Correlation of High Frequency Financial Time Series

This study addresses three problematic issues concerning the application of the linear correlation coefficient in the high-frequency financial data domain. First, correlation of intra-day, equally spaced time series derived from unevenly spaced tick-by-tick data deserves careful treatment if a data bias resulting from the classical missing value problem is to be avoided. We propose a simple and easy to use method which corrects for frequency differentials and data gaps by updating the linear correlation coefficient calculation with the aid of covolatility weights. We view the method as a bi-variate alternative to time scale transformations which treat heteroscedasticity by expanding periods of higher volatility while contracting periods of lower volatility. Second, it is generally recognized that correlations between financial time series are unstable, and we probe the stability of correlation as a function of time for seven years of high-frequency foreign exchange rate, implied forward interest rate and stock index data. Correlations estimated over time in turn allow for estimations of the memory that correlations have for their past values. Third, previous authors have demonstrated a dramatic decrease in correlation as data frequency enters the intra-hour level (the quot;Epps effectquot;). We characterize the Epps effect for correlations between a number of financial time series and suggest a possible relation between correlation attenuation and activity rates