Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics

TL;DR

This paper introduces a novel model selection method using Gap statistics to determine the optimal number of AR filters in a mixture model for non-stationary time series, enhancing modeling accuracy.

Contribution

It proposes a new approach for selecting the number of AR components in a mixture model using Gap statistics and a novel distance measure between AR filters.

Findings

Effective in identifying the correct number of AR filters

Improves modeling of non-stationary time series

Demonstrated through numerical experiments

Abstract

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.