ROLLING HORIZON PROCEDURES FOR THE SOLUTION OF AN OPTIMAL REPLACEMENT PROBLEM OF n-MACHINES WITH RANDOM HORIZON.pdf

Abstract

Autoregressive regime-switching models are being widely used in modelling financial and economic time series.
When the number of regimes is fixed statistical inference is relatively straightforward and asymptotic properties
of the estimates may be established. However, the problem of selecting number of regimes is far less obvious
and hasn’t been completely answered yet. When the number of regimes is unknown, identifiability problems
arise and, for example, likelihood ratio test statistic is no longer convergent to a χ2-distribution. The problem
we address in this paper is how to select number of regimes without knowing the form of the noise. One
possible method to answer this problem is to consider penalized criteria. Recently, consistency of a modified
BIC criterion was recently proven in the framework of likelihood criterion for linear switching models. We
extend these results to mixtures of nonlinear autoregressive models with mean square error criterion and prove
consistency of a penalized estimate for number of regimes under some regularity conditions. As an illustration,
we use this theoretical result to propose and compare effective criteria to find the true number of regimes on a
simple simulation.