Thoughts on the connections between threshold time series models and dynamical systems

Daren B.H. Cline

Abstract   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.

This paper will appear in Exploration of a Nonlinear World: An Appreciation of Howell Tong's Contributions to Statistics K.S. Chan, ed., (2009).  Please click on my name to email a request for a preprint.