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Topic: How to decide if a vector process is a Gaussian Vector processes?
Replies: 1   Last Post: May 24, 2006 10:18 AM

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David Reilly

Posts: 327
Registered: 12/7/04
Re: How to decide if a vector process is a Gaussian Vector processes?
Posted: May 24, 2006 10:18 AM
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The way I look at this is ...

1. By assumption the Expected Value is zero everywhere ....thus one
might wish to test this by implementing a CHOW TEST for constancy of
parameters ....essentially computing means for two distinct groups
i.e.observations before time period t and after t . One might find a
shift in the mean thus signaling a possible change in parameters over
time .

2. If there are no statistically significicanct difference between the
before and after for ALL BREAK POINTS t then ...

3. Is the variance of the errors CONSTANT for all SUB-GROUPS and is the
variability of the errors free of any dependence on the LEVEL of the
series .

If all of these tests conclude in NON-SIGNIFICANCE and if the ACF/PACF
of the Xt process indicates randomness ...then you might be good to go

Dave Reilly
Automatic Forecasting Systems

P.S. An example of time varying parameters is as follows

for observations 1 to t/2 y(t)=.9*y(t-1)+a(t)

t/2+1 to t y(t)=-.9*y(t-1) + a(t)

OVERALL the model is y(t)=0.*y(t-1) + a(t) BUT LOCALLY this is not
true. THis is why you should ask your time series software vendor if
they challenge the assertion that all t values should be used to
identify/estimate/forecast . AFS's software (
http://www.autobox.com/freef.exe ) challenges this assertion often
yielding the conclusion that there is TOO MUCH DATA or equivalently
that the parameters have changed over time this violoating one of
Karl's (Gauss ) premises.

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