Data-Driven Learning of the Number of States in Multi-State Autoregressive Models

TL;DR

This paper introduces a novel model selection method for multi-state autoregressive models using Gap statistics and a new distance measure, enabling better identification of the number of AR states in non-stationary time series.

Contribution

It proposes a new approach combining Gap statistics with a stable AR filter distance measure to accurately determine the number of states in multi-state AR models.

Findings

The method effectively identifies the correct number of AR states in simulations.

The approach improves model selection accuracy over existing techniques.

Numerical results validate the efficiency and robustness of the proposed method.

Abstract

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.