Volatility forecasting with bivariate multifractal models

• Author: Rangan Gupta,Mark Wohar,Riza Demirer,Ruipeng Liu
• Date: 01 March 2020
• DOI: http://doi.org/10.1002/for.2619
• Published date: 01 March 2020

Received: 26 April 2017 Revised: 4 June 2019 Accepted: 5 July 2019

DOI: 10.1002/for.2619

RESEARCH ARTICLE

Volatility forecasting with bivariate multifractal models

Ruipeng Liu1Riza Demirer2Rangan Gupta3,4 Mark Wohar5,6

1Department of Finance, Deakin Business

School, Deakin University, Melbourne,

Victoria, Australia

2Department of Economics and Finance,

Southern Illinois University Edwardsville,

Edwardsville, Illinois, USA

3Department of Economics, University of

Pretoria, Pretoria, South Africa

4IPAGBusiness School, Paris, France

5College of Business Administration,

University of Nebraska at Omaha, Omaha,

Nebraska, USA

6School of Business and Economics,

Loughborough University,Loughborough,

UK

Correspondence

Mark Wohar,College of Business

Administration, University of Nebraska

at Omaha, 6708 Pine Street, Omaha, NE

68182.

Email: mwohar@unomaha.edu

Abstract

This paper examines volatility linkages and forecasting for stock and for-

eign exchange markets from a novel perspective by utilizing a bivariate

Markov-switching multifractal model that accounts for possible interactions

between stock and foreign exchange markets. Examining daily data from major

advanced and emerging nations, we show that generalized autoregressive con-

ditional heteroskedasticity models generally offer superior volatility forecasts

for short horizons, particularly for foreign exchange returns in advanced mar-

kets. Multifractal models, on the other hand, offer significant improvements for

longer horizons, consistently across most markets. Finally, the bivariate multi-

fractal model provides superior forecasts compared to the univariate alternative

in most advanced markets and more consistently for currency returns, while its

benefits are limited in the case of emerging markets.

KEYWORDS

BRICS, long memory, multifractal models, simulation-based inference, volatility forecasting

1INTRODUCTION

Forecasting volatility in financial markets is not only crit-

ical for portfolio selection, risk management and the pric-

ing of derivatives, but is also of high importance for market

regulators as volatility shocks can have significant effects

on asset prices. Consequently, a large strand of the lit-

erature has focused on modeling volatility dynamics in

financial markets in the presence of statistical anomalies

including fat tails, volatility jumps, and other nonlinear-

ities in return series. Motivated by the renewed interest

in understanding the nature of information transmissions

across financial markets post the global financial crisis,

our study examines volatility linkages and forecasting for

stock and currency markets from a novel perspective by

utilizing multifractal models within a Markov-switching

framework. This approach allows us to account for some of

the well-documented statistical anomalies including per-

sistence, long memory and structural changes in volatility,

and thus provides a parsimonious framework for forecast-

ing volatility dynamics in the presence of these statistical

anomalies. The proposed model also accounts for possi-

ble causal effects across the stock and currency markets

via a bivariate specification and provides a novel approach

to volatility forecasting when compared to the models

employed in the literature that are primarily based on

univariate specifications.

Our empirical analysis focuses on the stock and currency

markets as volatility in these markets, as witnessed during

the recent “Great Recession,” have wide repercussions on

the economy as a whole via its effect on real economic

activity and public confidence. Hence volatility forecast-

ing models geared towards currency and equity markets

can provide signals regarding the vulnerability of the econ-

omy in general, and can, in turn, help policymakers design

appropriate policies to mitigate possible negative effects of

volatility shocks on the financial system. What is impor-

tant to highlight at this stage is that movements in these

Journal of Forecasting. 2020;39:155–167. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 155