Abstract

In this paper, we propose three new predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series; and the multi-step time-varying coefficient predictive regression model, in which the predictive variables are stochastically nonstationary. We also establish the estimation theory and asymptotic properties for these models in the short horizon and long horizon case. To evaluate the effectiveness of these models, we investigate their capability of stock return prediction. The empirical results show that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we find that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting.

Highlights

  • A fundamental issue in finance is whether future stock returns are predictable using publicly available information

  • To mitigate the curse of dimensionality we propose three new predictive models: the multi-step additive predictive regression model (APR), the multi-step time-varying coefficient predictive regression model (TVCPR), and the multi-step nonparametric predictive regression model (NPR)

  • We present the theoretical properties of our estimators of the regression functions in the short horizon and long horizon case, where by long horizon we mean that the horizon increases to infinity with the size of the sample

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Summary

Introduction

A fundamental issue in finance is whether future stock returns are predictable using publicly available information. Several researchers have focused on using linear models to predict stock returns (see for example, Lewellen, 2004; Campbell and Shiller, 1988). We assume that the predictive variables are locally stationary time series in the NPR and APR models and nonstationary in the TVCPR model. Vogt (2012) studied nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. Varying coefficient time series models have been widely applied because of its flexibility, and different theoretical results have been investigated (see for example, Cai et al, 2009; Cai, 2007; Li et al, 2002; Phillips et al, 2017). Many empirical studies consider the long horizon case and our results support the use of nonparametric methods in this setting. The proofs of the main results are given in an appendix

The NPR model
The TVCPR model
The APR model
Bandwidth selection
Truncation parameter choice
Full sample estimation
Out-of-sample evaluation
Long Horizon Return Prediction
Trading strategy
Conclusions
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