Estimation in an Integer-Valued Autoregressive Process with Negative Binomial Marginals (NBINAR(1))

The authors consider a stationary integer-valued autoregressive process of the first order with negative binomial marginals (NBINAR(1)). A set of estimators are considered and their asymptotic distributions are derived. Some numerical results of the estimates are presented. Also, the authors discuss a possible application of the process.

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

[2]  E. McKenzie,et al.  Autoregressive moving-average processes with negative-binomial and geometric marginal distributions , 1986, Advances in Applied Probability.

[3]  Harry Joe,et al.  Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning , 2006 .

[4]  Emad-Eldin A. A. Aly,et al.  Stationary solutions for integer-valued autoregressive processes , 2005, Int. J. Math. Math. Sci..

[5]  Dag Tjøstheim,et al.  Consistent Estimates for the Near(2) and Nlar(2) Time Series Models , 1988 .

[6]  Emad-Eldin A. A. Aly,et al.  Explicit stationary distributions for some galton-watson processes with immigration , 1994 .

[7]  H. Bakouch,et al.  Zero truncated Poisson integer-valued AR(1) model , 2010 .

[8]  Peter A. W. Lewis,et al.  Discrete time series generated by mixtures III: Autoregressive processes (DAR(p)) , 1978 .

[9]  Hassan S. Bakouch,et al.  A new geometric first-order integer-valued autoregressive (NGINAR(1)) process , 2009 .

[10]  Peter A. W. Lewis,et al.  Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties , 1978 .

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

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

[13]  A. Harvey Time series models , 1983 .

[14]  Alain Latour,et al.  Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process , 1998 .

[15]  Harry Joe,et al.  Negative binomial time series models based on expectation thinning operators , 2010 .

[16]  Somnath Datta,et al.  Inference for pth‐order random coefficient integer‐valued autoregressive processes , 2006 .

[17]  Somnath Datta,et al.  First-order random coefficient integer-valued autoregressive processes , 2007 .

[18]  Isabel Silva,et al.  Asymptotic distribution of the Yule–Walker estimator for INAR(p) processes , 2006 .

[19]  Harry Joe,et al.  A New Type of Discrete Self-Decomposability and Its Application to Continuous-Time Markov Processes for Modeling Count Data Time Series , 2003 .

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

[21]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[22]  Mohamed Alosh,et al.  First order autoregressive time series with negative binomial and geometric marginals , 1992 .

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

[24]  Christian H. Weiß,et al.  Thinning operations for modeling time series of counts—a survey , 2008 .

[25]  Peter A. W. Lewis,et al.  Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties , 1978 .

[26]  David R. Cox,et al.  The Theory of Stochastic Processes , 1967, The Mathematical Gazette.

[27]  Gerd Ronning,et al.  Estimation in conditional first order autoregression with discrete support , 2005 .

[28]  文魚 長谷川 D.R. Cox and H.D. Miller: The Theory of Stochastic Processes, Methuen. London, 1965, 398頁, 24×16cm, 4,200円. , 1966 .

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

[30]  E. Mckenzie Innovation distributions for gamma and negative binomial autoregressions , 1987 .

[31]  A. Alzaid,et al.  Some autoregressive moving average processes with generalized Poisson marginal distributions , 1993 .

[32]  Mohamed Alosh,et al.  First‐Order Integer‐Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties , 1988 .