  Using a proper model to characterize a time series is crucial in making
accurate predictions. In this work we use time-varying autoregressive process
(TVAR) to describe non-stationary time series and model it as a mixture of
multiple stable autoregressive (AR) processes. We introduce a new model
selection technique based on Gap statistics to learn the appropriate number of
AR filters needed to model a time series. We define a new distance measure
between stable AR filters and draw a reference curve that is used to measure
how much adding a new AR filter improves the performance of the model, and then
choose the number of AR filters that has the maximum gap with the reference
curve. To that end, we propose a new method in order to generate uniform random
stable AR filters in root domain. Numerical results are provided demonstrating
the performance of the proposed approach.
