Predictive ability and economic gains from volatility forecast combinations

• Published date: 01 March 2020
• Date: 01 March 2020
• DOI: http://doi.org/10.1002/for.2622
• Author: Vasiliki D. Skintzi,Stavroula P. Fameliti

RESEARCH ARTICLE

Predictive ability and economic gains from volatility

forecast combinations

Stavroula P. Fameliti | Vasiliki D. Skintzi

Department of Economics, School of

Economics, Management and Informatics,

University of Peloponnese, Tripolis,

Greece

Correspondence

Stavroula P. Fameliti, Department of

Economics, School of Economics,

Management and Informatics, University

of Peloponnese, Tripolis Campus, 22100

Tripolis, Greece

Email: sfameliti@uop.gr

Abstract

The availability of numerous modeling approaches for volatility forecasting

leads to model uncertainty for both researchers and practitioners. A large num-

ber of studies provide evidence in favor of combination methods for forecasting

a variety of financial variables, but most of them are implemented on returns

forecasting and evaluate their performance based solely on statistical evalua-

tion criteria. In this paper, we combine various volatility forecasts based on dif-

ferent combination schemes and evaluate their performance in forecasting the

volatility of the S&P 500 index. We use an exhaustive variety of combination

methods to forecast volatility, ranging from simple techniques to time‐

varying techniques based on the past performance of the single models and

regression techniques. We then evaluate the forecasting performance of single

and combination volatility forecasts based on both statistical and economic loss

functions. The empirical analysis in this paper yields an important conclusion.

Although combination forecasts based on more complex methods perform bet-

ter than the simple combinations and single models, there is no dominant com-

bination technique that outperforms the rest in both statistical and economic

terms.

KEYWORDS

combination methods, economic evaluation, forecastingperformance, statisticalevaluation, volatility

forecasting

1|INTRODUCTION

Over the last decades forecasting the second moments of

asset returns has been one of the most active areas in

financial econometrics. A vast literature on methods

and models for volatility forecasting has been developed,

though there is rarely any consensus on which model is

most appropriate in providing accurate forecasts.

Although a strand of literature has attempted to identify

the single best forecasting model in the context of finan-

cial applications, a limited number of studies in financial

forecasting have applied combination techniques to

aggregate numerous individual forecasts into a pooled

model. In this paper, we exploit the existing methodolo-

gies for combining forecasts in the context of volatility

forecasting, evaluating them according to standard statis-

tical loss functions, as well as economic‐based and risk

management loss functions.

Almost five decades of extensive research and promis-

ing applications, starting from the seminal work of Bates

and Granger (1969), provide theoretical support and

empirical evidence on the benefits of forecast combina-

tions. Clemen (1989) summarized the literature on fore-

cast combinations and concluded that combining

forecasts of various economic and financial variables led

to increased forecast accuracy. Similar conclusions were

Received: 27 September 2018 Revised: 5 July 2019 Accepted: 12 July 2019

DOI: 10.1002/for.2622

Journal of Forecasting. 2020;39:200–219.wileyonlinelibrary.com/journal/for© 2019 John Wiley & Sons, Ltd.200

reached by Aksu and Gunter (1992) based on macroeco-

nomic variables and firm‐specific series, by Makridakis

and Hibon (2003) based on the so‐called M3 competition,

by Stock and Watson (2003, 2004) across various eco-

nomic and financial variables, by Swanson and Zeng

(2001) using US macroeconomic variables, by Marsellino

(2004) on a large set of European macroeconomic vari-

ables, by Rapach, Strauss, and Zhou (2010) on equity pre-

mium prediction, and by Benavides and Capistrán (2012)

based on the Mexican peso–US dollar exchange rate.

From a more theoretical point of view, Timmermann

(2006) provided a theoretical justification for the superior

performance of combination methods. Following the suc-

cess of combination methods on forecasting the first

moments of economic or financial time series, the

research question arises of whether combination methods

can also improve the forecasts of the second moments.

