A Simple Asymptotic Analysis of Residual-Based Statistics

E. Andreou, B.J.M. Werker

Research output: Working paperDiscussion paperOther research output

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Abstract

What s the asymptotic null distribution of a rank-based serial autocorrelation test applied to residuals of an estimated GARCH model?What s the limiting distribution of estimated ACD parameters applied to the residuals of some first-stage modelling procedure?This paper addresses the often occurring situation in econometrics of applying standard statistics to residuals instead of innovations.The paper provides a simple and unified way of calculating the necessary adjustment in the limiting distribution, be it of tests or estimators. On the technical side, we also provide a novel approach to this problem using Le Cam s theory of convergence of experiments (in this paper restricted to Gaussian shift experiments).The resulting formula is simple and the regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages29
Volume2003-118
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-118

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Asymptotic Analysis
Statistics
Limiting Distribution
GARCH Model
Null Distribution
Econometrics
Regularity Conditions
Autocorrelation
Asymptotic distribution
Experiment
Adjustment
Estimator
Necessary
Modeling
Innovation
Standards

Keywords

  • statistics
  • estimation
  • ranking

Cite this

Andreou, E., & Werker, B. J. M. (2003). A Simple Asymptotic Analysis of Residual-Based Statistics. (CentER Discussion Paper; Vol. 2003-118). Tilburg: Econometrics.
Andreou, E. ; Werker, B.J.M. / A Simple Asymptotic Analysis of Residual-Based Statistics. Tilburg : Econometrics, 2003. (CentER Discussion Paper).
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Andreou, E & Werker, BJM 2003 'A Simple Asymptotic Analysis of Residual-Based Statistics' CentER Discussion Paper, vol. 2003-118, Econometrics, Tilburg.

A Simple Asymptotic Analysis of Residual-Based Statistics. / Andreou, E.; Werker, B.J.M.

Tilburg : Econometrics, 2003. (CentER Discussion Paper; Vol. 2003-118).

Research output: Working paperDiscussion paperOther research output

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Andreou E, Werker BJM. A Simple Asymptotic Analysis of Residual-Based Statistics. Tilburg: Econometrics. 2003. (CentER Discussion Paper).