Re: significance of correlation of a bandpass filtered time series

On Apr 14, 11:45=A0am, tuxwink <soc...@[EMAIL PROTECTED]
> wrote:
> I want to compare two different time series A and B. Both were
> bandpass filtered by applying transformations in spectral domain. I
> just set some Fourier coefficients to zero and retransformed it to
> time series. Now I want to calculate the significance levels for the
> correlation of A with B, but I don't know how!?
>
> Significance levels for a correlation coefficient depend on the number
> of degrees of freedom. Which is for an independent sample (N-2). In my
> case the data is dependent, which means that the number of time steps
> is bigger than N, with N being the equivalent sample size. How were
> the degrees of freedom reduced by my transformation? What is the size
> of N?
>
> Thanks in advance

Perhaps some reading on cross-correlations with time series might be
in order..

http://secamlocal.ex.ac.uk/people/staff/dbs202/cat/stats/corr.html

You might construct an ARMA filter for the first of the series
(suitably differenced ) and use it to pre-filter both stationary
series thus yielding pre-whitened cross-correlations which can be
useful in concluding about the correlative structure in the original
series.

Then do the same thing using the ARMA filter for the second series.

hope this helps

Dave Reilly
Automatic Forecasting Systems
http://www.autobox.com

P.S. There is a FREEWARE PROGRAM called (appropriately) Freefore which
performs this exercise ..
http://www.autobox.com/freef.exe