Statistical Learning Algorithms to Forecast the Equity Risk Premium in the European Union

Abstract

With the explosion of “Big Data”, the application of statistical learning models has become popular in multiple scientific areas as well as in marketing, finance or other business disciplines. Nonetheless, there is not yet an abundant literature that covers the application of these learning algorithms to forecast the equity risk premium. In this paper we investigate whether Classification and Regression Trees (CART) algorithms and several ensemble methods, such as bagging, random forests and boosting, improve traditional parametric models to forecast the equity risk premium. In particular, we work with European Monetary Union data for a period that spans from the EMU foundation at the beginning of 2000 to half of 2017.

The paper first compares monthly out-of-sample forecasting ability of multiple economic and technical variables using linear regression models and regression trees techniques. To check the out-of-sample accuracy, predictive regressions are compared to a popular benchmark in the literature: the historical mean average. Forecasts performance is analyzed in terms of the Campbell and Thompson R-squared (R² _OS), which compares the MSFE of regressions constructed with selected predictors, against the MSFE of the benchmark.