On Tue, 24 Nov 2009, David Scott wrote:
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?
I had presumed he might be referring to R and in particular
spectrum(), whilst ignoring the footer of this and every other R-help
message. I didn't see it in any other time-series package in R (and I
had expected it to be in timsac).
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.
That's why help pages have references, and ?spectrum points you to
the definitions used. See also the MASS online complements at
http://www.stats.ox.ac.uk/pub/MASS4/VR4stat.pdf which has an example
of interpreting the phase spectrum.
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.
I'd say the best way was to read the code, but both reading the code
and interpreting the output would need an 'infallible' human
interpreter.
David Scott
--
Brian D. Ripley, rip...@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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