Influence Diagnostics for Multivariate GARCH Processes

14 Pages Posted: 14 Jun 2010

See all articles by Jonathan Dark

Jonathan Dark

University of Melbourne; Financial Research Network (FIRN)

Xibin Zhang

Monash University

Nan Qu

affiliation not provided to SSRN

Abstract

This article presents diagnostics for identifying influential observations when estimating multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models. We derive influence diagnostics by introducing minor perturbations to the conditional variances and covariances. The derived diagnostics are applied to a bivariate GARCH model of daily returns of the S&P500 and IBM. We find that univariate diagnostic procedures may be unable to identify the influential observations in a multivariate model. Importantly, the proposed curvature-based diagnostic identified influential observations where the correlation between the two series had a major change. These observations were not identified as influential using the univariate diagnostics for each asset separately. When estimating the bivariate GARCH model allowing for weights at influential observations, we found that the time-varying correlations behaved differently from that implied by the model ignoring influential observations. The application therefore highlights the importance of extending univariate diagnostic procedures to multivariate settings.

Suggested Citation

Dark, Jonathan and Zhang, Xibin and Qu, Nan, Influence Diagnostics for Multivariate GARCH Processes. Journal of Time Series Analysis, Vol. 31, Issue 4, pp. 278-291, July 2010. Available at SSRN: https://ssrn.com/abstract=1622964 or http://dx.doi.org/10.1111/j.1467-9892.2010.00662.x

Jonathan Dark

University of Melbourne ( email )

185 Pelham Street
Carlton, Victoria 3053
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Xibin Zhang

Monash University ( email )

900 Dandenong Road
Caulfield East, Victoria
Australia
61-3-99032130 (Phone)
61-3-99032007 (Fax)

HOME PAGE: http://users.monash.edu.au/~xzhang/

Nan Qu

affiliation not provided to SSRN

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