Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR(p) models

Feike C. Drost (), Ramon van den Akker and Bas J. M. Werker

Journal of the Royal Statistical Society Series B, 2009, vol. 71, issue 2, 467-485

Abstract: Summary. Integer‐valued auto‐regressive (INAR) processes have been introduced to model non‐negative integer‐valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto‐regression coefficients and a probability distribution on the non‐negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the auto‐regression parameters and the innovation distribution.

Date: 2009
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