Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)

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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 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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages39
Volume2008-53
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-53

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Efficient estimation
Autoregression
Innovation
Integer
Parametric model
Coefficients
Autoregressive process
Estimator
Probability distribution
Immigration

Keywords

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

Cite this

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title = "Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)",
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",
author = "F.C. Drost and {van den Akker}, R. and B.J.M. Werker",
note = "Revision of DP 2007-23, Subsequently published in Journal of the Royal Statistical Society, Series B, 2009 Pagination: 39",
year = "2008",
language = "English",
volume = "2008-53",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23). / Drost, F.C.; van den Akker, R.; Werker, B.J.M.

Tilburg : Econometrics, 2008. (CentER Discussion Paper; Vol. 2008-53).

Research output: Working paperDiscussion paperOther research output

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AB - 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.

KW - count data

KW - nonparametric maximum likelihood

KW - infinite-dimensional Z-estimator

KW - semiparametric efficiency

M3 - Discussion paper

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T3 - CentER Discussion Paper

BT - Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)

PB - Econometrics

CY - Tilburg

ER -