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Testing for reduction to random walk in autoregressive conditional heteroskedasticity models

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  • Claudia Klüppelberg
  • Ross A. Maller
  • Mark van de Vyver
  • Derick Wee

Abstract

The autoregressive--ARCH (AR--ARCH) and autoregressive--GARCH (AR--GARCH) models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalized versions of the AR--ARCH(1) and AR--GARCH(1,1) models, and, under mild assumptions, calculate the asymptotic distributions of pseudo-likelihood ratio statistics for testing hypotheses that reflect these reductions. These hypotheses are of two kinds: the conditional volatility parameters may take their boundary values of zero, or the autoregressive component may take the form of a unit root process or not in fact be present. The limiting distributions of the resulting test statistics can be expressed in terms of functionals of Brownian motion related to the Dickey--Fuller statistic, together with independent chi-square components. The finite sample performances of the test statistics are assessed by simulations, and percentiles are tabulated. The results have applications in the analysis of financial time series and random coefficient models. Copyright Royal Economic Society, 2002

Suggested Citation

  • Claudia Klüppelberg & Ross A. Maller & Mark van de Vyver & Derick Wee, 2002. "Testing for reduction to random walk in autoregressive conditional heteroskedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 387-416, June.
    • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:2:p:387-416
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    Cited by:

    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    3. Giuseppe Cavaliere & Anders Rahbek, 2019. "A Primer On Bootstrap Testing Of Hypotheses In Time Series Models: With An Application To Double Autoregressive Models," Discussion Papers 19-03, University of Copenhagen. Department of Economics.
    4. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
    5. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.

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