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.sc...@auckland.ac.nz, Fax: +64 9 373 7018
Director of Consulting, Department of Statistics
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