Asymptotics of rank order statistics for ARCH residual empirical processes

S. Ajay Chandra, Masanobu Taniguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper gives the asymptotic theory of a class of rankorder 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.

Original languageEnglish
Pages (from-to)301-324
Number of pages24
JournalStochastic Processes and their Applications
Volume104
Issue number2
DOIs
Publication statusPublished - 2003 Apr 1
Externally publishedYes

Fingerprint

Autoregressive Conditional Heteroscedasticity
Rank order
Empirical Process
Order Statistics
Statistics
Two-sample Problem
ARMA Model
Asymptotic Relative Efficiency
Autoregressive Moving Average
Asymptotic Theory
Volatility
Confidence interval
Empirical process
Autoregressive conditional heteroscedasticity
Order statistics
Robustness
Estimator

Keywords

  • ARCH model
  • Asymptotic relative efficiency
  • Confidence intervals
  • Empirical processes
  • Robustness
  • Squared residuals
  • Two-sample rank order statistics

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability

Cite this

Asymptotics of rank order statistics for ARCH residual empirical processes. / Chandra, S. Ajay; Taniguchi, Masanobu.

In: Stochastic Processes and their Applications, Vol. 104, No. 2, 01.04.2003, p. 301-324.

Research output: Contribution to journalArticle

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