How important is the AR1 coefficient for WTC significance levels?

The definition of Wavelet coherence (WTC) effectively normalizes by the local power in time frequency space. Therefore WTC is very insensitive to the noise colour used in the null-hypothesis (see Grinsted et al. 2004). It can easily be demonstrated by example:

figure('color',[1 1 1])
set(gcf,'pos',get(gcf,'pos').*[1 .2 1 2]) %make high figure
X=randn(200,1);
Y=randn(200,1);
subplot(3,1,1);
orig_arcoefs=[ar1(X),ar1(Y)]
wtc(X,Y)
subplot(3,1,2);
X2=smooth(X,7);
Y2=smooth(Y,5);
smoothed_arcoefs=[ar1(X2),ar1(Y2)]
wtc(X2,Y2) %make the input data more red, by moving averages of the data.
subplot(3,1,3);
wtc(X2,Y2,'ar1',[0 0]) %Test the red series against white noise.

orig_arcoefs =
     0.024317    -0.096152
smoothed_arcoefs =
      0.85183      0.77571

The three figures are very similar.