Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models

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Abstract

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. 
Original languageEnglish
Pages (from-to)467-485
JournalJournal of the Royal Statistical Society, Series B
Volume71
Issue number2
Publication statusPublished - 2009

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Autoregression
Efficient Estimation
Integer
Non-negative
Efficient Estimator
Model
Immigration
Autoregressive Process
Regression Coefficient
Parametric Model
Two Parameters
Probability Distribution
Innovation
Efficient estimation
Restriction

Cite this

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title = "Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models",
abstract = "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. ",
author = "F.C. Drost and {van den Akker}, R. and B.J.M. Werker",
note = "Appeared earlier as CentER DP 2008-53",
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T1 - Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models

AU - Drost, F.C.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Appeared earlier as CentER DP 2008-53

PY - 2009

Y1 - 2009

N2 - 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. 

AB - 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. 

M3 - Article

VL - 71

SP - 467

EP - 485

JO - Journal of the Royal Statistical Society, Series B

JF - Journal of the Royal Statistical Society, Series B

SN - 1369-7412

IS - 2

ER -