Nonparametric Bayesian covariance estimation with noisy and non-synchronous asset prices
The asset return covariance matrix is the key input to many problems in finance and economics. This paper presents a nonparametric Bayesian method to estimate the ex post covariance matrix from high frequency data. The proposed estimator is robust to noise independent of market microstructure and non-synchronous exchanges and has several desirable characteristics. First, pooling is used to group high frequency observations with similar covariance in order to improve the precision of the estimate. Second, the increase in data is incorporated into the synchronization to reduce the bias of non-synchronous trade. Third, it is guaranteed that the proposed estimator is positive definite. Monte Carlo simulation shows that the nonparametric Bayesian method provides more precise covariance estimates in ideal and realistic contexts. Empirical applications evaluate the proposed covariance estimator from an economic point of view and show that it offers improved out-of-sample performance compared to several classical estimators.