Re: Find a period in multiple delayed time series

"Rusty" <rusty@xxxxxxxxxxxxxxx> wrote in message news:<d98fn0$ah$1@xxxxxxxxxxxxxxxxxxxx>...
> <Martin.Camitz@xxxxxxxxx> wrote in message
> news:1119257325.305081.169480@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > Hi!
> >
> > I'm a beginnner to time series analysis and I was wondering what
> > techniques there are for analysing multiple time-series with the same
> > period. In particular, if the time span of the data is shorter than the
> > expected period, is there a way to retrieve the period if you have
> > several time series and there is a delay (unknown or known) between
> > them?
>
> The most standardized technique is linear prediction. The series will all
> satisfy the same linear equation x(k+2) = a.x(k+1) + b.x(k) + error(k+2).
> So finding the period reduces to finding best values for fixed coefficients
> a and b. This might involve some initial principle component analysis to
> get rid of any white noise.
>
> Search on the web for Pisarenko, Prony, Burg algorithms or in IEEE
> Transaction on Signal Processing over that last three decades. This will
> reveal many hundreds if not thousands of theoretical and mathematical
> papers, perhaps rather fewer practical ones.
>
>
> rusty

Thanks to the both of you!

The data is on the incidence in Hepathitis among injectionists in a
few cities in Sweden. We expect there is a natural immunity-based
spike-like periodicity of around 10 years. We have data for 11 years
:) and it's not very good to tell you the truth. There are unknown
delays between symptoms and report, but that's not the issue, at least
not for the time being. You can't see the period in this data but you
can see one eruption in each city and a clear delay due to geography.

That's basically it. I'll follow the trails you have provided and see
how I do, unless you can give me a short cut based on this new info.

Really appreciate you help!

Martin
.

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