A1334
Title: INAR processes based on convolution thinning operator with dependent innovations
Authors: Jean Peyhardi - University of Montpellier (France) [presenting]
Dimitris Karlis - RC Athens University of Economics and Business (Greece)
Abstract: Classical INAR models combine thinning operators with independent innovations, leading in some specific cases to explicit stationary distributions and tractable probabilistic properties. Building on convolution-closed families of discrete distributions introduced by Joe (1996), recent work has formalized convolution thinning operators and characterized stationary distributions via additive power-series families, enlarging the class of tractable INAR models. Extensions to positively dependent innovations replace the innovation distribution by inverse convolution distributions whose parameters depend on the previous count, while keeping the same thinning operators. The stationarity of the process relies on closure under addition, generalizing closure under convolution. This framework preserves the INAR interpretation in terms of survivors and arrivals while introducing feedback between past and future counts. Transition probabilities, stationary distributions, moments, and autocorrelation can be derived analytically. Beyond preserving analytical tractability, this class considerably enlarges the range of available INAR models and generates quadratic conditional variance functions. It therefore provides a thinning-based alternative to overdispersed count time series models such as negative binomial INARCH processes, while retaining a direct interpretation at the level of individual counts.
