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

From   Paul Borochin <>
Subject   st: A curious arima(1,0,1) coefficient pattern
Date   Thu, 15 Dec 2011 16:54:09 -0500

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,

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