Volatility spillover from the US to international stock markets: A heterogeneous volatility spillover GARCH model

• Published date: 01 April 2018
• Author: Zhiyuan Pan,Chongfeng Wu,Yudong Wang
• Date: 01 April 2018
• DOI: http://doi.org/10.1002/for.2509

Received: 26 April 2017 Revised: 3 November 2017 Accepted: 2 December 2017

DOI: 10.1002/for.2509

RESEARCH ARTICLE

Volatility spillover from the US to international stock

markets: A heterogeneous volatility spillover GARCH model

Yudong Wang1Zhiyuan Pan2Chongfeng Wu3

1School of Economics and Management,

Nanjing University of Science and

Technology,Nanjing 210094, China

2Institute of Chinese Financial Studies,

Southwestern University of Finance and

Economics, Collaborative Innovation

Center of Financial Security, Chengdu

611130, China

3Antai College of Economics and

Management, Shanghai Jiao Tong

University, China

Correspondence

Zhiyuan Pan, Institute of Chinese

Financial Studies, Southwestern

University of Finance and Economics,

Collaborative Innovation Center of

Financial Security, Liutai Avenue555,

Wenjiang District, Chengdu 611130,

China.

Email: panzhiyuancd@126.com

Funding information

National Natural Science Foundational of

China, Grant/AwardNumber: 71501095,

71722015, 71601161 and 71320107002

Abstract

A recent study by Rapach, Strauss, and Zhou (Journal of Finance, 2013, 68(4),

1633–1662) shows that US stock returns can provide predictive content for

international stock returns. We extend their work from a volatility perspective.

We propose a model, namely a heterogeneous volatility spillover–generalized

autoregressive conditional heteroskedasticity model, to investigate volatility

spillover. The model specification is parsimonious and can be used to analyze

the time variation property of the spillover effect. Our in-sample evidence shows

the existence of strong volatility spillover fromthe US to five major stock markets

and indicates that the spillover was stronger during business cycle recessions in

the USA. Out-of-sample results show that accounting for spillover information

from the USA can significantly improvethe forecasting accuracy of international

stock price volatility.

KEYWORDS

BEKK-GARCH, business cycle, forecasting, HVS-GARCH, volatility spillover

1INTRODUCTION

Modeling and forecasting volatility is an important issue in

financial economics. Volatility has important implications

for option pricing, ass et allocation, and risk management.

Volatility spillover is of particular interest to academics.

Our goal is to investigate the time-varying volatility

spillover effects from the US to international stock mar-

kets. We find significant volatility spillover from both

in-sample and out-of-sample perspectives.

We propose a model to investigate the role of

volatility spillover, namely a heterogeneous volatility

spillover–generalized autoregressive conditional het-

eroskedasticity model (HVS-GARCH). The idea comes

from the component GARCH-type models of Engle and

Rangel (2008) and Engle, Ghysels, and Sohn (2013), which

decompose daily volatility into two components such that

the conditional volatility is the product of these two com-

ponents. As the exact consistency, the first component in

our model that captures the persistence in the volatility of

the financial asset of interest follows a standard GARCH

process (Bollerslev, 1986). However, the second compo-

nent accounting for the volatility spillover is described

using a regression that takes the lagged daily, weekly, and

monthly volatility of another asset as the explanatory vari-

ables. The idea originates from the seminal heterogeneous

autoregressive model of realized volatility (HAR-RV) of

Corsi (2009). The HAR-RV model is a predictive regres-

sion that uses past realized volatility over three horizons

as the predictors of current realized volatility. Although

Journal of Forecasting. 2018;37:385–400. wileyonlinelibrary.com/journal/for Copyright © 2018 John Wiley & Sons, Ltd. 385

386 WAN G ETAL.

the specification is simple, it is found to reproduce some

important stylized facts in volatility research such as long

memory and multiscaling behavior.

In the literature, the BEKK-GARCH (Engle & Kroner,

1995) and VAR-GARCH (Ling & McAleer, 2003; McAleer

& Da Veiga, 2008) are the most popular models used

to analyze volatility spillover. The superiority of our

HVS-GARCH over these two models is in two dimensions.

First, it is much more parsimonious and therefore suffers

less from estimation error. This is particularly important

for out-of-sample forecasting because the parameters need

to be estimated hundreds of times with the in-sample esti-

mation period moving forward during the forecasting pro-

cedure. A sophisticated model with high estimation error

is more likely to result in a worse forecasting outcome.

