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

CentER Discussion Paper Series No. 2007-23

38 Pages Posted: 22 May 2007

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: March 2007

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

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 (March 2007). CentER Discussion Paper Series No. 2007-23, Available at SSRN: https://ssrn.com/abstract=987791 or http://dx.doi.org/10.2139/ssrn.987791

Feike C. Drost

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 (Contact Author)

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

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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