Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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On Asymptotic Properties of Bootstrap for Autoregressive Processes with Regularly Varying Tail Probabilities

  • Kang, Hee-Jeong (Department of Statistics, Chonbuk National University, Chonju, Chonbuk 561-756)
  • Published : 1997.03.01
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Abstract

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

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References

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