Coherence-Based Method to Detect Time Shifts Smaller than the Sampling Rate of Time Series

摘要

The paper presents a method to evaluating the average time shift between two time series by exploiting both components of the complex-valued cross coherence function: the magnitude and the relative phase. What is new is there are detected temporal shifts smaller than the sampling interval of the series which could be useful to the timing of macro-economic indicators according to process evolution, not to the calendar day of publication. Depending on the key quantities grouped in the descriptor the method is able to detect time gaps as small as one tenth of the sampling rate. The method applies on non stationary series that are lacking long run correlations. In the paper is presented the theoretical justification of the technique, the calibration procedure, a validation test using aggregate replicas as well as how the technique could be applied onto the series of exchange rates, aggregate index BET of the Bucharest stock exchange market, and macro-economic indicators. When used to ordering the series inside groups of coherent clusters, the results should be cautiously concatenated to establishing the relative time succession among more than two series.