Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued Ar(P) Models

Abstract

Integer-valued autoregressive (INAR) processes have been introduced to model nonnegative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of autoregression coefficients and a probability distribution on the nonnegative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. This 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 autoregression parameters and the innovation distribution.

Keywords: count data, nonparametric maximum likelihood, infinite-dimensional Z-estimator, semiparametric efficiency

JEL Classification: C13, C14, C22