The goal of this paper is to estimate time-varying covariance matrices.
Since the covariance matrix of financial returns is known to change
through time and is an essential ingredient in risk measurement, portfolio
selection, and tests of asset pricing models, this is a very important
problem in practice. Our model of choice is the Diagonal-Vech version of
the Multivariate GARCH(1,1) model. The problem is that the estimation of
the general Diagonal-Vech model model is numerically infeasible in
dimensions ...
The goal of this paper is to estimate time-varying covariance matrices.
Since the covariance matrix of financial returns is known to change
through time and is an essential ingredient in risk measurement, portfolio
selection, and tests of asset pricing models, this is a very important
problem in practice. Our model of choice is the Diagonal-Vech version of
the Multivariate GARCH(1,1) model. The problem is that the estimation of
the general Diagonal-Vech model model is numerically infeasible in
dimensions higher than 5. The common approach is to estimate more restrictive
models which are tractable but may not conform to the data. Our contribution
is to propose an alternative estimation method that is numerically feasible,
produces positive semi-definite conditional covariance matrices, and does
not impose unrealistic a priori restrictions. We provide an empirical
application in the context of international stock markets, comparing the
new estimator to a number of existing ones.
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