Measuring Similarity between Trend Behaviors of Multivariate Time Series

We propose a novel approach for estimating the similarity between the trends of two time series, which has been an important problem in the fields of finance, economics and econophysics. We introduce the exit-time correlation (EC) to measure this similarity based on the exit-time method recently used as inverse statistics in financial time series analysis. We use a phase-noise induced Fourier transform method to illustrate the efficiency of our approach compared with the multiscale cross correlation method. The exit-time correlation serves as the inverse statistics for the multiscale cross correlation in analyzing correlation between multivariate time series. The application of our approach to high-frequency foreign exchange rates reveals that the exit-time correlation is related to time organization structure in interactions with a long-range time scale