Forecast Linear AugmentedProjection (FLAP): A Free Lunch to Reduce Forecast Error Variance

We propose a novel forecast linear augmented projection (FLAP) method that can reduce the forecasterror variance of any multivariate forecast. The method first constructs new component series which are linear combinations of the original series. Forecasts are then generated for both the original and component series. Finally, the full vector of forecasts is projected onto a linear subspace where the constraints implied by the combination weights hold. We show that the projection using the original forecast error covariance matrix will result in improved forecasts. Notably, the new forecast error variance of each series is non-increasing with the number of components, and mild conditions are established for which it is strictly decreasing. It is also shown that the proposed method achieves maximum forecast error variance reduction among linear projection methods. We demonstrateour proposed method with an estimated covariance matrix using simulations and two empirical applications based on Australian tourism and FRED-MD data. In all cases, forecasts are improved. Notably, using FLAP with Principal Component Analysis (PCA) to construct the new series leads tosubstantial forecast error variance reduction.