Designing bivariate timeseries with controlled Granger causality
Keyword(s):
In this manuscript, we analyzed vector auto-regressive (VAR) model in order to draw a design principle for bivariate timeseries with a controlled statistical inter-relationship. We show how to generate bivariate timeseries with given covariance and Granger causality, and showed the trade-off relationship between these two types of statistical interaction. In principle, covariance and Granger causality are controllable independently, but the ranges of their values, which let VAR be proper and have stationary distribution, are constrained by each other. Thus, there is an essential tri-lemma among the stability and properness of VAR, the controllability of covariance, and that of Granger causality.