The Annals of Applied Probability · 1991 · 72 citations · 0 references
Natural SciencesMathematicsDynamical SystemsStochastic ProcessesTime Series AnalysisErgodic TheoryAutoregressive ProcessesErgodic ProcessesErgodic PropertiesErgodicityErgodicity ConditionsThreshold AutoregressionThreshold Autoregressive Models
This paper establishes a necessary and sufficient condition for geometrical ergodicity for the general first-order threshold autoregressive processes. This is achieved by investigating the nonlinear dynamic behavior generated by the delay parameter of a threshold model. The ergodic region turns out to be unbounded which is different from that of a linear process.