How do I compute significance levels for the wavelet phase difference of two time series?
The phase angle should be distributed “uniformly” between -180° and +180°. You can’t really do a significance test since there is no “preferred” value (e.g. for wavelet power the preferred value is the background spectrum). But what you can do is a “confidence interval” about your actual phase differences. If the 95% confidence interval doesn’t overlap zero, then you can be confident that the phase difference is significant. By the Central Limit Theorem, if X1, X2,… are independent random variables with finite mean m and variance s2, then the average of X1 + X2 + … + Xn is normally distributed with mean m and variance s2/n. The uniform distribution for the interval [a,b] has m=0.5(a+b) and s2=(b-a)2/12. By the Central Limit Theorem, the average of n phase angles (interval [-Pi,+Pi]) is normally distributed with m=0 and s2=4 Pi2/12n. The 95% confidence interval for the average of n phase angles is ±1.96 s = ±1.96 (2 Pi) (12n)-½. In degrees this is ±204° n-½. Despite the above di
