Journal of Financial Econometrics Advance Access originally published online on September 8, 2009
Journal of Financial Econometrics 2009 7(4):373-411; doi:10.1093/jjfinec/nbp013
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Modeling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model
Queensland University of Technology
Aarhus University
Address correspondence to Annastiina Silvennoinen, School of Economics and Finance, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia, or e-mail: silvennoinen{at}qut.edu.au
JEL Classification: C12, C32, C51, C52, G1
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Abstract |
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In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.
KEYWORDS: constant conditional correlation, dynamic conditional correlation, multivariate GARCH, return comovement, variable correlation GARCH model, volatility model evaluation
This research has been supported by the Jan Wallander and Tom Hedelius Foundation, Grants J03-41 and P2005-0033:1, the Danish National Research Foundation, OP Bank Group Research Foundation, The Foundation for Promoting Finnish Equity Markets, and Yrjö Jahnsson Foundation, and University of Technology Sydney, Faculty of Business Research Grant 2007. We would like to thank Pierre Giot and two anonymous referees for valuable comments, and Robert Engle for providing us with the data for the first application. Part of the work was done when the first author was visiting CORE, whose kind hospitality is gratefully acknowledged. Our special thanks go to Luc Bauwens for making the visit possible. The visit was financially supported by a Marie Curie Fellowship. Material from this paper has been presented at the Conference on Multivariate Modeling in Finance and Risk Management, Sandbjerg Manor, Denmark, June 2006; the Econometric Society Australasian Meeting, Alice Springs, July 2006; Conference on Multivariate Volatility Modelling, Faro, Portugal, October 2007; and in seminars at Université catholique de Louvain, Louvain-la-Neuve, Cracow University of Economics, WISE, Xiamen University, Ente Einaudi, Rome, and CREATES, University of Aarhus. Comments of participants in these occasions are gratefully acknowledged. The responsibility for any errors and shortcomings in this paper remains ours.
Received January 18, 2008; revised December 18, 2008; accepted July 29, 2009