Forecast Linear Augmented Projection (FLAP): A free lunch to reduce forecast error variance

TL;DR

The paper introduces FLAP, a new linear projection method that reduces forecast error variance in multivariate forecasts without bias, validated through simulations and empirical data, especially with PCA.

Contribution

FLAP is a novel method that constructs component series and projects forecasts to minimize forecast error variance, outperforming existing linear projection techniques.

Findings

FLAP reduces forecast error variance significantly in simulations.

Using PCA with FLAP enhances forecast accuracy.

Empirical applications show substantial variance reduction.

Abstract

A novel forecast linear augmented projection (FLAP) method is introduced, which reduces the forecast error variance of any unbiased multivariate forecast without introducing bias. 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. It is proven that the trace of the forecast error variance 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. The theoretical results are validated through simulations and two empirical applications based on Australian tourism and FRED-MD data. Notably, using FLAP with Principal Component Analysis (PCA) to construct the new series leads to substantial forecast error variance reduction.