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Abstract:
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Estimation of covariance matrix and multivariate volatility is difficult when the dimension is high. In this study, we consider and compare various methods to estimate the covariance matrix and volatility of asset returns when the number of assets is large. The methods considered included Cholesky stochastic volatility models of Lopes, McCulloch and Tsay (2008), dynamic factor model, dynamic cross-correlation model of Engle (2002) and Tse and Tsui (2002). For general covariance matrix estimation, we consider Cholesky decomposition with penalized likelihood of Huang, Liu, Pourahmadi and Liu (2006) and methods with constrained and/or sparse principal component analysis. Applications in risk management and asset allocation are used in the comparison.
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