Combining multivariate volatility forecasts using weighted losses

• Published date: 01 July 2020
• Date: 01 July 2020
• DOI: http://doi.org/10.1002/for.2647
• Author: Adam Clements,Mark Bernard Doolan

Received: 11 December 2018 Revised: 18 November 2019 Accepted: 2 January 2020

DOI: 10.1002/for.2647

RESEARCH ARTICLE

Combining multivariate volatility forecasts using weighted

losses

Adam Clements Mark Bernard Doolan

School of Economics and Finance,

Queensland University of Technology,

4001 Qld, Brisbane, Australia

Correspondence

Mark Bernard Doolan School of

Economics and Finance Queensland

University of Technology Brisbane, 4001

Qld, Australia.

Email: m.doolan@qut.edu.au

The ability to improve out-of-sample forecasting performance by combining

forecasts is well established in the literature. This paper advances this literature

in the area of multivariate volatility forecasts by developing two combination

weighting schemes that exploit volatility persistence to emphasise certain losses

within the combination estimation period. A comprehensive empirical analysis

of the out-of-sample forecast performance across varying dimensions, loss

functions, sub-samples and forecast horizons show that new approaches

significantly outperform their counterparts in terms of statistical accuracy.

Within the financial applications considered, significant benefits from com-

bination forecasts relative to the individual candidate models are observed.

Although the more sophisticated combination approaches consistently rank

higher relative to the equally weighted approach, their performance is statisti-

cally indistinguishable given the relatively low power of these loss functions.

Finally, within the applications, further analysis highlights how combination

forecasts dramatically reduce the variability in the parameterof interest, namely

the portfolio weight or beta.

KEYWORDS

combination forecasts, forecast evaluation, model confidence set, multivariate volatility

JEL CLASSIFICATION

C22G00

1INTRODUCTION

Combination forecasts have a long record of success in

the forecasting literature. The seminal study of Bates and

Granger (1969) demonstrated how even simple combina-

tion forecasts could produce lower mean squared forecast

errors than the set of candidate models on which they were

based. The intuition being that the combination forecast

reduces forecast errors as the errors from the candidate

models are not perfectly correlated. Essentially, this is the

same intuition that underpins the diversification benefit

that permeates modern finance theory. Subsequent

research has sought to develop more sophisticated tech-

niques for generating optimal combination forecasts, see

Clemen (1989) and Timmerman (2006) for a detailed

summary of this literature. Interestingly,the work on com-

bination forecasts gave rise to the ‘Combination Puzzle’

where many of the approaches developed could not out-

perform a simple equally weighted average of forecasts.

Smith and Wallis (2009) investigated this puzzle and

highlighted how ex-ante forecasting benefits from restric-

tions on the estimated weights, such as equal weighting,

as there is no gain to estimating optimal combination

weights when the variance of forecasts errors are similar.

This paper contributes to the literature by proposing

two new approaches for estimating forecast combination

weights. Specifically, this paper develops a ‘time’ and a

‘state’ dependent combination approach that are capable

© 2020 John Wiley & Sons, Ltd. Journal of Forecasting. 2020;39:628–641.

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