Verification of the Identifiability Conditions in Some Nonlinear Time Series Models

This paper investigates the identifiability conditions of M-estimation for some nonlinear time series models. We present primitive conditions for the identifiability in smooth transition GARCH, nonlinear Poisson autoregressive, and multiple regime smooth transition AR models. As an unexpected result, the smooth transition GARCH model turns out not to require the familiar common root condition for the identifiability. The method for verification is anticipated to be applicable to other nonlinear models.