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

Research output: Working paperDiscussion paperOther research output

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

Fingerprint

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 for Semiparametric Integer-Valued AR(p) Models (Subsequently replaced by DP 2008-53)",
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.",
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 = "Subsequently replaced by CentER DP 2008-53 Pagination: 38",
year = "2007",
language = "English",
volume = "2007-23",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models (Subsequently replaced by DP 2008-53). / Drost, F.C.; van den Akker, R.; Werker, B.J.M.

Tilburg : Econometrics, 2007. (CentER Discussion Paper; Vol. 2007-23).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models (Subsequently replaced by DP 2008-53)

AU - Drost, F.C.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Subsequently replaced by CentER DP 2008-53 Pagination: 38

PY - 2007

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N2 - 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.

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: essentially there are no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of 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

VL - 2007-23

T3 - CentER Discussion Paper

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

PB - Econometrics

CY - Tilburg

ER -