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Re: st: A curious arima(1,0,1) coefficient pattern


From   Robson Glasscock <glasscockrc@vcu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: A curious arima(1,0,1) coefficient pattern
Date   Fri, 16 Dec 2011 15:52:26 -0500

Hi Paul,
Did you look at the predictions from the model? It seems like the AR
and MA components are netting each other out, and i wonder what the
y_hats would therefore look like. Are the predictions systematically
close to returns in period t-1? Are they simply white noise? Something
else?

best,
Robson Glasscock

On Thu, Dec 15, 2011 at 4:54 PM, Paul Borochin <pb.stuff@gmail.com> wrote:
> I fit an arima(1,0,1) model to several time series of returns, and
> observed a pattern that I'd like to ask your help with.
> Unsurprisingly, there were some series where the model was not
> significantly meaningful, and some where it was.  However, in the
> cases where the model was most statistically significant, with the
> highest Chi-square statistic for a Wald test of overall fit, and the
> highest Z-statistics for the Phi and Theta parameters estimated, I
> very consistently got Phi=.9, and Theta =-1.0.  I got these
> coefficient estimates for several (seemingly) independent return
> series.  It occurs in different time samples, and data tests reject
> both white noise and unit root for the returns.
>
> These coefficient estimates are so consistent between return series
> that I suspect that there must be a mechanical explanation for what's
> going on.  I'm wondering if this could be the result of a
> mis-specified model, like trying to fit arima(1,0,1) to data that is
> actually arima(n,0,m).  Have you come across this sort of situation
> before, or have any idea what is causing it?
>
> Thank you,
>
> Paul
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