Spectral Subsampling MCMC for Stationary Multivariate Time Series with Applications to Vector ARTFIMA Processes

TL;DR

This paper extends spectral subsampling MCMC to multivariate stationary time series, demonstrating significant computational speed-ups while maintaining accuracy, especially for complex models like multivariate ARTFIMA.

Contribution

It introduces a multivariate generalisation of spectral subsampling MCMC and applies it to multivariate ARTFIMA models, showing substantial efficiency gains.

Findings

Spectral subsampling MCMC achieves up to 100x speed-up.

The method maintains accuracy comparable to full data approaches.

Application to multivariate ARTFIMA models demonstrates practical effectiveness.

Abstract

Spectral subsampling MCMC was recently proposed to speed up Markov chain Monte Carlo (MCMC) for long stationary univariate time series by subsampling periodogram observations in the frequency domain. This article extends the approach to multivariate time series using a multivariate generalisation of the Whittle likelihood. To assess the computational gains from spectral subsampling in challenging problems, a multivariate generalisation of the autoregressive tempered fractionally integrated moving average model (ARTFIMA) is introduced and some of its properties derived. Bayesian inference based on the Whittle likelihood is demonstrated to be a fast and accurate alternative to the exact time domain likelihood. Spectral subsampling is shown to provide up to two orders of magnitude additional speed-up, while retaining MCMC sampling efficiency and accuracy, compared to spectral methods using the full dataset. Keywords: Bayesian, Markov chain Monte Carlo, Semi-long memory, Spectral analysis, Whittle likelihood.