Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 577: Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations

Annastiina Silvennoinen () and Timo Teräsvirta ()
Additional contact information
Annastiina Silvennoinen: School of Finance and Economics, Postal: Queensland University of Technology, Faculty of Business, Brisbane, Australia
Timo Teräsvirta: CREATES, Aarhus University, Postal: Building 1322, DK-8000 Aarhus, Denmark

Abstract: In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The approach adopted here is based on the decomposition of the covariances into correlations and standard deviations. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to an endogenous or exogenous transition variable. An LM test is derived to test the constancy of correlations and LM and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the Standard & Poor 500 stock index completes the paper. The model is estimated for the full five-dimensional system as well as several subsystems and the results discussed in detail.

Keywords: Multivariate GARCH; Constant conditional correlation; Dynamic conditional correlation; Return comovement; Volatility model evaluation

JEL-codes: C12; C32; C51; C52; G10

38 pages, First version: January 7, 2005. Revised: October 1, 2005. Earlier revisions: October 1, 2005.

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