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Higher Order Asymptotic Theory When A Parameter Is On A Boundary With An Application To Garch Models

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  • Iglesias, Emma M.
  • Linton, Oliver B.

Abstract

Andrews (1999, Econometrica 67, 1341–1383) derived the first-order asymptotic theory for a very general class of estimators when a parameter is on a boundary. We derive the second-order asymptotic theory in this setting in some special cases. We focus on the behavior of the quasi maximum likelihood estimator (QMLE) in stationary and nonstationary generalized autoregressive conditionally heteroskedastic (GARCH) models when constraints are imposed in the maximization procedure. We show how in this case both a first- and a second-order bias appear in the estimator and how the bias can be quite large. We provide two types of bias correction mechanisms for the researcher to choose in practice: either to bias correct only for a first-order bias or for a first- and second-order bias. We show that when some constraints are imposed, it is advisable to bias correct not only for the first-order bias but also for the second-order bias.We thank Bruce Hansen and two referees for helpful comments. The first author gratefully acknowledges financial support from the MSU Intramural Research Grants Program. The second author gratefully acknowledges financial support from the ESRC.

Suggested Citation

  • Iglesias, Emma M. & Linton, Oliver B., 2007. "Higher Order Asymptotic Theory When A Parameter Is On A Boundary With An Application To Garch Models," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1136-1161, December.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:06:p:1136-1161_07
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    Cited by:

    1. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    2. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    3. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Papers 1905.01798, arXiv.org.
    4. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    5. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
    6. Fan, Yanqin & Park, Sang Soo, 2014. "Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV," Journal of Econometrics, Elsevier, vol. 178(P1), pages 45-56.
    7. Antonis Demos & Dimitra Kyriakopoulou, 2011. "Bias Correction of ML and QML Estimators in the EGARCH(1,1) Model," DEOS Working Papers 1108, Athens University of Economics and Business.
    8. Arvanitis Stelios & Demos Antonis, 2014. "Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 183-235, July.
    9. Christian Francq & Jean-Michel Zakoïan, 2008. "Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero," Working Papers 2008-07, Center for Research in Economics and Statistics.
    10. Rivera-Alonso, David & Iglesias, Emma M., 2024. "Is the Chinese crude oil spot price a good hedging tool for other crude oil prices, and in special for the main Russian oil benchmarks and during international sanctions?," Resources Policy, Elsevier, vol. 90(C).

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