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Testing for volatility interactions in the constant conditional correlation GARCH model. (English) Zbl 1190.62160
Summary: We propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation generalized autoregressive conditional heteroskedasticity (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 volatilities but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatilities 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.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M07 Non-Markovian processes: hypothesis testing
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G70 Statistical methods; risk measures
65C05 Monte Carlo methods
Software:
R
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