Cross-spectrum Analysis - Squared Coherency, Gain, and Phase Shift

There are additional statistics that will be displayed in the complete summary spreadsheet.

Element Name Description
Squared coherency One can standardize the cross-amplitude values by squaring them and dividing by the product of the spectrum density estimates for each series. The result is called the squared coherency, which can be interpreted similar to the squared correlation coefficient (see Correlations Overview), that is, the coherency value is the squared correlation between the cyclical components in the two series at the respective frequency. However, the coherency values should not be interpreted by themselves; for example, when the spectral density estimates in both series are very small, large coherency values may result (the divisor in the computation of the coherency values will be very small), even though there are no strong cyclical components in either series at the respective frequencies.
Gain The gain value is computed by dividing the cross-amplitude value by the spectrum density estimates for one of the two series in the analysis. Consequently, two gain values are computed, which can be interpreted as the standard least squares regression coefficients for the respective frequencies
Phase shift Finally, the phase shift estimates are computed as tan-1 of the ratio of the quad density estimates over the cross-density estimate. The phase shift estimates (usually denoted by the Greek letter ψ) are measures of the extent to which each frequency component of one series leads the other.