On the directional predictability of equity premium using machine learning techniques

• Date: 01 April 2020
• DOI: http://doi.org/10.1002/for.2632
• Published date: 01 April 2020

Received: 28 November 2018 Revised: 22 October 2019 Accepted: 28 October 2019

DOI: 10.1002/for.2632

RESEARCH ARTICLE

On the directional predictability of equity premium using

machine learning techniques

Jonathan Iworiso Spyridon Vrontos

Department of Mathematical Sciences,

University of Essex, Colchester, UK

Correspondence

Spyridon Vrontos, Department of

Mathematical Sciences, University of

Essex, Wivenhoe Park, Colchester CO4

3SQ, UK.

Email: svrontos@essex.ac.uk

Abstract

This paper applies a plethora of machine learning techniques to forecast the

direction of the US equity premium. Our techniques include benchmark binary

probit models, classification and regression trees, along with penalized binary

probit models. Our empirical analysis reveals that the sophisticated machine

learning techniques significantly outperformed the benchmark binary probit

forecasting models, both statistically and economically. Overall, the discrimi-

nant analysis classifiers are rankedfirst among all the models tested. Specifically,

the high-dimensional discriminant analysis classifier ranks first in terms of sta-

tistical performance, while the quadratic discriminant analysis classifier ranks

first in economic performance. The penalized likelihood binary probit models

(least absolute shrinkage and selection operator, ridge, elastic net) also outper-

formed the benchmark binary probit models, providing significant alternatives

to portfolio managers.

KEYWORDS

binary probit, CART, directional predictability,forecasting, penalized binary probit, recursive win-

dow

1INTRODUCTION

Stock market participants aim at maximizing returns on

portfolio investments at minimal risk. Consequently,fore-

casting stock market returns has received considerable

attention in recent years. The majority of papers have

focused on the forecast accuracy of competing models

and examined whether there is evidence of predictabil-

ity, which can lead to economic gains. However, devising

successful trading strategies is contingent on the direc-

tional accuracy of the underlying models. The literature

on directional predictability is sparse, and the empirical

findings offer limited support. For example, the findings of

Chevapatrakul (2013), Christoffersen and Diebold (2006),

and Nyberg and Pönkä (2016) provide weak evidence of

directional stock market predictability. Although the pre-

dictive power of the models employed so far are shown to

be weak in statistical terms, they seem to provide economic

value. Thus the emphatic challenge lies in the develop-

ment of a suitable directional predictive model involving

the relevant financial and economic variables.

The application of some benchmark econometric mod-

els used in previous findings are shown to be weak

in terms of predictive performance. The introduction of

out-of-sample estimation and forecasting techniques used

by Nyberg (2011) and Pönkä (2016) provide statistically

significant evidence of the directional predictability of

stock market returns, but the predictive power of the mod-

els are shown to be relatively weak, and hence there is

a need to introduce sophisticated machine learning tech-

niques, as proposed in this paper,to improve the predictive

task of the models.

This paper focuses on the application of sophisti-

cated machine learning techniques on binary probit and

classification models to forecast the direction of US

excess stock market returns. The machine learning tech-

Journal of Forecasting. 2020;39:449–469. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 449

IWORISO AND VRONTOS

niques employed include classification and regression

trees (CART), such as bagging, boosting and discriminant

analysis classifiers, Bayesian classifiers, neural networks

(NNET), and regularization techniques, such as ridge,

least absolute shrinkage and selection operator (LASSO),

and elastic net. To compare our findings with the previ-

ous literature, we also include four variants of the bench-

mark binary probit models, namely the static, stepwise

static, dynamic, and stepwise dynamic models. The appli-

cation of CART forecasting models aims to explore all

covariates as ensembles to learn the data, train the clas-

sification model, recognize patterns, classify instances,

and to forecast future binary outcomes. With respect to

penalized binary probit models, we should note that the

presence of shrinkage penalty vector norms could result

in a bias in coefficient estimates, reduction in the fore-

cast errors, and improvement in predictive performance

via the so-called bias–variance tradeoff. Thus the proposal

of CART and penalized predictive models in this paper

aims at yielding superior statistical predictive performance

and economic significance compared to the benchmark

econometric models typically employed in the literature

to date.