Second, our HVS-GARCH can capture the time variation

property of spillover effects. It is unlikely that the volatil-

ity spillover is strong and constant over time. However,

one cannot observe changes in spillover effects from the

popular bivariate GARCH models.

We first compare the performance of HVS-GARCH

with BEKK-GARCH and VAR-GARCH using a simula-

tion study. Model performance is evaluated by assess-

ing how far the model-implied conditional volatility is

from the true volatility. We consider data-generating

processes (DGPs) with both strong and weak spillover

effects. Our results show that HVS-GARCH is much more

robust to model misspecification than the two popular

bivariate models. This feature has important implications

for volatility forecasting because the true joint dynam-

ics between US and international market volatility are

unknown and model misspecification is considered a

major source of forecasting loss.

Our empirical analysis extends the recent work of

Rapach, Strauss, and Zhou (2013), which finds that US

stock returns can predict international stock returns. We

revisit the predictive content of US market information

from the volatility perspective. Using daily stock price data

for the US and five major international markets covering

the period from January 1991 to December 2015, we find a

strong role for the US stock market as a source of volatility

information. The spillover effect displays countercyclical

behavior: it becomes stronger when the real US business

cycle changes from expansion to recession.

We now turn to out-of-sample analysis. We com-

pare the out-of-sample forecasting performance of our

HVS-GARCH and two existing bivariate models. The sim-

ple univariate volatility models without spillover effects

are also considered to investigate whether US volatility

information is helpful in improving the out-of-sample

forecasting accuracy for international marketvolatility. We

use two popular loss functions—mean squared predic-

tive error and mean absolute predictive error—to assess

forecasting accuracy and the statistical test of Diebold and

Mariano (1995) and West (1996) to examine whether the

difference in loss functions for HVS-GARCH and each

of the alternative models is significant. Our results show

that HVS-GARCH can significantly beat the univariate

volatility models, suggesting that accounting for volatility

spillover can generate more accurate forecasts. However,

the usefulness of spillover effects for improving fore-

casting performance disappears when BEKK-GARCH or

VAR-GARCHis used. Whether either of these two models

works better than simple univariate models is indetermi-

nate and depends on the evaluation criterion of the loss

function and the country. Of course, HVS-GARCH per-

forms significantly better than the BEKK and VARmodels.

Next, forecasting accuracy is evaluatedduring two reces-

sion periods. The first recession period is from April 2001

to November 2001, and the second is from January 2008 to

June 2009. We find that the superior predictive ability of

HVS-GARCH over the volatility models without spillover

effects is more prominent when the US economy is in

recession. A plausible explanation is that the volatility

spillover is stronger during these two periods.

Thus far, our out-of-sample analysis has focused on

1-day-ahead volatility forecasting. We now extend our

forecasting analysis to longer horizons. We consider

20-day-ahead forecasting and find highly consistent evi-

dence for the significantly superior performance of

HVS-GARCH over its competitors.

Rapach et al.'s (2013) explanation for the lead–lag rela-

tionship between US and international stock returns can

also be applied to volatility spillover. They consider infor-

mation frictions that cause certain shocks to adjust more

slowly to economy-wide information. Many investors pay

attention to particular segments of the stock market

(Corwin & Coughenour, 2008; Hong, Tu, & Zhou, 2007).

These information-processing limitations imply that infor-

mation from certain segments diffuse to the broader mar-

ket slowly.Rapach et al. argue that because the US market

is the largest in the world investors focus more intently on

it. Therefore, the information reflecting the economic fun-

damentals of global stock markets diffuses from the US to

other countries' markets, creating the volatility spillover.

This paper is related to a growing number of papers

on volatility spillover in stock markets (see, e.g., Barunik,

Krehlik, & Vacha, 2016; Bonato, Caporin, & Ranaldo,

2013; Buncic & Gisler, 2016; Dean, Faff, & Loudon,

2010; Eun & Shim, 1989; Fengler & Gisler, 2015; Hamao,

Masulis, & Ng, 1990; Lin, Engle, & Ito, 1994). Most

of these studies, except for Bonato et al. (2013) and

Buncic and Gisler (2016), are limited to in-sample evi-

dence concerning the presence or absence of volatil-

ity spillover but do not give out-of-sample results. It is

widely accepted that good in-sample performance does