  In this work, we consider the class of multi-state autoregressive processes
that can be used to model non-stationary time-series of interest. In order to
capture different autoregressive (AR) states underlying an observed time
series, it is crucial to select the appropriate number of states. We propose a
new model selection technique based on the Gap statistics, which uses a null
reference distribution on the stable AR filters to check whether adding a new
AR state significantly improves the performance of the model. To that end, we
define a new distance measure between AR filters based on mean squared
prediction error (MSPE), and propose an efficient method to generate random
stable filters that are uniformly distributed in the coefficient space.
Numerical results are provided to evaluate the performance of the proposed
approach.
