Page 76 - Contributed Paper Session (CPS) - Volume 3

CPS1947 Hsein K. et al.

Semi-parametric single-index predictive
regression
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Hsein Kew , Weilun Zhou , Jiti Gao , David Harris
1 Monash University, Melbourne, Australia
2 The University of Melbourne, Melbourne, Australia

Abstract
This paper proposes a semi-parametric single-index predictive model with
multiple integrated predictors that exhibit cointegrating behaviour. We apply
this predictive model to re-examine stock return predictability in the United
States. It is well documented in the empirical finance literature that the most
commonly used predictors (such as dividend-price ratio and earning-price
ratio) can be characterised as integrated time series. We consider the case in
which these integrated predictors can plausibly be modelled as cointegrated.
We present some new evidence that the quarterly U.S. stock market returns
are nonlinearly predictable when we account for cointegration among the
predictors over the 1927-2017 periods and the post-1952 period.

Keywords
Stock return predictability; Single index model; Cointegration; Semi-
parametric models

1. Introduction
Linear predictive models have been widely used in empirical economics
and finance. For example, there is by now a large empirical literature that
examines the predictability of stock returns using a variety of lagged financial
and macroeconomic variables, including dividend-price ratio, earning-price
ratio, dividend-payout ratio, book-to-market ratio, cay, interest rates, term
spreads and default spreads; see for example Cochrane (2011), Lattau and
Ludvigson (2001) and Rapach and Zhou (2013). They consider a multivariate
predictive model of the form

T
= + −1 + ℯ

where is the dependent variable, typically is the stock return at time , −1

is a × 1 vector of predictors, typically is the lagged financial variables
known at time − 1, and ℯ is an error term. They provide empirical evidence

stock return are predictable because they reject the following null hypothesis
of no predictability : = ∙∙∙ = 0.
1

0
Numerous studies, including Campbell and Yogo (2006) and Kostakis,
Magdalinos and Stamatogiannis (2015) have found evidence that many of
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