Bayesian nonparametric covariance estimation with noisy and nonsynchronous asset prices

Jia Liu

Journal of Risk

Abstract: The covariance matrix of asset returns is the key input for many problems in finance and economics. This paper introduces a Bayesian nonparametric method to estimate the ex post covariance matrix from high-frequency data. The proposed estimator is robust to independent market microstructure noise and nonsynchronous trading and has several desirable features. First, pooling is employed to cluster high-frequency observations with similar covariance to improve estimation accuracy. Second, data augmentation is incorporated in synchronization to reduce the bias from nonsynchronous trading. Third, the proposed estimator is guaranteed to be positive definite. Monte Carlo simulation shows that the Bayesian nonparametric method provides more precise covariance estimates in both ideal and realistic settings. Empirical applications evaluate the proposed covariance estimator from an economic perspective and show that it offers improved out-of-sample performance compared with several classical estimators.

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