V-uniform ergodicity of threshold autoregressive nonlinear time series

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Title: V-uniform ergodicity of threshold autoregressive nonlinear time series
Author: Boucher, Thomas Richard
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: http : / /hdl .handle .net /1969 .1 /292
Date: 2004-09-30

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V-uniform ergodicity of threshold autoregressive nonlinear time series. Available electronically from http : / /hdl .handle .net /1969 .1 /292 .

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