Despite the importance of volatility forecasting and the

wide variety of combination models developed, the earli-

est study in combining various volatility forecasts dates

back to 2008, when Becker and Clements investigated

the forecasting performance of combination forecasts on

S&P 500 index volatility, indicating the superior forecast-

ing performance of combination techniques. Further-

more, Liu and Maheu (2009), as well as Wang, Ma, Wei

and Chongfeng (2016), based on high‐frequency data,

used the Bayesian model averaging technique to con-

struct realized volatility and density forecasts, concluding

that Bayesian model averaging provided adequate density

forecasts and modest improvements in volatility forecast-

ing. Clark and McCracken (2009) combined recursive and

rolling forecasts and concluded that these combinations

often led to improved forecasting accuracy. In a similar

framework, Patton and Sheppard (2009) combined indi-

vidual realized volatility estimators through various loss

functions, concluding that none of the combined estima-

tors could be outperformed by any individual estimator.

Fuertes, Izzeldin, and Kalotychou (2009) combined four

different nonparametric estimators of daily price variabil-

ity, suggesting that the four intraday volatility measures

were impacted by microstructure noise in different ways,

leading to increased forecasting accuracy.

Optimal combination procedures have also been

applied to improve the accuracy of individual quantile

forecasts. For instance, Giacomini and Komunjer (2005)

applied a quantile regression combining framework

through encompassing tests to the S&P 500 VaR estimates

based on two volatility forecasting methods. Moreover,

McAleer, Jiménez Martín, and Pérez‐Amaral (2011)

examined simple deterministic value‐at‐risk (VaR) fore-

casts, while Halbleib and Pohlmeier (2012) combined

VaR forecasts based on the maximization of conditional

coverage rates and the minimization of the distance

between the population quantiles and VaR combinations,

and concluded that optimal combinations improved VaR

performance during turbulent periods. Jeon and Taylor

(2013) also combined VaR forecasts using the so‐called

CAViaR models and implied volatility estimates through

weights estimated by quantile regression indicating the

superior performance of combination techniques. Hall

and Mitchell (2007) combined density forecasts through

minimization of the Kullback–Leibler information crite-

rion (KLIC), which minimizes the distance between the

forecasted and the true but unknown density. Alternative

combination procedures for optimally combining individ-

ual VaR models have been developed by Tsiotas (2015),

Kapetanios, Mitchell, Price, and Fawcett (2015), and

Opschoor, Van Dijk, and Van der Wel (2017), among

others, through density combination forecasting.

The literature on volatility forecasting models is vast.

The seminal papers of Engle (1982) and Bollerslev

(1986) introduced the class of generalized autoregressive

conditional heteroskedasticity (GARCH) volatility

models, which have been proved to improve forecasting

performance, while several extensions have been pro-

posed—for example, EGARCH, GJR‐GARCH, and

FIGARCH models, among others. Similarly, Engle,

Ghysels, and Sohn (2013) proposed a new class of

GARCH model, the so‐called GARCH‐MIDAS models,

which decompose volatility into a short‐run and a long‐

run component. The long‐run volatility component is a

slowly decaying function either of realized volatility or

macroeconomic variables. Another strand of the litera-

ture has explored the availability of high‐frequency data,

and several studies have shown that using realized vola-

tility measures based on intraday data improve forecast

performance (Andersen, Bollerslev, Diebold, & Labys,

2003). Under a similar perspective, Corsi (2009) proposed

the heterogeneous autoregressive models of realized vola-

tility (HAR‐RV), considering different volatility compo-

nents realized over different time horizons, which led to

good forecasting performance. However, instability in

financial markets during the global financial crisis of

2007–2009 was characterized by extreme asset price

movements and high volatility, revealing the insuffi-

ciency of the existing single volatility methods. Investors

faced extreme losses, while these losses underlined the

need for accurate volatility forecasting. The common vol-

atility models seem to provide accurate forecasts during

tranquil periods but not in turbulent periods.

The purpose of this paper is twofold. The first objective

is to combine numerous forecasting volatility models

using an exhaustive set of combination techniques.

Becker and Clements (2008) argued that combination

forecasts had the potential to generate forecasts of supe-

rior predictive ability as different models captured

FAMELITI AND SKINTZI 201