On variable ordination of modified Cholesky decomposition for estimating time-varying covariance matrices |
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Authors: | Xiaoning Kang Xinwei Deng Kam-Wah Tsui Mohsen Pourahmadi |
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Institution: | 1. Institute of Supply Chain Analytics and International Business College, Dongbei University of Finance and Economics, Dalian, China;2. Department of Statistics, Virginia Tech, Blacksburg, Virginia;3. Department of Statistics, University of Wisconsin-Madison, Madison, Wisconsin;4. Department of Statistics, Texas A&M University, College Station, Texas |
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Abstract: | Estimating time-varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order-averaged Cholesky-log-GARCH (OA-CLGARCH) model for estimating time-varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition. The proposed method is to transform the vector at each time as a linear transformation of uncorrelated latent variables and then to use simple univariate GARCH models to model them separately. But the modified Cholesky decomposition relies on a given order of variables, which is often not available, to sequentially orthogonalize the variables. The proposed method develops an order-averaged strategy for the Cholesky-GARCH method to alleviate the effect of order of variables. The merits of the proposed method are illustrated through simulations and real-data studies. |
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Keywords: | ensemble estimate multivariate time series order of variables |
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