noise in time series

David Riano <driano <at> ucdavis.edu> writes:

I have two time series. Both measure the same thing and I would like 
to determine which one is noisier.
Would it be a good measure of the noise in each time series the 
absolute lag difference?
Is this a good measure? Any other measure I could use?

You could fit an arima model and compare the residuals. It should
be could enough to get an estimate, even if I see some theoretical
problems in "measure the same thing".

Dieter

Hi,

here's a possibility!

Your problem can be restated as "given 2 observers giving 2 measures what
is their level of agreement" - the classical measure here is the Kappa (see
sec 10.5 of Categorical Data Analysis by Alan Agresti (in Ed 1 - Ed 2
should also have it!) and you can also model the situation (same section of
book).

I had a similar problem comparing time series modelled by two (or more)
different methods in my PhD some years back. I had several series so it was
a bit easier.

Obviously, it's a bit of a problem with 2 time series but if they are
sufficiently long (say 200+ obs) you could proceed as follows:

   Take k sub-sample series of length say 35+ obs.
   Then fit say about 5 different arima models to each (if you know
   seasonal adjustment X11ARIMA the 5 basic models used there are good
   options - I can't remember them!)

   You can now create a 2X2 table (method 1 X method 2) each with 5 outcome
   model types and then count the number of models falling into each cell.
   Then apply the agreement measure!

Obviously, there will be dependence across the selected series that will
not be accounted for in the outcome frequencies, but if the time series are
reasonably long this shouldn't be too bad.

good luck with it!

Gerard





                                                                           
             Dieter Menne                                                  
             <dieter.menne at men                                             
             ne-biomed.de>                                              To 
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David Riano <driano <at> ucdavis.edu> writes:

I have two time series. Both measure the same thing and I would like
to determine which one is noisier.
Would it be a good measure of the noise in each time series the
absolute lag difference?
Is this a good measure? Any other measure I could use?

You could fit an arima model and compare the residuals. It should
be could enough to get an estimate, even if I see some theoretical
problems in "measure the same thing".

Dieter

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