Thanks to all who replied to my query.
> I have several hundred time series with an integer count value for each
day
> over a year. I want to test that the observations for a single time
series
> are independent and that the time series are independent of each other.
Can
> anyone recommend a way forward?
What sort of data is this?
If your count rate is high: consider some transformation to make
the distribution less skewed (e.g. log or sqrt). Then use the usual
tests for white-noise for each time series.
If the count rate is low, the problem is not trivial. See the
paper by Zeger in Biometrika (around 1988 I think) for a
general technique. You can also group the data into bigger
time units (weekly or monthly) to increase the count rate.
Dealing with several hundred time series won't be easy, even
when they are Gaussian. It's better to think of what sort of
non-dependence structure you expect to see, then use some
sort of Monte-Carlo method to test the observed pattern.
Good luck,
-Yudi-
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Yudi Pawitan: [log in to unmask]
Department of Statistics, UCD
Dublin 4, Ireland
Ph : 353-1-706 7641
Fax: 353-1-706 1186
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Dear Glenn,
to test for the dependence structre in time series of counts no standard
method
is available in the literature so far. I have developed a method in my
dissertation (written in German) though. To apply the method successfully
it is
of great importance to have knowlegde about the data generating process.
Basically you have to distinguish between stock type data (e.g. the number
of
people waiting at a counter sampled every x-minutes) and flow type data
(e.g.
daily mortality in a certain region or city).
If you are interested we can exchange more information (you about your data
and
I about my method).
I cannot offer a specific method to test for the independence between
different
series though.
Robert Jung
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You can do distribution-free inference using basic non-parameteric methods.
Most of this stuff was worked out in the 50s and 60s (sometimes under the
title
of order statistics.)
My favourite primer is "Nonparametric Statistical Inference" by Jean
Dickson
Gibbons ISBN 0-8247-7327-6
(Look particularly at Chap 3, 6, 12 and 13.)
SvN
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Glenn, To examine whether the observations in a singles time series are
independent, I would suggest looking at the pattern of autocorrelations.
Significant autocorrelation indicates a lack of independence. To test if
the
time series are independent of each other, I would suggest looking at the
correlation matrix and the associated eigenvalues and eigenvectors. If
there is
a significant correlation among subsets of the time series, you may want to
consider principal component analysis or factor analysis to reduce the
dimensionality of the data. Most statistical packages (SAS,SPSS,BMDP,NCSS,
etc.,) have routines to perform these types of analysis. I hope this
helps.
Dick March, Ph. D.
South Florida Water Management District
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Glenn Treacy wrote:
>
> I have several hundred time series with an integer count value for each
day
> over a year. I want to test that the observations for a single time
series
> are independent
"of each other "
This can be handled via ARIMA modelling where the autoprojective
scheme can be identified in a robust manner. Please see
http://www.autobox.com for more on ARIMA model identification.
If the final model is y = constant + a(t) where a(t) is n.i.i.d.
and that the time series are independent of each other.
Prewhitening EACH pair by an appropriate ARIMA filter will lead to
cross-correlations and impulse response weights and a model ...
which can lead to the identification of pulses,level shifts which can
give a cleaner ESTIMATION and a better test of the "causality"
regards
dave r.
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Glenn,
Runs tests are usually recommended to see whether the
observations within a series are independent. Between
series independence is another matter.
You may want to run a matrix of crosscorrelations between
the series to ascertain whether some of the series are interrelated.
Regards,
Bob Yaffee
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