Proximity-Structured Multivariate Volatility Models

In many multivariate volatility models, the number of parameters increases faster than the cross-section dimension, hence creating a curse of dimensionality problem. This paper discusses specification and identification of structured parameterizations based on weight matrices induced by economic proximity. It is shown that structured specifications can mitigate or even solve the curse of dimensionality problem. Identification and estimation of structured specifications are analyzed, rank and order conditions for identification are given and the specification of weight matrices is discussed. Several structured specifications compare well with alternatives in modelling conditional covariances of six returns from the New York Stock Exchange