Dynamic multiscale spatiotemporal models for multivariate Gaussian data

Abstract

We propose a novel class of multiscale spatiotemporal models for multivariate Gaussian data. First, we decompose the multivariate data and the underlying latent process with a novel multivariate multiscale decomposition. This decomposition results in multiscale coefficient matrices with elements that are multiscale approximations of spatial directional derivatives. We then assume that the associated latent multiscale coefficient matrices evolve through time with matrix-variate state-space equations. We allow for different speeds of change through time for each latent multiscale coefficient matrix, which induces distinct spatiotemporal dynamics for the mean process in different regions at multiple spatial scales of resolution. This flexible model framework allows for both stationary and nonstationary latent multiscale spatiotemporal processes. Further, we develop a singular matrix-variate forward filter backward sampler for efficient posterior exploration. Importantly for practical purposes, our proposed multiscale spatiotemporal algorithm scales linearly with dataset size and is fully parallelizable. To illustrate the usefulness and flexibility of our dynamic multivariate multiscale framework, we present an application to the spatiotemporal NCEP/NCAR Reanalysis-I dataset on stratospheric temperatures over North America from 1951 to 2016. Our analysis indicates substantial long-term trends in stratospheric temperatures.