The remaining structure of the paper is laid out as fol-

lows: Section 2 discusses the relevant literature; Section 3

describes the research methodology; Section 4 presents the

data and the empirical findings; and Section 5 concludes

the paper.

2LITERATURE REVIEW

A notable quest in modern financial econometric litera-

ture is the application of suitable techniques to predict the

sign of stock market returns. A reviewof relevant empirical

literature has revealed that the use of econometric mod-

els for the directional predictability of excess stock returns

is known to produce weak predictive power, poor statisti-

cal goodness of fit, and low predictive accuracies, among

others (see Chevapatrakul, 2013; Leitch & Tanner, 1991;

Leung, Daouk, & Chen, 2000; Nyberg, 2011; Pesaran &

Timmermann, 1995; Pönkä, 2016), even though the empir-

ical results seems to provide economic significance.

The previous findings on directional predictability by

Anatolyev and Gospodinov (2010) and Hong and Chung

(2003) employed a logistic regression model to predict

the sign of US stock market returns using relevant finan-

cial variables as the key predictors, and their results

provide evidence of predictability, but the overall predic-

tive power is relatively weak as compared to a rule of

thumb. In an attempt to determine market timing and ass

et allocation decisions between stocks and risk-free assets,

some researchers considered the role of conditional mean

and volatility while predicting the sign of asset returns.

Christoffersen and Diebold (2006) have opined that the

direction of asset returns is predictable, as volatility depen-

dence produces sign dependence, so long as expected

returns are nonzero. Thi s notion seems to be true, as other

existing papers have also provided significant statistical

evidence of the sign predictability of the US stock market

returns and economic recession status by application of

static, dynamic, autodynamic, and error correction mod-

els, both in-sample and out-of-sample (Kauppi & Saikko-

nen, 2008; Nyberg, 2011, 2013; Nyberg & Pönkä, 2016).

The static and dynamic probit models proposed

by Nyberg (2011) to predict the direction of monthly

US excess stock returns recursively appears to have

outperformed the autoregressive moving average

with exogenous inputs models (ARMAX), vector

autoregressive-generalized autoregressive conditional

heteroskedasticity models (VAR-GARCH), etc., used by

previous researchers. The idea was based on the approach

used by Kauppi and Saikkonen (2008) and Estrella and

Mishkin (1998) to obtain US economic recession forecasts

using variables such as the US term spread and lagged

stock returns, among others.

However, according to the Nyberg (2011) paper, Estrel-

la's statistical goodness-of-fit values in the various probit

models are very low in all cases. The positive values of

the Sharpe ratios signified that investors are likely to have

positive returns on portfolio investments. The percentage

of correct matches as a statistical performance evaluation

measure in the existing papers are relatively low—hence

the need to employ more advanced sophisticated models

that can yield a better degree of accuracy with the smallest

prediction error.

The underlying challenges associated with the use

of financial and economic variables to predict stock

market returns have prompted researchers to introduce

sophisticated statistical or machine learning algorithms to

improve the predictive task and the overall performance

evaluation of the resulting models under consideration.

It is noticeable from the empirical literature that statis-

tical learning techniques, which include random forest,

linear discriminant analysis (LDA), k-nearest neighbor,

tree-based classification, recursive partitioning, bagging

and boosting, logistic regression, support vector machine

(SVM), ridge regression, LASSO,least angle regression and

elastic nets, are useful for the analysis of financial econo-

metric time series (Chen, 2016; Hajek, Olej, & Myskova,

2014; Hsu, Hung, & Chang, 2008; Inoue & Kilian, 2008;

Kim & Swanson, 2014; Li & Chen, 2014; Lin & McClean,

2001; Pahwa, Khalfay, Soni, & Vora, 2017; Park & Sakaori,

2013; Roy, Mittal, Basu, & Abraham, 2015; Sermpinis,

Tsoukas, & Zhang, 2018; Shen, Wang, & Ma, 2014; Stock

& Watson, 2012; Swanson & White, 1997; Zhou, Lu, &

Fujita, 2015). Khaidem, Saha, and Dey (2016) used the

450