How to interpret the phase spectrum?
Peter Dalgaard wrote:
sdlywjl666 wrote:
Dear all,
I would like to know whether positive or negative values of the phase spectrum indicate that the time series leads or lags.
In my work, x and y have peak nearly at the same frequency,(eg:f=1/56);and the coherency is peak where f=1/56,the phase is 0.5 where f=1/56.
Can I get the conclusion that x lead y 0.5*56=28 at the frquency f=1/56?
if not,how can I compute the lag/lead by phase and frequency.
Are you referring to a particular piece of software? As far as I know, this is completely dependent on choice of notation, so the question really only makes sense in a specified context. In the cases I remember seeing (I'm no time series expert, though), the phase is an _angle_ between 0 and 2*pi or between -pi and +pi, or sometimes in degrees, but I suppose it could be scaled to (-1 , 1) or (0, 1) as well. Also lead/lag for cyclic functions is a matter of convention; in particular, there's no difference between leading and lagging by half a cycle.
Following up on Peter's comment. Different authors define the cross-covariance and hence cross-spectrum differently. Time series seems to me to be plagued by inconsistencies in definitions. There is a way out though, and when faced with different software, it is a step which should always be undertaken before any interpretation is attempted. Generate a series, a simple sinusoid will do, change the phase to generate a leading or lagged series, and see how the cospectrum looks. That is really the only infallible way of determining what the software is doing. David Scott
_________________________________________________________________ David Scott Department of Statistics The University of Auckland, PB 92019 Auckland 1142, NEW ZEALAND Phone: +64 9 923 5055, or +64 9 373 7599 ext 85055 Email: d.scott at auckland.ac.nz, Fax: +64 9 373 7018 Director of Consulting, Department of Statistics