Abstract   We survey results on the stability of various nonlinear time series, both parametric and nonparametric.  The emphasis will be on identifying the role that the "error term" has in determining stability.  The error term can indeed affect stability, even when additive and for simple, common parametric models.  The stability of the time series is not necessarily the same as that of its related (noiseless) dynamical system.  In particular, this means that care must be taken to ensure that estimates are actually within the valid parameter space when analyzing a nonlinear time series.