Random subspace methods are a novel approach to obtain accurate forecasts in high-dimensional regression settings. We provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables. We focus on two approaches. The first is random subset regression, where random subsets of predictors are used to construct a forecast. Second, we discuss random projection regression, where artificial predictors are formed by randomly weighting the original predictors. Using recent results from random matrix theory, we obtain a tight bound on the mean squared forecast error for both randomized methods. We identify settings in which one randomized method results in more precise forecasts than the other and than alternative regularization strategies, such as principal component regression, partial least squares, lasso, and ridge regression. The predictive accuracy on the high-dimensional macroeconomic FRED-MD data set increases substantially when using the randomized methods, with random subset regression outperforming any one of the above mentioned competing methods for at least 66% of the series.

Additional Metadata
Keywords dimension reduction, random projections, random subset regression, principal components analysis, forecasting
JEL Time-Series Models; Dynamic Quantile Regressions (jel C32), Forecasting and Other Model Applications (jel C53), Large datasets: Modelling and Analysis (jel C55)
Persistent URL hdl.handle.net/1765/97926
Series Tinbergen Institute Discussion Paper Series
Boot, T, & Nibbering, D. (2016). Forecasting Using Random Subspace Methods (No. 16-073/III). Tinbergen Institute Discussion Paper Series. Retrieved from http://hdl.handle.net/1765/97926