Coherence-based multivariate analysis of high frequency stock market values

The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need to be collected for a longer period and then they have to be detrended. An effective technique based on averaging a metric function on short subperiods of the observation horizon is suggested. Since a standard correlation-based metric is not capable of catching dependencies at different time instants, it is not expected to perform the best when dealing with high frequency data. Hence, the choice of a more suitable metric is discussed. In particular, a coherence-based metric is proposed, for it is able to detect any possible linear relation between two times series, even at different time instants. The averaging technique is employed to analyze a set of 100 high volume stocks of the New York Stock Exchange, observed during March 2008.