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Summary: Submitted to the Annals of Statistics
MAXIMUM LIKELIHOOD ESTIMATION FOR -STABLE
AUTOREGRESSIVE PROCESSES
By Beth Andrews, Matthew Calder and Richard A. Davis,,
Northwestern University, PHZ Capital Partners and Columbia University
We consider maximum likelihood estimation for both causal and
noncausal autoregressive time series processes with non-Gaussian -
stable noise. A nondegenerate limiting distribution is given for max-
imum likelihood estimators of the parameters of the autoregressive
model equation and the parameters of the stable noise distribution.
The estimators for the autoregressive parameters are n1/
-consistent
and converge in distribution to the maximizer of a random function.
The form of this limiting distribution is intractable, but the shape
of the distribution for these estimators can be examined using the
bootstrap procedure. The bootstrap is asymptotically valid under
general conditions. The estimators for the parameters of the stable
noise distribution have the traditional n1/2
rate of convergence and
are asymptotically normal. The behavior of the estimators for finite
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