IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1807.08390.html
   My bibliography  Save this paper

Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models

Author

Listed:
  • Bal'azs Csan'ad Cs'aji

Abstract

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.

Suggested Citation

  • Bal'azs Csan'ad Cs'aji, 2018. "Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models," Papers 1807.08390, arXiv.org.
    • Handle: RePEc:arx:papers:1807.08390
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1807.08390
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. 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.
    4. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    5. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    6. 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.
    7. László Gerencsér & Zsanett Orlovits, 2012. "Real time estimation of stochastic volatility processes," Annals of Operations Research, Springer, vol. 200(1), pages 223-246, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Spierdijk, Laura, 2016. "Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 545-559.
    2. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    3. Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.
    4. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    5. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    6. Hoga, Yannick, 2021. "The uncertainty in extreme risk forecasts from covariate-augmented volatility models," International Journal of Forecasting, Elsevier, vol. 37(2), pages 675-686.
    7. Dimitris Politis & Dimitrios Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Papers 0005, University of Peloponnese, Department of Economics.
    8. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers CWP25/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    10. 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.
    11. Francq, Christian & Zakoian, Jean-Michel, 2015. "Looking for efficient qml estimation of conditional value-at-risk at multiple risk levels," MPRA Paper 67195, University Library of Munich, Germany.
    12. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    13. Yun Gong & Zhouping Li & Liang Peng, 2010. "Empirical likelihood intervals for conditional Value‐at‐Risk in ARCH/GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 65-75, March.
    14. Szczygielski, Jan Jakub & Brzeszczyński, Janusz & Charteris, Ailie & Bwanya, Princess Rutendo, 2022. "The COVID-19 storm and the energy sector: The impact and role of uncertainty," Energy Economics, Elsevier, vol. 109(C).
    15. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    16. João Henrique G. Mazzeu & Gloria González-Rivera & Esther Ruiz & Helena Veiga, 2020. "A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 971-990, November.
    17. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    18. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    19. Ngozi G. Emenogu & Monday Osagie Adenomon & Nwaze Obini Nweze, 2020. "On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-25, December.
    20. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1807.08390. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.