Re: significance of correlation of a bandpass filtered time series

tuxwink 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!?
>=20
> 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?
>=20
> Thanks in advance

If you want an answer that is not hedged around with "approimations" and =
with trying to use concepts of "degrees of freedom" where they don't =
apply, then you should think about doing some simulations where you =
generate series with no cross-dependence, but otherwise simiilar to your =
observed data, then apply exactly the same processing steps as you have =
for your data analysis until you get to the stage of looking at the =
cross-correlations. Compare what you get from the real data set and from =
the simulations in the usual way to get a significance test.

David Jones.