Random Environment Integer-Valued Autoregressive Process with Discrete Laplace Marginal Distributions

Abstract

A new random environment integer-valued autoregressive process of order 1 with discrete Laplace marginal distributions and with r states (abbrev. RrDLINAR1(M, A)) is introduced. It is shown that this process is distributed as a difference of two independent generalized random environment integer-valued autoregressive processes, when their orders are equal to 1. Other distributional and correlation properties of the RrDLINAR1(M, A) process are discussed. Strongly consistent Yule-Walker estimates are defined. The method of moments is implemented for different cases of simulated samples. Finally, the proposed model is applied to real-life data and the obtained results show its effectiveness.

Keywords

• random environment
• INAR(1)
• RrDLINAR1(M;A)
• DLINAR(1)
• discrete Laplace distribution