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Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability

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  • Marc S. Paolella

    (Department of Banking and Finance, University of Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland
    Swiss Finance Institute, Walchestrasse 9 CH-8006 Zurich, Switzerland)

Abstract

A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index 1 < α < 2 are used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence against the stable as the correct innovations assumption for all stocks and time periods, though for many stocks and windows of data, the stable hypothesis is not rejected.

Suggested Citation

  • Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:2:p:25-:d:69492
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    Cited by:

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    3. Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2021. "Analytic moments for GJR-GARCH (1, 1) processes," International Journal of Forecasting, Elsevier, vol. 37(1), pages 105-124.
    4. Malek, Jiri & Nguyen, Duc Khuong & Sensoy, Ahmet & Tran, Quang Van, 2023. "Modeling dynamic VaR and CVaR of cryptocurrency returns with alpha-stable innovations," Finance Research Letters, Elsevier, vol. 55(PA).
    5. Simon Hediger & Jeffrey Näf & Marc S. Paolella & Paweł Polak, 2023. "Heterogeneous tail generalized common factor modeling," Digital Finance, Springer, vol. 5(2), pages 389-420, June.
    6. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.
    7. Broda, Simon A. & Krause, Jochen & Paolella, Marc S., 2018. "Approximating expected shortfall for heavy-tailed distributions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 184-203.
    8. Santiago Carrillo Menéndez & Bertrand Kian Hassani, 2021. "Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes," Mathematics, MDPI, vol. 9(17), pages 1-20, September.

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