Degeneracy of time series models: the best model is not always the correct model.
There are a number of good techniques for finding, in some sense, the best model of a deterministic system given a time series of observations. We examine a problem called model degeneracy, which has the consequence that even when a perfect model of a system exists, one does not find it using the best techniques currently available. The problem is illustrated using global polynomial models and the theory of Grobner bases.
Judd
Kevin
K
School of Mathematics and Statistics, The University of Western Australia, Nedlands, Perth, Western Australia, 6009 Australia.
Nakamura
Tomomichi
T
D000465:Algorithms; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D010825:Physics / Q000379:methods*; D013598:Systems Theory; D013997:Time Factors