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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

 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

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
http://www.autobox.com

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.