Simultaneous Decorrelation of Matrix Time Series

TL;DR

This paper introduces a bilinear transformation for large matrix time series that simplifies modeling by creating uncorrelated block structures, improving forecasting accuracy and computational efficiency.

Contribution

It proposes a novel bilinear transformation that decorrelates matrix time series into smaller blocks, enabling more parsimonious and effective modeling of high-dimensional data.

Findings

Transformation achieves uniform convergence rates.

Improves forecasting performance in simulations and real data.

Equivalent to decorrelation of a vector time series of dimension max(p,q).

Abstract

We propose a contemporaneous bilinear transformation for a $p\times q$ matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when $p$ and/or $q$ are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence an overall parsimonious model is achieved by modelling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, i.e. it is technically equivalent to the decorrelation of a vector time series of dimension max$(p,q)$ instead of $p\times q$. The proposed method is illustrated numerically via both simulated and real data examples.