Colloquium
The Department of Statistics
presents
Daren Cline
Texas A&M University
Verifying the Stability of
Nonlinear Time Series
Abstract
Fitting nonlinear time series models has become quite popular
recently. However, the stability of such models is still only partly
understood. This is particularly true for generally defined models such
as may be fit nonparametrically, say
Et = a(Et-1,..., Et-p)+et
Among the first to study general models, K.C. Chan and H. Tong showed that
if the autoregression function a(.) is sufficiently smooth then stability
of the time series is essentially equivalent to stability of the
associated noiseless dynamical system. This, however, does not include
the popular threshold or threshold-like models when pĀ1.
We provide new conditions, both for stability and for non
stability,
which apply more generally and which open the door for further research.
We present new examples and extend many old ones and show that the time
series and its associated dynamical system need not have the same
conditions for stability.
Monday, March 16, 1998
4:10 P.M., 1070 CEB (Duncan Hall)
4:00 P.M.: Coffee, 1044 CEB
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