The Gerber Statistic : A Robust Measure of Correlation

We introduce the Gerber statistic, a robust measure of correlation. The statistic extends Kendall's Tau by counting the proportion of simultaneous co-movements in series when their amplitudes exceed data-dependent thresholds. This is unlike the standard Pearson correlation that is sensitive to outliers or the Spearman correlation that relies on ranking observations. Since the statistic is neither affected by extremely large or extremely small movements, it is especially suited to financial time series since these can exhibit extreme movements as well as a great amount of noise. Therefore, the statistic can advantageously be converted into a robust estimate of a covariance matrix that is suitable for portfolio optimization