A multivariate positive definite estimator of the integrated covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model where microstructure noise is interpreted as measurement error, and asynchronous trading as missing observations...

Motivated by the need of an unbiased and positive-semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra-high-frequency asset prices in a state-space framework with missing data. We then estimate the covariance matrix of the latent states...

We propose a Bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes (RUP) introduced in Muliere et al. (2000). The estimated default probability becomes our prior information in a parametric model for the prediction of the...