Publication:
Multivariate Volatility Impulse Response Analysis of GFC News Events

Loading...
Thumbnail Image
Official URL
Full text at PDC
Publication Date
2015-07
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
This paper applies the Hafner and Herwartz (2006) (hereafter HH) approach to the analysis of multivariate GARCH models using volatility impulse response analysis. The data set features ten years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index from the London Stock Exchange, from 3 January 2005 to 31 January 2015. This period captures both the Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The attraction of the HH approach is that it involves a novel application of the concept of impulse response functions, tracing the effects of independent shocks on volatility through time, while avoiding typical orthogonalization and ordering problems. Volatility impulse response functions (VIRF) provide information about the impact of independent shocks on volatility. HH’s VIRF extends a framework provided by Koop et al. (1996) for the analysis of impulse responses. This approach is novel because it explores the effects of shocks to the conditional variance, as opposed to the conditional mean. HH use the fact that GARCH models can be viewed as being linear in the squares, and that multivariate GARCH models are known to have a VARMA representation with non-Gaussian errors. They use this particular structure to calculate conditional expectations of volatility analytically in their VIRF analysis. A Jordan decomposition of Σt is used to obtain independent and identically distributed innovations. A general issue in the approach is the choice of baseline volatilities. VIRF is defined as the expectation of volatility conditional on an initial shock and on history, minus the baseline expectation that conditions on history. This makes the process endogenous, but the choice of the baseline shock within the data set makes a difference. We explore the impact of three different shocks, the first marking the onset of the GFC, which we date as 9 August 2007 (GFC1). This began with the seizure in the banking system precipitated by BNP Paribas announcing that it was ceasing activity in three hedge funds that specialised in US mortgage debt. It took a year for the financial crisis to come to a head, but it did so on 15 September 2008, when the US government allowed the investment bank Lehman Brothers to go bankrupt (GFC2). The third shock is 9 May 2010, which marked the point at which the focus of concern switched from the private sector to the public sector. A further contribution of this paper is the inclusion of leverage, or asymmetric effects. Our modelling is undertaken in the context of a multivariate GARCH model featuring pre-whitened return series, which are then analysed using both BEKK and diagonal BEKK models with the t-distribution. A key result is that the impact of negative shocks is larger, in terms of the effects on variances and covariances, but shorter in duration, in this case a difference between three and six months, in the context of the return series.
Description
For financial support, the first author wishes to thank the Australian Research Council and the second author wishes to acknowledge the Australian Research Council and the National Science Council, Taiwan. The authors are grateful to Tom Doan and Estima for helpful assistance with RATS coding.
Unesco subjects
Keywords
Citation
Baba, Y., R.F. Engle, D. Kraft and K.F. Kroner (1985), Multivariate simultaneous generalized ARCH, Unpublished manuscript, Department of Economics, University of California, San Diego, CA, USA. Black, F. (1976), Studies of stock market volatility changes, in Proceedings of the American Statistical Association, Business and Economic Statistics Section, Washington, DC, USA, 1976, pp. 177-181. Chang, C.-L. Y.-Y. Li and M. McAleer (2015), Volatility spillovers between energy and agricultural markets: A critical appraisal of theory and practice, Econometric Institute Research Paper EI2015-18, Erasmus School of Economics, Erasmus University Rotterdam. Comte, F. and O. Lieberman (2003), Asymptotic theory for multivariate GARCH processes, Journal of Multivariate Analysis, 84, 61-84. Engle, R.F. and V.K. Ng (1993), Measuring and testing the impact of news on volatility, Journal of Finance, 48, 1749-1778 Engle, R.F. and K.F. Kroner (1995), Multivariate simultaneous generalized ARCH, Econometric Theory, 11, 122-150. Drost, F. and T. Nijman (1993), Temporal aggregation of GARCH processes, Econometrica, 61, 909-927. Gallant, A.R., P.E. Rossi and G. Tauchen (1993), Nonlinear dynamic structures, Econometrica, 61, 871-907. Hafner, C.M. and H. Herwartz (2006), Volatility impulse responses for multivariate GARCH models: An exchange rate illustration, Journal of International Money and Finance, 25, 719-740. Jeantheau, T. (1998), Strong consistency of estimators for multivariate ARCH models, Econometric Theory, 14, 70-86. Koop, G., M.H. Pesaran and S.M. Potter (1996). Impulse response analysis in nonlinear multivariate models. Journal of Econometrics, 74, 119-147. Lin, W.-L. (1997), Impulse response function for conditional volatility in GARCH models, Journal of Business & Economic Statistics, 15, 15-25. McAleer, M., S. Hoti and F. Chan (2009), Structure and asymptotic theory for multivariate asymmetric conditional volatility, Econometric Reviews, 28, 422-440. Sims, C. (1980), Macroeconomics and reality, Econometrica 48, 1-48. Tauchen, G., H. Zhang, and M. Liu (1996), Volume, volatility and leverage: A dynamic analysis, Journal of Econometrics, 74, 177-208.