Interpretation of coherence estimates determined for time series of limited length

Abstract

Coherence of multichannel time series data has been calculated by the method of G. C. Carter and J. F. Ferrie [A Coherence and Cross Spectrum Estimation Program, Programs for Digital Signal Processing (IEEE,New York,1979), No. 2.3‐1‐18]. The properties of this statistic has been contrasted through simulation studies at known noise levels for short and long time series through a range of 40 data segments. Results at less than eight data segments are shown to be difficult to interpret; however, modest improvements in the coherence estimate can be made by adjustments indicated by these studies. A method of calculating coherence estimates through a technique referred to as frequency bin averaging is described. The results obtained are contrasted with the conventional method of Carter. Although reliable estimation of coherence for short time series data (transient data) is difficult to obtain in the conventional sense, the comparisons made should provide a basis for interpretation of coherence estimates as well as suggest corrections that may be applied to relatively short time series sequences. [Work supported by NORDA.]