Journal of Risk

Bayesian nonparametric covariance estimation with noisy and nonsynchronous asset prices

Jia Liu

  • This paper designs a Bayesian nonparametric covariance estimator by integrating the pooling method, vector moving average adjustment and synchronization with data augmentation.
  • The proposed covariance estimator is robust to microstructure noise and nonsynchronous trading and is guaranteed to be positive definite.
  • Simulation studies confirm the Bayesian nonparametric covariance estimator is very competitive with existing estimators, and empirical applications show that the proposed covariance measure enhances the economic value of volatility timing.

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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