Title: Joint semiparametric INAR bootstrap inference for model coefficients and innovation parameters
Authors: Maxime Faymonville - TU Dortmund University (Germany) [presenting]
Carsten Jentsch - TU Dortmund University (Germany)
Christian Weiss - Helmut Schmidt University (Germany)
Boris Aleksandrov - Helmut Schmidt University (Germany)
Abstract: For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on an autoregressive-type structure, such as the well-known integer-valued autoregressive (INAR) models, are very popular in practice. Besides the binomial thinning, these models are determined by autoregressive coefficients and a discrete innovation distribution. The literature mainly deals with the parametric estimation of INAR models, which restricts the flexibility of the considered model class in applications. Using semiparametric estimation, it is possible to jointly estimate the autoregressive coefficients and the innovation distribution, where the estimation of the innovation distribution works fully non-parametric. Using empirical process theory, the resulting semiparametric estimator is known to be consistent with some complicated limiting distribution which enables asymptotic inference and model diagnostics on the innovations. We consider a corresponding semiparametric INAR bootstrap procedure. We show that the bootstrap estimator for the autoregressive model coefficients and the innovation distribution provides the same limiting distribution such that the semiparametric bootstrap becomes asymptotically valid for the estimation of the innovation distribution. Simulations are used to illustrate the finite sample performance of the semiparametric INAR bootstrap using several common and uncommon innovation distributions.