Thoughts on the Connections Between Threshold Time Series Models and Dynamical Systems
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2009 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. When introducing threshold time series models some 30 years ago, Howell Tong noted possible close connections with certain dynamical systems. This idea has generated much interest and study. One such connection compares stability of dynamical systems with that of nonlinear time series. I examine this relationship, noting when their conclusions agree and identifying parallels even when they diverge.