On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

Abstract

Two types of shifted geometric integer valued autoregressive models of order one (SGINAR 1 ) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR 1 models.

Zero‐Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

“…Other works that have recently appeared in the literature dealing with INAR processes are those of Barczy et al (), Nastić (), Nastić & Ristić (), Ristić et al (), Weiß (), Weiß & Kim (), Meintanis & Karlis (), Schweer & Weiß () and Bisaglia & Canale () just to name a few.…”

Higher Order Moments, Spectral and Bispectral Density Functions for INAR(1)

“…5 and Fig. 6 represent the estimate of the bispectrum and normalized bispectrum modulus with M=7 by Parzen window using (8), (10) and (9). Tables 1 Theoretical bispectral Table 2 show that the normalized bispectrum modulus of the NSINAR(1) model is more flat than the non-normalized one given in Table 1 .…”

“…Fig. 2 represent theoretical spectrum and the estimate of the spectral density using Parzen window with M=7 as in (7) and (9). Fig.…”

“…where {Y i } is a sequence of i.i.d random variables with geometric ( 1 1+α ) distribution independent of X t−1 , {X t } is a stationary process has shifted geometric ( 1 1+µ ) distribution and {η t } are i.i.d random variables independent of Y i and of X t−i , i ≥ 1. The pgf of X t and η t are given by respectively (see [9])…”

“…17 and Fig. 18 represent the estimate of the bispectrum and normalized bispectrum modulus with M=7 by Parzen window using (8), (10) and (9). From Fig.…”