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Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation
Type
working paper
Date Issued
2012
Author(s)
Abstract
Motivated by the need for 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 through a Kalman smoother and Expectation Maximization (KEM) algorithm. In the expectation step, by means of the Kalman filter with missing data, we reconstruct the smoothed and synchronized series of the latent price processes. In the maximization step, we search for covariance matrices that maximize the expected likelihood obtained with the reconstructed price series. Iterating between the two EM steps, we obtain a KEM-improved covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive-semidefinite by construction.
Extensive Monte Carlo simulations show the superior performance of the KEM estimator over several alternative covariance matrix estimates introduced in the literature. The application of the KEM estimator in practice is illustrated on a 10-dimensional US stock data set.
Extensive Monte Carlo simulations show the superior performance of the KEM estimator over several alternative covariance matrix estimates introduced in the literature. The application of the KEM estimator in practice is illustrated on a 10-dimensional US stock data set.
Language
English
Keywords
High frequency data
Realized covariance matrix
Market microstructure noise
Missing data
Kalman filter
EM algorithm
Maximum likelihood
HSG Classification
contribution to scientific community
HSG Profile Area
SEPS - Quantitative Economic Methods
Refereed
No
Publisher
SEPS Working Paper Series
Publisher place
St. Gallen
Subject(s)
Division(s)
Eprints ID
209167