A Parametric Study for the First-Order Signed Integer-Valued Autoregressive Process

Abstract

In recent years, many attempts have been made to find accurate models for integer-valued times series. The SINAR (for Signed INteger-valued AutoRegressive) process is one of the most interesting. Indeed, the SINAR model allows negative values both for the series and its autocorrelation function. In this paper, we focus on the simplest SINAR(1) model under some parametric assumptions. Explicitly, we obtain the form the probability mass function of the innovation when the marginal distribution of the process is known. Moreover, we give an implicit form of the stationary distribution for a known innovation. Simulation experiments as well as analysis of real data sets are carried out to attest the models performance. Keywords Integer-valued time series • INAR models • SINAR models • Rademacher(p) − N class • Skellam distribution.

A metamodel-based Monte Carlo simulation approach for responsive production planning of manufacturing systems

“…Model 3: N-SINAR N-SINAR is the non-stationary extension of the signed integer-valued autoregressive (SINAR) model introduced in [67] and [84]. The general model (4) takes the form…”

“….} are independent and identically distributed random variables with the probability distribution given as below [84]…”

Thinning-based models in the analysis of integer-valued time series: a review

“…In particular, they introduced the signed INAR(1) (SINAR(1)) process by the recursion X t = F * X t−1 + Z t , with (Z t ) taking values on Z Z and F charging zero with positive probability and |E[ 1 ]| < 1. Chesneau and Kachour (2012) analyzed the particular SINAR(1) model in which the distribution F is defined as follows: P( 1 = −1) = (1 − ) 2 , P( 1 = 0) = 2 (1 − ) and P( 1 = 1) = 2 , where ∈ (0; 1). Note that 1 d = 1 − 1 with 1 ∼ Bi(2, ) and .…”

A parametric time series model with covariates for integers in Z

“…Kim and Park (2008) used conditional least square estimation to estimate the parameters. Moment estimation of this model is also done in Chesneau and Kachour (2012). Later in this article we will apply conditional maximum likelihood estimation and show its superior precision by means of a Monte Carlo study.…”