Nonparametric prediction of stock returns based on yearly data: The long-term view

Abstract

One of the most studied questions in economics and finance is whether empirical models can be used to predict equity returns or premiums. In this paper, we take the actuarial long-term view and base our prediction on yearly data from 1872 through 2014. While many authors favor the historical mean or other parametric methods, this article focuses on nonlinear relationships between a set of covariates. A bootstrap test on the true functional form of the conditional expected returns confirms that yearly returns on the S&P500 are predictable. The inclusion of prior knowledge in our nonlinear model shows notable improvement in the prediction of excess stock returns compared to a fully nonparametric model. Statistically, a bias and dimension reduction method is proposed to import more structure in the estimation process as an adequate way to circumvent the curse of dimensionality.

Forecasting benchmarks of long-term stock returns via machine learning

“…Their results indicate a more complex structure than additivity, as the fully nonparametric models always do better in terms of validated R 2 than the additive counterparts. Scholz et al (2015) propose a semiparametric bias reduction method for the purpose of importing more structure based on a multiplicative correction with a parametric pilot estimate. Alternatively, Scholz et al (2016) make use of economic theory saying that the price of a stock is driven by fundamentals and investors should focus on forward earnings and profitability.…”

“…The purpose of the current research is to make the first few investigations on suitable benchmark selection from an econometric perspective. We achieve this by machine learning based on the cross-validated time series approach of Nielsen and Sperlich (2003) , Scholz et al (2015) and Scholz et al (2016) to optimize the fully nonparametric statistical estimation and forecasting of the risky asset returns in excess of four different benchmarks: the risk free rate, the long-term interest rate, the earnings-by-price ratio, and the inflation. Our method lets the data speak in themselves via training and learning, while being intuitively informative so that we can identify the covariates driving the system.…”

A Note on Combining Machine Learning with Statistical Modeling for Financial Data Analysis

“…The Editors of this Special Issue also urge practitioners not to ignore what has already been learned about financial data when using presumably fully automatic ML methods. Regarding financial data for example, Buch-Larsen et al (2005), Bolancé et al (2012), Scholz et al (2015Scholz et al ( , 2016, and Kyriakou et al (2019) (among others) have shown the significant gains in estimation and prediction when including prior knowledge in nonparametric prediction. The first two showed how knowledge-driven data transformation improves nonparametric estimation of distribution and operational risk; the third paper used parametrically-guided ML for stock return prediction; the fourth imputed bond returns to improve stock return predictions; and the last proposed comparing different theory-driven benchmark models regarding their predictability.…”

Multi-step non- and semi-parametric predictive regressions for short and long horizon stock return prediction

“…Chen and Hong (2010) developed a nonparametric predictability test to examine whether there exists a kind of predictability for equity returns for both short and long horizons and show that the nonparametric model can outperform the linear model. Scholz, Nielsen and Sperlich (2015) used nonparametric and semiparametric techniques to investigate the prediction of stock return over one-year horizon based on yearly data. Despite the significant volume of subsequent research, the predictability debate, and many econometric issues, in terms of the size and power of the existing tests, still remain unsolved (see for example, Stambaugh, 1999;Campbell and Yogo, 2006).…”