Abstract
This paper studies a semi-parametric single-index predictive regression model with multiple nonstationary predictors that exhibit co-movement behaviour. Orthogonal series expansion is employed to approximate the unknown link function in the model and the estimator is derived from an optimization under the constraint of identification condition for index parameter. The main finding includes two types of super-consistency rates of the estimators of the index parameter along two orthogonal directions in a new coordinate system. The central limit theorem is established for a plug-in estimator of the unknown link function. In the empirical studies, we provide evidence in favour of nonlinear predictability of the stock return using long term yield and treasury bill rate.
Highlights
Whether stock returns are predictable or not is a fundamental issue in finance
The first problem is that several financial predictors are highly persistent or even nonstationary, yet the equity premium behaves like a stationary process
Considering monthly and quarterly data over the 1927 to 2017 sample period and the 1952 to 2017 sub-period, we examine the predictability of the equity premium using four pairs of nonstationary predictors, and find significant evidence of nonlinear predictability
Summary
In the study of a standard predictive regression, predictability is examined in the context of a parametrically linear model: yt = α + β × xt−1 + et, (1.1). Where yt is the equity premium, xt−1 is the lagged financial predictor and et is a martingale difference sequence. The second problem is that the parametrically linear models may not be robust to functional form misspecification. To address these two problems, Kasparis et al (2015) proposed a nonparametric predictive regression model and estimated it with a kernel-based method.
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