Non‐linear GARCH models for highly persistent volatility

Summary  In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persistent volatility. The underlying idea is that high persistence in conditional variance is related to relatively infrequent changes in regime, which can be captured by a suitable specification of the new model. Using the theory of Markov chains, we provide sufficient conditions for the stationarity and existence of moments of various smooth transition GARCH models and even more general nonlinear GARCH models. An empirical application to an exchange rate return series demonstrates the differences between the new model and conventional GARCH models.