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Fitting and Testing Vast Dimensional Time-Varying Covariance Models

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 which have troubled existing methods when applied to 1,000s of assets. The theory of this new strategy is developed in some detail, allowingformal 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.