On causal and non‐causal cointegrated vector autoregressive time series

Previous-30 treatments of multivariate non-causal time series have assumed stationarity. In this article, we consider integrated processes in a setting. We generalize the Johansen–Granger representation for causal vector autoregressive (VAR) models to allow dependence on future errors and discuss how parameters can be estimated. The asymptotic distribution trace statistic is also considered. Some Monte Carlo simulations are presented.