Scandinavian Working Papers in Economics

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

No 649: Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model

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

Abstract: In this paper we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation GARCH model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that model in which volatility is modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the model. Monte Carlo experiments show that the proposed test has satisfactory finite sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables.

Keywords: Multivariate GARCH; Volatility interactions; Lagrange multiplier test; Monte Carlo simulation; Conditional correlations

JEL-codes: C12; C32; C51; C52; G19

21 pages, First version: January 5, 2007. Revised: May 4, 2008. Earlier revisions: January 24, 2007, May 7, 2007, May 4, 2008.

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