Nonlinear GARCH Models for Highly Persistent Volatility1

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. Empirical applications to two exchange rate return series demonstrate the differences between the new model and conventional GARCH models. We would like to thank Mika Meitz for useful comments. The usual disclaimer applies. Financial support from the Research Unit of Economic Structures and Growth (RUESG) in the University of Helsinki, the Yrjö Jahnsson Foundation, and the European Comission under the Training and Mobility of Researchers Programme is gratefully acknowledged. Part of this research was done while the first author was visiting the Institute of Statistics and Econometrics at the Humboldt University in Berlin, whose hospitality is gratefully acknowledged.