts and propose a parameter‐driven Poisson regression model for its analysis. In our proposed model, we employ a latent autoregressive process, AR(p) to accommodate the temporal correlations in the two series. We compute the familiar maximum likelihood estimators of the model parameters and their standard errors via a Bayesian data cloning approach. We apply the model to the analysis of a bivariate time series arising from asthma‐related visits to emergency rooms across the Canadian province of Ontario.

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Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts

Cited by 38 publications

References 57 publications

Multivariate count autoregression

Multivariate count autoregression

Negative Binomial Autoregressive Process with Stochastic Intensity

A bivariate autoregressive Poisson model and its application to asthma‐related emergency room visits

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