Thanks you! I should have realized that without explicitly engaging some form of averaging (which raises a windowing question) that the coh is always 1. On 7/12/2011 4:48 AM, Rolf Turner wrote:
On 12/07/11 09:04, Joseph Park wrote: Greetings, I would like to estimate a spectral coherence between two timeseries. The stats : spectrum() returns a coh matrix which estimates coherence (squared). A basic test which from which i expect near-zero coherence: x = rnorm(500) y = rnorm(500) xts = ts(x, frequency = 10) yts = ts(y, frequency = 10) gxy = spectrum( cbind( xts, yts ) ) plot( gxy $ freq, gxy $ coh ) yields a white spectrum of 1. Clearly i'm not using this correctly... or i mis-interpret the coh as a cross-spectral density estimate of coherence |Gxy|^2/(Gxx Gyy) Thanks in advance! By default spectrum() calls spec.pgram() with spans=NULL. The result is that it calculates the coherence between x and y as |I_{xy}(omega)|^2 / (I_{xx}(omega) * I_{yy}(omega)) where I_{xy}() is the cross periodogram and I_{xx}() and I_{yy}() are the respective periodograms. This quantity will indeed be identically 1 --- see equation 10.1 in Bloomfield, second ed., page 203. It would be nice if the help on spectrum mentioned this. According to Bloomfield what is needed is not the periodograms but rather estimated spectra, smoothed versions of the periodograms, s_{xy}() etc. Equation 10.4 in Bloomfield, second ed., page 206 indicates that the spectral estimates satisfy an *inequality* |s_{xy}(omega)|^2 <= s_{xx}(omega) * s_{yy}(omega) whence the coherence is always between 0 and 1. To resolve the problem you need to specify the spans argument in the call to spectrum, e.g. gxy <- spectrum(cbind(xts,yts),spans=c(5,7)) HTH cheers, Rolf Turner ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.