First-order random coefficient integer-valued autoregressive processes

A first-order random coefficient integer-valued autoregressive (RCINAR(1)) model is introduced. Ergodicity of the process is established. Moments and autocovariance functions are obtained. Conditional least squares and quasi-likelihood estimators of the model parameters are derived and their asymptotic properties are established. The performance of these estimators is compared with the maximum likelihood estimator via simulation.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  Jim Freeman,et al.  Stochastic Processes (Second Edition) , 1996 .

[3]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[4]  A. Schick.  √n-CONSISTENT ESTIMATION IN A RANDOM COEFFICIENT AUTOREGRESSIVE MODEL , 1996 .

[5]  Ed McKenzie.  The distributional structure of finite moving-average processes , 1988 .

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

[7]  P. Hall,et al.  Martingale Limit Theory and its Application. , 1984 .

[8]  E. McKenzie,et al.  Some ARMA models for dependent sequences of poisson counts , 1988, Advances in Applied Probability.

[9]  I. Basawa,et al.  Estimation for a class of generalized state-space time series models , 2002 .

[10]  Mohamed Alosh,et al.  Binomial autoregressive moving average models , 1991 .

[11]  Subir Ghosh.  Asymptotics, Nonparametrics, and Time Series , 2000 .

[12]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

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

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

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

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

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

[18]  Patrick Billingsley,et al.  Statistical inference for Markov processes , 1961 .

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

[20]  Paul I. Nelson,et al.  On Conditional Least Squares Estimation for Stochastic Processes , 1978 .