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Description:
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We investigate conditions for the ergodicity of threshold autoregressive time series by embedding the time series in a general state Markov chain and apply a FosterLyapunov drift condition to demonstrate ergodicity of the Markov chain . We are particularly interested in demonstrating V uniform ergodicity where the test function V ( ) is a function of a norm on the statespace . In this dissertation we provide conditions under which the general state space chain may be approximated by a simpler system , whether deterministic or stochastic , and provide conditions on the simpler system which imply V uniform ergodicity of the general state space Markov chain and thus the threshold autoregressive time series embedded in it . We also examine conditions under which the general state space chain may be classified as transient . Finally , in some cases we provide conditions under which central limit theorems will exist for the V uniformly ergodic general state space chain . |