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    V-uniform ergodicity of threshold autoregressive nonlinear time series

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    Date
    2004-09-30
    Author
    Boucher, Thomas Richard
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    Abstract
    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.
    URI
    https://hdl.handle.net/1969.1/292
    Subject
    ergodicity
    V-uniform
    nonlinear time series
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    • Electronic Theses, Dissertations, and Records of Study (2002– )
    Citation
    Boucher, Thomas Richard (2003). V-uniform ergodicity of threshold autoregressive nonlinear time series. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /292.

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