Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel way of estimating models of time-varying covariances that overcome some of the computational problems and an undiagnosed incidental parameter problem which have troubled existing methods when applied to hundreds or even thousands of assets. The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method. The out of sample hedging performance of various models estimated using this method are compared.
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