Recursive MEWMA Projections of Conditional Covolatilities in Large Portfolios

Dynamic predictions of large dimensional conditional covariance matrices are considered in the context of large financial portfolios. Since numerically simple prediction methods are usually recommended for multivariate conditional covariances (covolatilities), one prefers in this paper the multivariate EWMA (exponentially weighted moving average) processes extending the recursive estimation of EWMA processes to the multivariate case. Moreover, various modifications of recursive MEWMA projections are suggested to improve the quality of covolatility projections. An extensive numerical study for real stock indices portfolios compares types of covolatility projections employing various criteria and tests.