Uno studio sulla distribuzione asintotica della metrica autoregressiva

Abstract

In a number of practical problems we need to group time series into homogeneous classes or clusters. In this paper we consider a parametric approach which establishes the dissimilarity between dynamic structures by means of the comparison of the corresponding linear models. In particular, we refer to the metric introduced by Piccolo (1984) on the class of ARIMA invertible models as the Euclidean distance between the weights of their Autoregressive expansions. We derive the asymptotic distribution of that criterion in the case of stationary and independent time series and show how it can be adequately approximated. A simulation study concludes the paper.