Spectral Subsampling MCMC for Stationary Multivariate Time Series

Event: La Trobe Statistics and Stochastic Colloquium
Speaker: Dr Matias Quiroz (University of Technology Sydney)
Title: Spectral Subsampling MCMC for Stationary Multivariate Time Series
Date: 12:00 noon, Thursday 19 August 2021
Zoom: https://latrobe.zoom.us/j/98357628534
PDF slides: unavailable

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 talk presents an extension of the approach to stationary multivariate time series. We also propose a multivariate generalisation of the autoregressive tempered fractionally differentiated moving average model (ARTFIMA). 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.