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Asymptotics of rank order statistics for ARCH residual empirical processes

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  • Chandra, S. Ajay
  • Taniguchi, Masanobu

Abstract

This paper gives the asymptotic theory of a class of rank order statistics {TN} for two-sample problem pertaining to empirical processes based on the squared residuals from two classes of ARCH models. An important aspect is that, unlike the residuals of ARMA models, the asymptotics of {TN} depend on those of ARCH volatility estimators. Such asymptotics provide a useful guide to the reliability of confidence intervals, asymptotic relative efficiency and ARCH affection. We consider these aspects of {TN} for some ARCH residual distributions via numerical illustrations. Moreover, a measure of robustness for {TN} is introduced. These studies help to highlight some important features of ARCH residuals in comparison with the i.i.d. or ARMA settings.

Suggested Citation

  • Chandra, S. Ajay & Taniguchi, Masanobu, 2003. "Asymptotics of rank order statistics for ARCH residual empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 301-324, April.
    • Handle: RePEc:eee:spapps:v:104:y:2003:i:2:p:301-324
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    References listed on IDEAS

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    1. S. Chandra & Masanobu Taniguchi, 2001. "Estimating Functions for Nonlinear Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 125-141, March.
    2. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
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