Correlation Estimates from Asynchronously Observed Series

In this work the performance of a number of correlation estimators are compared on uniform but asynchronously observed timeseries. Correlation estimates for a sample of main index equity indices: H225, HSI, BSE30, FTSE100, and SPX500, will be examined, contrasting the bias and efficiency of various approaches to dealing with the fact that the final end of day index levels are observed at different times during the day. Using a standard correlation estimator without correcting for asynchronicity is well known to result in downward biased estimated of correlation, and we demonstrate that while the use of longer horizon or overlapping observations reduces the bias, the resulting estimates are inefficient (i.e., they have a large standard error). It is shown that efficient estimates are produced by including lagged observations in the covariance estimate using 1-day returns, and unless the correlation is large (∼90%) these estimates are as efficient as maximum likelihood estimates. The use of lagged observations also allows one to estimate the degree of asynchronicity, and estimators for this quantity are also introduced. Estimates of the asynchronicity factor produced by maximum likelihood analysis are shown to be the most efficient out of the methods examined.