IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2004v5i2p283-298.html
   My bibliography  Save this article

A Heavy-Tailed Distribution for ARCH Residuals with Application to Volatility Prediction

Author

Listed:
  • Dimitris N. Politis

    (Department of Mathematics, University of California)

Abstract

The quest for the `best' heavy-tailed distribution for ARCH/GARCH residuals appears to still be ongoing. In this connection, we propose a new distribution that arises in a natural way as an outcome of an implicit model. The challenging application of prediction of squared returns is also discussed; an optimal predictor is formulated, and the usefulness of the new distribution for prediction is demonstrated on three real datasets.

Suggested Citation

  • Dimitris N. Politis, 2004. "A Heavy-Tailed Distribution for ARCH Residuals with Application to Volatility Prediction," Annals of Economics and Finance, Society for AEF, vol. 5(2), pages 283-298, November.
    • Handle: RePEc:cuf:journl:y:2004:v:5:i:2:p:283-298
    as

    Download full text from publisher

    File URL: http://www.aeconf.net/Articles/Nov2004/aef050206.pdf
    Download Restriction: no
    File URL: http://down.aefweb.net/AefArticles/aef050206.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    4. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    5. 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.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yoon Hong & Ji-chul Lee & Guoping Ding, 2017. "Volatility Clustering, New Heavy-Tailed Distribution and the Stock Market Returns in South Korea," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 6(3), pages 164-169, September.
    2. Hung, Jui-Cheng & Lee, Ming-Chih & Liu, Hung-Chun, 2008. "Estimation of value-at-risk for energy commodities via fat-tailed GARCH models," Energy Economics, Elsevier, vol. 30(3), pages 1173-1191, May.
    3. Laporta, Alessandro G. & Merlo, Luca & Petrella, Lea, 2018. "Selection of Value at Risk Models for Energy Commodities," Energy Economics, Elsevier, vol. 74(C), pages 628-643.
    4. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
    5. Dimitrios Thomakos & Johannes Klepsch & Dimitris N. Politis, 2020. "Model Free Inference on Multivariate Time Series with Conditional Correlations," Stats, MDPI, vol. 3(4), pages 1-26, November.
    6. Dimitris Politis & Dimitrios Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Papers 0005, University of Peloponnese, Department of Economics.
    7. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    8. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Value-at-risk methodologies for effective energy portfolio risk management," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 197-212.
    9. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    10. Su, Jung-Bin & Hung, Jui-Cheng, 2011. "Empirical analysis of jump dynamics, heavy-tails and skewness on value-at-risk estimation," Economic Modelling, Elsevier, vol. 28(3), pages 1117-1130, May.
    11. Halkos, George & Tsirivis, Apostolos, 2019. "Using Value-at-Risk for effective energy portfolio risk management," MPRA Paper 91674, University Library of Munich, Germany.
    12. Politis, D N, 2006. "Can the Stock Market be Linearized?," University of California at San Diego, Economics Working Paper Series qt8th5q5hq, Department of Economics, UC San Diego.
    13. Michael Day & Mark Diamond & Jeff Card & Jake Hurd & Jianping Xu, 2017. "GARCH model and fat tails of the Chinese stock market returns - New evidences," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 43-49.
    14. Huang, Yu-ting & Bai, Yu-long & Yu, Qing-he & Ding, Lin & Ma, Yong-jie, 2022. "Application of a hybrid model based on the Prophet model, ICEEMDAN and multi-model optimization error correction in metal price prediction," Resources Policy, Elsevier, vol. 79(C).
    15. Panos Pouliasis & Ioannis Kyriakou & Nikos Papapostolou, 2017. "On equity risk prediction and tail spillovers," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 22(4), pages 379-393, October.
    16. J. A. Jiménez & V. Arunachalam & G. M. Serna, 2015. "Option Pricing Based On A Log–Skew–Normal Mixture," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-22, December.
    17. Chevallier, Julien & Ielpo, Florian, 2017. "Investigating the leverage effect in commodity markets with a recursive estimation approach," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 763-778.

    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. Politis, Dimitris N., 2004. "A heavy-tailed distribution for ARCH residuals with application to volatility prediction," University of California at San Diego, Economics Working Paper Series qt7r89639x, Department of Economics, UC San Diego.
    2. Das, Suman & Roy, Saikat Sinha, 2023. "Following the leaders? A study of co-movement and volatility spillover in BRICS currencies," Economic Systems, Elsevier, vol. 47(2).
    3. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    4. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    5. Prono Todd, 2018. "Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-25, December.
    6. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    7. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    8. Chen, Min & Zhu, Ke, 2015. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 189(2), pages 313-320.
    9. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    10. N. Antonakakis & J. Darby, 2013. "Forecasting volatility in developing countries' nominal exchange returns," Applied Financial Economics, Taylor & Francis Journals, vol. 23(21), pages 1675-1691, November.
    11. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    12. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    13. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
    14. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Malik, Farooq, 2003. "Sudden changes in variance and volatility persistence in foreign exchange markets," Journal of Multinational Financial Management, Elsevier, vol. 13(3), pages 217-230, July.
    16. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    17. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    18. Pandey, Ajay, 2003. "Modeling and Forecasting Volatility in Indian Capital Markets," IIMA Working Papers WP2003-08-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    19. 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.
    20. repec:dau:papers:123456789/2285 is not listed on IDEAS
    21. 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.

    More about this item

    Keywords

    Heteroscedasticity; Kyrtosis; Maximum likelihood; Time series;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

    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:cuf:journl:y:2004:v:5:i:2:p:283-298. 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: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    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.