Two-Step Optimal Prediction Under Phillips Triangular Cointegrated System

This study proposes a two-step optimal best linear predictor (OBLP) under Phillips triangular cointegrated system, deduced from a two-step optimal forecasting method, for non-stationary level variables cointegrated with fundamental variables. In the first step, a cointegration equilibrium is estimated. The difference between the cointegration equilibrium and the other predicted variables is optimally forecasted in the second step, with conditional expectations estimated by the lagged fundamental differences and cointegration errors and summed with the cointegration equilibrium. We show that the OBLP has the lowest mean squared forecasting error among linear forecasting methods, such as random walk, cointegration, and augmented error correction models. In the second step, the cointegration error correction model is converted into a vector autoregression model consisting of the cointegration error and the fundamental differences of the variables and is used to estimate conditional expectations. Simulation results comparing the other predictors with the OBLP and forecast results for the US GDP and consumption applying the OBLP support the theoretical predictions of the forecasting efficiency of the OBLP.