Learning the Structure of a Nonstationary Vector Autoregression

We adapt graphical causal structure learning methods to apply to nonstationary time series data, specifically to processes that exhibit stochastic trends. We modify the likelihood component of the BIC score used by score-based search algorithms, such that it remains a consistent selection criterion for integrated or cointegrated processes. We use this modified score in conjunction with the SVAR-GFCI algorithm, which allows us to recover qualitative structural information about the underlying data-generating process even in the presence of latent (unmeasured) factors. We demonstrate our approach on both simulated and real macroeconomic data.