Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models (Subsequently replaced by DP 2008-53)

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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: essentially there are no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of the autoregression parameters and the innovation distribution.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages38
Volume2007-23
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-23

Keywords

  • count data
  • nonparametric maximum likelihood
  • infinite-dimensional Z-estimator
  • semiparametric efficiency

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