Analysis of Nonstationary Time Series Using Locally Coupled Gaussian Processes

TL;DR

This paper presents a novel Gaussian process framework for analyzing complex nonstationary time series by coupling locally stationary models with hidden Markov processes, enabling flexible modeling of signals with varying dynamics.

Contribution

Introduces a new framework combining locally stationary Gaussian processes with hidden Markov models for nonstationary time series analysis, allowing closed-form parameter estimation.

Findings

Successfully modeled synthetic nonstationary signals with varying frequency.

Effectively distinguished dynamical states in time series.

Applied method to real brain activity data.

Abstract

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzing nonstationary time series using locally stationary Gaussian process analysis with parameters that are coupled through a hidden Markov model. The main advantage of this framework is that arbitrary complex nonstationary covariance functions can be obtained by combining simpler stationary building blocks whose hidden parameters can be estimated in closed-form. We demonstrate the flexibility of the method by analyzing two examples of synthetic nonstationary signals: oscillations with time varying frequency and time series with two dynamical states. Finally, we report an example application on real magnetoencephalographic measurements of brain activity.