Semiparametric estimation of INAR models using roughness penalization

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.

spINAR: An R Package for Semiparametric and Parametric Estimation and Bootstrapping of Integer-Valued Autoregressive (INAR) Models

“…Regarding the estimation, it allows for moment-and maximum likelihood-based parametric estimation of INAR models with Poisson, geometrically or negative binomially distributed innovations (see for example Weiß (2018) for details), but the main contribution lies in the semiparametric maximum likelihood estimation of INAR models introduced by Drost et al (2009) which they proved to be efficient. Additionally, a finite sample refinement for the semiparametric setup consisting of an estimation approach, that penalizes the roughness of the innovation distribution as well as a validation function for the penalization parameters is implemented (Faymonville, Jentsch, Weiß, & Aleksandrov, 2022). Furthermore, the package includes the possibility to bootstrap INAR data.…”

Partial Autocorrelation Diagnostics for Count Time Series

“…It should be noted that for the INAR(p) model, also a semi-parametric specification exists (where the innovations' distribution is left unspecified). The corresponding semiparametric CML estimator was analyzed by Drost et al [16]; see also the small-sample refinement by Faymonville et al [17]. It leads to non-parametric estimates for the probabilities p ,k = P( t = k) for k between some finite bounds 0 ≤ l < u < ∞ (and p ,k = 0 for k ∈ {l, .…”