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Abstract:
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Estimation of time-varying covariance matrices is of great importance in the analysis of financial data and most of the multivariate GARCH models are known to break down for dimensions larger than ten or so. Orthogonal transformation is a viable method for overcoming the curse of dimensionality. It writes a p-dimensional random vector as a linear transformation of p orthogonal latent variables and then univariate GARCH models are used to model them one-at-a-time. The modi?ed Cholesky decomposition (MCD) is an important example of orthogonal transformations which sequentially orthogonalizes the variables (assets), and provides a statistically interpretable parametrization of the covariance matrix. However, it requires an order among the variables. In this paper, we propose a novel order-averaged MCD-based method for estimating covariance matrices. The ensuing methodology provides accurate covariance matrix estimation and prediction. The merits of the proposed method are illustrated through three real financial data sets of dimensions p = 12, 97, 200. Comparison with several approaches reveals the superior empirical performance of the proposed order-averaged method.
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