SSA for testing causality between series

Multivariate (or multichannel) SSA (shortly, MSSA) is a direct extension of the standard SSA for simultaneous analysis of several time series. Assume that we have two series, x = (x₁,...,x_N ) and y = (y₁,...,y_N). The (joint) trajectory matrix of the two-variate series (x; y) can be defined as Z = (X,Y), where X and Y are the trajectory matrices of the individual series x and y. Matrix Z is block-Hankel rather than simply Hankel. Other stages of MSSA are identical to the stages of the univariate SSA except that we build a block-Hankel (rather than ordinary Hankel) approximation to the trajectory matrix Z. MSSA may be very useful for analyzing several series with common structure. MSSA may also be used for establishing causality between two series. Indeed, the absence of causality of y on x implies that the knowledge of y does not improve the quality of forecasts of x. Hence an improvement in the quality of forecasts for x which we obtain using MSSA against univariate SSA forecasts for x gives us a family of SSA-causality tests.

Selected publication

• Hassani, H; Zhigljavsky, A; Patterson, K; Soofi, A. (2011). A Comprehensive Causality Test Based on the Singular Spectrum Analysis, Causality in Science (eds. P. M. Illari, F. Russo and J. Williamson), Oxford University press, 379-404.