Statistica Sinica 11(2001), 273-287
Abstract: In this paper we provide conditions for nonlinear time series to be geometrically explosive with positive probability. The paper complements earlier work by the authors on geometrically ergodic nonlinear time series, showing that the conditions for examples in the earlier paper are sharp. We also study the transience of polynomial autoregression models.
Key words and phrases: Markov chain, nonlinear time series, transience.