Dynamic Equicorrelation

Robert Engle and Bryan Kelly
The Stern School, New York University

ABSTRACT A new covariance matrix estimator is proposed under the
assumption that at every time period all pairwise correlations are equal.
This assumption, which is pragmati- cally applied in various areas of
finance, makes it possible to estimate arbitrarily large covariance
matrices with ease. The model, called DECO, is a special case of the CCC
and DCC models which involve first adjusting for individual volatilities
and then es- timating the correlations. DECO continues to give consistent
parameter estimates when DCC is the true model highlighting its usefulness
when the equicorrelation assumption is violated. Generalizations to block
equicorrelation structures, models with exogenous variables, and
alternative specifications to accommodate changing cross sec- tion
constituents and residual equivariance are all explored. Diagnostic tests
for the equicorrelation model are proposed. Estimation is evaluated by
Monte Carlo and on stock return data.