Abstract
In this paper, we propose a simple approach to testing and modelling nonlinear predictability of stock returns using Hermite Functions. The proposed test suggests that there exists a kind of nonlinear predictability for the dividend yield. Furthermore, the out-of-sample evaluation results suggest the dividend yield has nonlinear predictive power for stock returns while the book-to-market ratio and earning-price ratio have little predictive power.
Highlights
Whether the stock returns are predictable or not is one of the most important questions in finance
Nelson and Kim (1993), and Stambaugh (1999) point out that persistence leads to biased coefficients in predictive regressions if innovations in the predictor variable are correlated with the returns
We can summarize from Table 2: (1) Both dy and log(dy) can predict stock returns; (2) After controlling the first component, the addition of the other two components make little contribution to predict stock return; (3) The forecasting power of dividend yield is greater for vwny than ewny
Summary
Whether the stock returns are predictable or not is one of the most important questions in finance. The proposed nonlinear models are not shown to catch the co-existence of highly persistent predictors and far less persistent stock returns. We propose an integrable model for the predictive regression and provide a general methodology for testing and estimating the nonlinear function. It partially addresses the model imbalance issue inherent in the linear predictive regression and gives a closed-form description of the nonlinear function. The technical assumptions and proofs are collected in an appendix
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