Authors: Faymonville, Maxime
Jentsch, Carsten
Weiß, Christian H.
Aleksandrov, Boris
Title: Semiparametric estimation of INAR models using roughness penalization
Language (ISO): en
Abstract: Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without any parametric assumption on the innovation distribution. However, for small sample sizes, the estimation performance of this semiparametric estimation approach may be inferior. Therefore, to improve the estimation accuracy, we propose a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other. This is the case, for example, in the frequently used INAR models with Poisson, negative binomially or geometrically distributed innovations. For the data-driven selection of the penalization parameter, we propose two algorithms and evaluate their performance. In Monte Carlo simulations, we illustrate the superiority of the proposed penalized estimation approach and argue that a combination of penalized and unpenalized estimation approaches results in overall best INAR model fits.
Subject Headings: Count data
Penalized estimation
Integer-valued autoregressions
Innovation distribution
Issue Date: 2022-09-21
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Appears in Collections:Institut für Wirtschafts- und Sozialstatistik

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