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For a class of asymmetric multivariate exponential volatility models we
establish the strong consistency and the asymptotic normality of the Whittle
estimator of the parameters under a variety of parameterisations that
include long-range dependence in the volatility dynamics. We contribute to
the long-memory statistical literature by establishing the convergence of
quadratic forms of vector linear processes whose innovations need not be
identically distributed and whose spectral density function might not be
factorable.We assess the finite sample properties of the estimator with a
Monte Carlo simulation and compare them with those of the the maximum
likelihood estimator, showing that in some cases they perform comparably. An
empirical application, using three market indexes (FTSE100, S\&P 500 and
Nikkei 225) suggests the potential of the model to capture the joint
dynamics of asset returns volatilities.
