Pipelined HAC Estimation Engines for Multivariate Time Series

Heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimation, or HAC estimation in short, is one of the most important techniques in time series analysis and forecasting. It serves as a powerful analytical tool for hypothesis testing and model verification. However, HAC estimation for long and high-dimensional time series is computationally expensive. This paper describes a pipeline-friendly HAC estimation algorithm derived from a mathematical specification, by applying transformations to eliminate conditionals, to parallelise arithmetic, and to promote data reuse in computation. We discuss an initial hardware architecture for the proposed algorithm, and propose two optimised architectures to improve the worst-case performance. Experimental systems based on proposed architectures demonstrate high performance especially for long time series. One experimental system achieves up to 12 times speedup over an optimised software system on 12 CPU cores.