Journal of Computational Finance

The Brownian bridge E-M algorithm for covariance estimation with missing data

William Morokoff


An algorithm is developed here to compute a maximum likelihood estimate of the covariance matrix for financial time series data for which a number of observations are unobserved or unreported. The data are returns on assets that are cumulative since the last observation of the asset, so that missing data information is included in the next reported observation. This paper describes an extension of a standard missing data method for covariance estimation - the expectation-maximization (E-M) algorithm - to handle the cumulative nature of the data through the use of a generalized Brownian bridge technique.

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