Spectral Subsampling MCMC for Stationary Multivariate Time Series

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 stationary multivariate time series. It also proposes a multivariate generalisation of the autoregressive tempered fractionally differentiated moving average model (ARTFIMA) and establishes some of its properties. The new model is shown to provide a better fit compared to multivariate autoregressive moving average models for three real world examples. We demonstrate that spectral subsampling may provide up to two orders of magnitude faster estimation, while retaining MCMC sampling efficiency and accuracy, compared to spectral methods using the full dataset.