On Estimation of the Bivariate Poisson INAR Process

In a recent article, Pedeli and Karlis (2010) examined the extension of the classical Integer–valued Autoregressive (INAR) model to the bivariate case. In the present article, we examine estimation methods for the case of bivariate Poisson innovations. This is a simple extension of the classical INAR model allowing for two discrete valued time series to be correlated. Properties of different estimators are given. We also compare their properties via a small simulation experiment. Extensions to incorporate covariate information is discussed. A real data application is also provided.

[1]  Haris Papageorgiou,et al.  Multivariate Discrete Distributions , 2014 .

[2]  Dimitris Karlis,et al.  A bivariate INAR(1) process with application , 2011 .

[3]  Anirban DasGupta.  Multivariate Discrete Distributions , 2011 .

[4]  D. Karlis,et al.  BIVARIATE INAR ( 1 ) MODELS , 2009 .

[5]  D. Karlis,et al.  INAR(1) modeling of overdispersed count series with an environmental application , 2008 .

[6]  Geert Wets,et al.  Studying the effect of weather conditions on daily crash counts using a discrete time-series model. , 2008, Accident; analysis and prevention.

[7]  A. Alzaid,et al.  First-Order Integer-Valued Autoregressive Process : Distributional and Regression Properties , 2008 .

[8]  P. Duchesne,et al.  Diagnostic checking of multivariate nonlinear time series models with martingale difference errors , 2007 .

[9]  Martin A. Tanner,et al.  Modelling nonlinear count time series with local mixtures of Poisson autoregressions , 2007, Comput. Stat. Data Anal..

[10]  Robert C. Jung,et al.  Binomial thinning models for integer time series , 2006 .

[11]  A. M. M. Shahiduzzaman Quoreshi,et al.  Bivariate Time Series Modeling of Financial Count Data , 2006 .

[12]  B. McCabe,et al.  Asymptotic properties of CLS estimators in the Poisson AR(1) model , 2005 .

[13]  D. Karlis,et al.  Analysis of sports data by using bivariate Poisson models , 2003 .

[14]  Andréas Heinen,et al.  Multivariate modelling of time series count data: an autoregressive conditional poisson model , 2003 .

[15]  Kurt Brännäs,et al.  EXPLANATORY VARIABLES IN THE AR(1) COUNT , 2003 .

[16]  Eddie McKenzie,et al.  Discrete variate time series , 2003 .

[17]  Kurt Brännäs,et al.  A Bivariate Integer Valued Allocation Model for Guest Nights in Hotels and Cottages , 2000 .

[18]  Charles E. Brown.  Multivariate Time Series Modeling , 1998 .

[19]  Alain Latour,et al.  The Multivariate Ginar(p) Process , 1997, Advances in Applied Probability.

[20]  J. Franke,et al.  Conditional maximum likelihood estimates for INAR(1) processes and their application to modelling epileptic seizure counts , 1993 .

[21]  Li Yuan,et al.  THE INTEGER‐VALUED AUTOREGRESSIVE (INAR(p)) MODEL , 1991 .

[22]  Mohamed Alosh,et al.  An integer-valued pth-order autoregressive structure (INAR(p)) process , 1990, Journal of Applied Probability.

[23]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[24]  Mohamed Alosh,et al.  FIRST‐ORDER INTEGER‐VALUED AUTOREGRESSIVE (INAR(1)) PROCESS , 1987 .

[25]  Ed. McKenzie,et al.  SOME SIMPLE MODELS FOR DISCRETE VARIATE TIME SERIES , 1985 .

[26]  Fw Fred Steutel,et al.  Discrete analogues of self-decomposability and stability , 1979 .