Scandinavian Working Papers in Economics

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

No 675: Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models

Tomoaki Nakatani () and Timo Teräsvirta ()
Additional contact information
Tomoaki Nakatani: Dept. of Economic Statistics, Stockholm School of Economics, Postal: P.O. Box 6501, SE-113 83 Stockholm, Sweden
Timo Teräsvirta: CREATES, School of Economics and Management, University of Aarhus, Postal: Building 1322, DK-8000 Aarhus C, Denmark

Abstract: In this article, we derive a set of necessary and sufficient conditions for positivity of the vector conditional variance equation in multivariate GARCH models with explicit modelling of conditional correlation. These models include the constant conditional correlation GARCH model of Bollerslev (1990) and its extensions. Under the new conditions, it is possible to introduce negative volatility spillovers in the model. An empirical example illustrates usefulness of having such conditions in practice.

Keywords: Multivariate GARCH; positivity constraints; conditional correlation

JEL-codes: C32; C51; G19

10 pages, First version: October 15, 2007. Revised: February 14, 2008. Earlier revisions: November 15, 1007, January 15, 2008, February 14, 2008.

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