confidence limits for wavelet cross-spectra

From: Bryan K Woods <bryan.woods_at_nyahnyahspammersnyahnyah>
Date: Thu, 20 Sep 2007 16:41:18 -0400

Hi all,
I have been going over the Torrence and Compo 1998 BAMS article on
wavelets and am slightly confused about how to calculate confidence
limits for wavelet cross spectra. In their paper they say it can be done
but give instructions that confuse me. I have constructed what seems to
be work (qualitatively), but I think I could be off by some scaling
factor. Below is my function which is past two returned objects from the
wavelet function with a Morlet transform:

function cowave_ci (wx[2][*][*]:numeric,wy[2][*][*]:numeric)
local df, Px, Py, distrib, pLow, pHigh, xLow, xHigh
begin
  df = wx_at_dof
  pLow = conform(df,0.05,-1) ; confidence levels
  pHigh = conform(df,0.95,-1)
  Px = wx_at_fft_theor
  Py = wy_at_fft_theor
  distrib = True
  distrib_at_red = 3.999/2*sqrt(abs(Px*Py)) ; 3.999/2 = Zv(95%)/v from
Torrence & Compo 1998 eq. 31
  xLow = chiinv (pLow, df)/df ; lower confidence
  xHigh = chiinv (pHigh, df)/df ; upper confidence
  distrib_at_ciHigh = distrib_at_red*xHigh
  distrib_at_ciLow = distrib_at_red*xLow
 
  return (distrib)
end

Do I need to normalize by the chi-square at the end and/or is the factor
of 3.999/2 needed?

Thanks
Bryan

-- 
Bryan Woods
Dept. of Geology & Geophysics
Yale University, KGL 234
210 Whitney Ave
New Haven, CT 06511
978.726.3462 (cell)
203.432.3134 (fax)
203.404.3365 (home)
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Received on Thu Sep 20 2007 - 14:41:18 MDT

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