Maximum Pseudolikelihood Estimation for Model-Based Clustering of Time Series Data

TL;DR

This paper introduces a maximum pseudolikelihood estimation method for mixture autoregressions, enabling effective clustering of time series data without numerical issues associated with maximum likelihood estimation.

Contribution

It proposes a consistent MPL estimator for MoAR models that can be computed via EM algorithm, overcoming ML estimation limitations in long time series.

Findings

MPL estimator performs well compared to ML in simulations.

Method successfully applied to resting-state fMRI data.

Provides a practical solution for clustering long time series.

Abstract

Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal random variables. In practical scenarios, these products converge to zero as the length of the time series increases, and thus the ML estimation of MoAR models becomes infeasible without the use of numerical tricks. We propose a maximum pseudolikelihood (MPL) estimation approach as an alternative to the use of numerical tricks. The MPL estimator is proved to be consistent and can be computed via an EM (expectation--maximization) algorithm. Simulations are used to assess the performance of the MPL estimator against that of the ML estimator in cases where the latter was able to be calculated. An application to the clustering of time series data arising from a resting-state fMRI experiment is presented as a demonstration of the methodology.