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Stable limits for the Gaussian QMLE in the non-stationary GARCH(1,1) model

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  • Arvanitis, Stelios
  • Louka, Alexandros

Abstract

We derive the limit theory of the Gaussian QMLE in the non-stationary GARCH(1,1) model when the squared innovation process lies in the domain of attraction of a stable law. Analogously to the stationary case, when the stability parameter lies in 1,2, we find regularly varying rates and stable limits for the QMLE of the ARCH and GARCH parameters.

Suggested Citation

  • Arvanitis, Stelios & Louka, Alexandros, 2017. "Stable limits for the Gaussian QMLE in the non-stationary GARCH(1,1) model," Economics Letters, Elsevier, vol. 161(C), pages 135-137.
    • Handle: RePEc:eee:ecolet:v:161:y:2017:i:c:p:135-137
    DOI: 10.1016/j.econlet.2017.09.035
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    References listed on IDEAS

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    1. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    2. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    3. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, March.
    4. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    5. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    6. Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2016. "Nonstationary GARCH with t-distributed innovations," Economics Letters, Elsevier, vol. 138(C), pages 19-21.
    7. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    8. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
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    Cited by:

    1. Hong, Yun & Li, Yi, 2020. "Housing prices and investor sentiment dynamics: Evidence from China using a wavelet approach," Finance Research Letters, Elsevier, vol. 35(C).
    2. Arvanitis, Stelios, 2019. "Stable limit theory for the Gaussian QMLE in a non-stationary asymmetric GARCH model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 166-172.
    3. Stelios Arvanitis & Sofia Anyfantaki, 2020. "On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 341-350, March.

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    More about this item

    Keywords

    Martingale limit theorem; Domain of attraction; Stable distribution; Slowly varying sequence; Non-Stationarity; Gaussian QMLE; Regularly varying rate;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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