Subspace Methods

Abstract

With increasingly many variables available to macroeconomic forecasters, dimension reduction methods are essential to obtain accurate forecasts. Subspace methods are a new class of dimension reduction methods that have been found to yield precise forecasts when applied to macroeconomic and financial data. In this chapter, we review three subspace methods: subset regression, random projection regression, and compressed regression. We provide currently available theoretical results, and indicate a number of open avenues. The methods are illustrated in various settings relevant to macroeconomic forecasters.