JSM 2004 - Toronto

Abstract #300862

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Activity Number: 57
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: Business and Economics Statistics Section
Abstract - #300862
Title: Stability of Cyclic Threshold Autoregressive Time Series Models
Author(s): Thomas R. Boucher*+ and Daren B.H. Cline
Companies: Virginia Polytechnic Institute and State University and Texas A&M University
Address: Dept. of Statistics, Blacksburg, VA, 24061-0439,
Keywords: ergodicity ; Markov chain ; nonlinear time series ; threshold autoregressive time series
Abstract:

We investigate the stability of the threshold autoregressive time series model by embedding the time series in a general state Markov chain and deriving conditions under which the Markov chain, and thus the time series embedded in it, is either V-uniformly ergodic or is transient. We concentrate in particular on what we term cyclic threshold autoregressive time series models. These models exhibit asymptotic cyclic behavior, that is, the process cycles through one of a number of sets of subregions of the state space when the process is large. In this case, conditions for V-uniform ergodicity or transience of the process can be determined through analysis of the deterministic skeleton of the process. We apply stochastic drift conditions to demonstrate this. Our methods can be applied to cases where the model has multiple cycles and/or affine thresholds, thereby extending beyond current results.

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