A bivariate INAR(1) process with application

Pedeli, Xanthi; Karlis, Dimitris

doi:10.1177/1471082x1001100403

Cited by 126 publications

(103 citation statements)

References 19 publications

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“…Moreover, in accordance to the BINAR(1) process, dependence between any two series that comprise the MINAR(1) process is introduced by allowing for dependence between the respective innovation terms. Thus, if , it can be shown that Similarities with the corresponding properties of the BINAR(1) model (Pedeli and Karlis, 2011a) are apparent.…”

Section: The Multivariate Inar(1) Processmentioning

confidence: 86%

“…This study focus on the definition and study of appropriate models for multivariate count series. The proposed MINAR(1) model is a generalization of the BINAR(1) model (Pedeli and Karlis, 2011a) to the multi–dimensional space. Thus, it can be regarded as a useful tool for modelling more than two time series of correlated count data simultaneously.…”

Section: Discussionmentioning

confidence: 99%

“…Some extensions to the multivariate case have been proposed by Franke and Rao (1995), Latour (1997), McKenzie (1988), Quoeshi (2006), Heinen and Rengifo (2007) and Pedeli and Karlis (2011a). In this study we aim to extend the BINAR(1) model proposed in Pedeli and Karlis (2011a) to the multi‐dimensional space. Such a generalization is not straightforward since many computational issues arise especially for the estimation of the parameters.…”

Section: Introductionmentioning

confidence: 99%

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On composite likelihood estimation of a multivariate INAR(1) model

Pedeli

Karlis

2012

Journal Time Series Analysis

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In several circumstances the collected data are counts observed in different time points, while the counts at each time point are correlated. Current models are able to account for serial correlation but usually fail to account for cross‐correlation. Motivated by the lack of appropriate tools for handling such type of data, we define a multivariate integer‐valued autoregressive process of order 1 (MINAR(1)) and examine its basic statistical properties. Apart from the general specification of the MINAR(1) process, we also study two specific parametric cases that arise under the assumptions of a multivariate Poisson and a multivariate negative binomial distribution for the innovations of the process. To overcome the computational difficulties of the maximum likelihood approach we suggest the method of composite likelihood. The performance of the two methods of estimation, that is, maximum likelihood and composite likelihood, is compared through a small simulation experiment. Extensions of the time‐invariant model to a regression model are also discussed. The proposed model is applied to a trivariate data series related to daily traffic accidents in three areas in the Netherlands.

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Section: The Multivariate Inar(1) Processmentioning

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On composite likelihood estimation of a multivariate INAR(1) model

Pedeli

Karlis

2012

Journal Time Series Analysis

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“…Since it is usually very difficult to obtain the likelihood of higher-order INAR process, then WE procedure can be a good choice for the parameter estimation. Furthermore, the bivariate INAR process has been studied in the integer-valued time series literature (Pedeli and Karlis, 2011;Ristić, et al, 2012), then our proposed estimation and test idea can also be applied to these bivariate integer-valued time series processes.…”

Section: Discussionmentioning

confidence: 99%

Inference for Random Coefficient INAR(1) Process Based on Frequency Domain Analysis

Zhang

Wang

2014

Communications in Statistics - Simulation and Computation

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In this article, we present the explicit expressions for the higher-order moments and cumulants of the first-order random coefficient integer-valued autoregressive (RCINAR(1)) process. The spectral and bispectral density functions are also obtained, which can characterize the RCINAR(1) process in the frequency domain. We use a frequency domain approach which is named Whittle criterion to estimate the parameters of the process. We propose a test statistic which is based on the frequency domain approach for the hypothesis test, H 0 : α = 0 ←→ H 1 : 0 < α < 1, where α is the mean of the random coefficient in the process. The asymptotic distribution of the test statistic is obtained. We compare the proposed test statistic with other statistics that can test serial dependence in time series of count via a typically numerical simulation, which indicates that our proposed test statistic has a good power.

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“…This family is a generalization of the BINAR model of Pedeli and Karlis (2011) [15]. Likelihood-based estimators for model parameters were derived and their asymptotic properties obtained and prediction was also addressed.…”

Section: Discussionmentioning

confidence: 99%

The Macrodynamics of Employment Under Uncertainty

Mota

Vasconcelos

2015

CIM Series in Mathematical Sciences

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The CIM Series in Mathematical Sciences is published on behalf of and in collaboration with the Centro Internacional de Matemática (CIM) in Coimbra, Portugal. Proceedings, lecture course material from summer schools and research monographs will be included in the new series. 37-02, 37-06, 91-01, 91-02 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) mpaulo@fep.up.pt ForewordI was very honored to be invited by Professor Alberto Adrego Pinto to the lecture at the Advanced School Planet Earth, Dynamics, Games and Science II (DGS II) from August 28 to August 30, 2013, and to speak at the associated international conference from September 2 to September 4, 2013. I have known Alberto since I was a graduate student at the CUNY Graduate Center in the 1980s. After both of us completed our Ph.D. degrees, we worked on a similar subject: smooth rigidity for one-dimensional dynamical systems and its generalization to Anosov dynamical systems of the two-torus, for many years. I was impressed by his work with his collaborators, using techniques and methods in smooth dynamical systems to develop many excellent results on smooth rigidity. Meanwhile, my collaborators and I tried to develop smooth rigidity into symmetric rigidity by applying techniques and methods in quasiconformal mappings theory and Teichmüller theory, and to build up a new Teichmüller theory for dynamical systems. So I knew that attending the DGS II would be stimulating and rewarding. Also, I knew that Alberto is an outstanding organizer and has the talent to lead a successful advanced school and conference, and indeed, his organizational skills and talents were proven again. I had a wonderful time in Lisbon, Portugal, and enjoyed many fruitful discussions with Alberto and his ...

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A bivariate INAR(1) process with application

Cited by 126 publications

References 19 publications

On composite likelihood estimation of a multivariate INAR(1) model

On composite likelihood estimation of a multivariate INAR(1) model

Inference for Random Coefficient INAR(1) Process Based on Frequency Domain Analysis

The Macrodynamics of Employment Under Uncertainty

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