Evaluating the Lyapounov Exponent and Existence of Moments for Threshold AR-ARCH Models

We demonstrate a reliable and computationally feasible method for determining whether a given threshold autoregression autoregressive conditional heteroscedastic (AR-ARCH) model is ergodic, and for determining which moments exist when it is ergodic. This method may be used to delineate the parameter space of the model. We show (for an order 2 model) that the parameter space is much less constrained than commonly is assumed. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.