Multivariate Mixture-of-Normals Hypothesis in Exchange Rates
35 Pages Posted: 27 Jul 2011 Last revised: 8 May 2013
Date Written: May 1, 2013
Abstract
This paper proposes methods for testing the multivariate mixture of normals hypothesis. It uses multivariate measures of integrated variance to standardize (in a matrix sense) daily returns. Because replacing the unobserved integrated covariance by its estimator introduces a finite-sample distortion, a correction is implemented to alleviate this problem. In the empirical application to foreign exchange rates, the mixture-of-normals hypothesis is soundly rejected. The rejection appears to be due to the deviations of the marginals from standard normality rather than the dependence structure being inconsistent with a normal copula. To shed more light on the joint distribution of the Euro, Dollar and Yen exchange rates, a five-equation parametric model is estimated for the bivariate standardized returns, realized volatilities and realized correlation, allowing for time-varying volatility of the realized measures as well as non-normal innovations. The model fits data well and uncovers nonlinear dependencies between return and volatility innovations.
Keywords: mixture of normals, realized covariance, continuous time models, high frequency data
JEL Classification: C12, C32, F31
Suggested Citation: Suggested Citation
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