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

CentER Discussion Paper Series No. 2008-53 (revision of Paper No. 2007-23)

39 Pages Posted: 9 Jun 2008

See all articles by Feike C. Drost

Feike C. Drost

Tilburg University - Center for Economic Research (CentER)

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Multiple version iconThere are 2 versions of this paper

Date Written: May 1, 2008

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

Suggested Citation

Drost, Feike C. and Van den Akker, Ramon and Werker, Bas J.M., Efficient Estimation of Autoregression Parameters and Innovation Distributions for Semiparametric Integer-Valued Ar(P) Models (May 1, 2008). CentER Discussion Paper Series No. 2008-53 (revision of Paper No. 2007-23) , Available at SSRN: https://ssrn.com/abstract=1142763 or http://dx.doi.org/10.2139/ssrn.1142763

Feike C. Drost (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
P.O. Box 90153
5000 LE Tilburg
Netherlands
+31 13 466 3038 (Phone)

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR ( email )

K-623
PO Box 90153
Tilburg, 5000 LE
Netherlands

HOME PAGE: http://sites.google.com/site/rvdnakker/

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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