On parameter estimation of threshold autoregressive models

  title={On parameter estimation of threshold autoregressive models},
  author={Ngai Hang Chan and Yury A. Kutoyants},
  journal={Statistical Inference for Stochastic Processes},
  • N. Chan, Y. Kutoyants
  • Published 18 March 2010
  • Mathematics
  • Statistical Inference for Stochastic Processes
This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit likelihood ratio. Furthermore, convergence of moments of the estimators is also established. The limit distribution can be computed via explicit simulations from which testing and inference for the threshold parameter can be conducted. The obtained results are… 
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1 Diffusion Processes and Statistical Problems.- 2 Parameter Estimation.- 3 Special Models.- 4 Nonparametric Estimation.- 5 Hypotheses Testing.- Historical Remarks.- References.
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1 Auxiliary Results.- 1.1 Poisson process.- 1.2 Estimation problems.- 2 First Properties of Estimators.- 2.1 Asymptotic of the maximum likelihood and Bayesian estimators.- 2.2 Minimum distance