ALTERNATIVE FORMS OF GRANGER CAUSALITY, HETEROGENEITY, AND NONSTATIONARITY

Granger causality testing is an increasingly popular approach to determine causal relations among dynamic processes and it can be generalized in various important ways. This chapter considers generalizations to nonstationary and heterogeneous processes including reference to an innovative and extremely successful way to obtain a valid common time series model for a given set of heterogeneous replications. It presents an innovative alternative approach in which the decision whether a standard vector autoregressive models (VAR), a structural VAR, or a hybrid VAR best describes the stochastic dynamic system underlying a given observed time series, is determined in a data-driven way. In an application to data generated by a hybrid VAR(1), incorporating both a directed contemporaneous relation and a contemporaneous correlation among a pair of univariate components of the white process noise, the new approach correctly recovers the true model and therefore also can yield the correct results about lagged Granger causality.