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Nonstationary GARCH with t-distributed innovations

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  • Pedersen, Rasmus Søndergaard
  • Rahbek, Anders

Abstract

We consider joint estimation of the GARCH parameters and the degrees of freedom parameter in the GARCH model with t-distributed innovations for the nonstationary case. With T denoting the sample size, T-consistency and asymptotic normality are derived for the estimators of the GARCH parameters jointly with the degrees of freedom parameter. Thus consistency and asymptotic normality at the standard rate hold for both the nonstationary case as well as for the stationary case treated in existing literature. Finally, an explicit formula is given for the asymptotic covariance matrix.

Suggested Citation

  • Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2016. "Nonstationary GARCH with t-distributed innovations," Economics Letters, Elsevier, vol. 138(C), pages 19-21.
    • Handle: RePEc:eee:ecolet:v:138:y:2016:i:c:p:19-21
    DOI: 10.1016/j.econlet.2015.11.016
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    3. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    4. Bertsatos, Georgios & Sakellaris, Plutarchos & Tsionas, Mike G., 2017. "Did the financial crisis affect the market valuation of large systemic U.S. banks?," Journal of Financial Stability, Elsevier, vol. 32(C), pages 115-123.
    5. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    6. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    7. Christian M. Dahl & Emma M. Iglesias, 2021. "Asymptotic normality of the MLE in the level-effect ARCH model," Statistical Papers, Springer, vol. 62(1), pages 117-135, February.
    8. Helen Caraveli & Ioannis Chatzigiatroudakis & Evangelos Paravalos, 2018. "Determinants of growth differences between Eastern and Southern EU countries: A panel-data approach," Working Papers 201803, Athens University Of Economics and Business, Department of Economics.
    9. George C. Bitros, 2017. "Germany and Greece: A mapping of their great divide and its EU implications," Working Papers 201706, Athens University Of Economics and Business, Department of Economics.
    10. Xiaqing Su & Zhe Liu, 2021. "Sector Volatility Spillover and Economic Policy Uncertainty: Evidence from China’s Stock Market," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    11. Stelios Arvanitis, 2017. "Non-Emptyness of Stochastic Dominance Effiicient Sets via Stochastic Spanning," Working Papers 201710, Athens University Of Economics and Business, Department of Economics.
    12. Natasha Miaouli & Panagiota Koliousi, 2018. "Efficient bargaining versus Right to manage in the era of liberalization," Working Papers 201804, Athens University Of Economics and Business, Department of Economics.
    13. 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.
    14. Stylianos G. Gogos & Dimitris Papageorgiou & Vanghelis Vassilatos, 2017. "Rent Seeking Activities and Aggregate Economic Performance - The Case of Greece," Working Papers 201712, Athens University Of Economics and Business, Department of Economics.
    15. George C. Bitros, 2017. "Still in the Woods," Working Papers 201711, Athens University Of Economics and Business, Department of Economics.

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    More about this item

    Keywords

    Asymptotic theory; GARCH; Maximum likelihood; Nonstationarity; t-distribution;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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