IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.10135.html
   My bibliography  Save this paper

Modelling volatile time series with v-transforms and copulas

Author

Listed:
  • Alexander J. McNeil

Abstract

An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the time series and quantiles of the distribution of a predictable volatility proxy variable. They can be represented as copulas and permit the formulation and estimation of models that combine arbitrary marginal distributions with copula processes for the dynamics of the volatility proxy. The idea is illustrated using a Gaussian ARMA copula process and the resulting model is shown to replicate many of the stylized facts of financial return series and to facilitate the calculation of marginal and conditional characteristics of the model including quantile measures of risk. Estimation is carried out by adapting the exact maximum likelihood approach to the estimation of ARMA processes and the model is shown to be competitive with standard GARCH in an empirical application to Bitcoin return data.

Suggested Citation

  • Alexander J. McNeil, 2020. "Modelling volatile time series with v-transforms and copulas," Papers 2002.10135, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:2002.10135
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.10135
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    2. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    3. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    6. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    7. repec:cdl:ucsdec:qt0xh8q1g3 is not listed on IDEAS
    8. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    11. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    12. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    13. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    14. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    15. Yanqin Fan & Andrew J. Patton, 2014. "Copulas in Econometrics," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 179-200, August.
    16. 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. Martin Bladt & Alexander J. McNeil, 2021. "Time series models with infinite-order partial copula dependence," Papers 2107.00960, arXiv.org.
    2. Bladt Martin & McNeil Alexander J., 2022. "Time series with infinite-order partial copula dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 87-107, January.
    3. Martin Bladt & Alexander J. McNeil, 2020. "Time series copula models using d-vines and v-transforms," Papers 2006.11088, arXiv.org, revised Jul 2021.
    4. Ahmet Faruk Aysan & Asad Ul Islam Khan & Humeyra Topuz, 2021. "Bitcoin and Altcoins Price Dependency: Resilience and Portfolio Allocation in COVID-19 Outbreak," Risks, MDPI, vol. 9(4), pages 1-13, April.

    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. Alexander J. McNeil, 2021. "Modelling Volatile Time Series with V-Transforms and Copulas," Risks, MDPI, vol. 9(1), pages 1-26, January.
    2. Martin Bladt & Alexander J. McNeil, 2020. "Time series copula models using d-vines and v-transforms," Papers 2006.11088, arXiv.org, revised Jul 2021.
    3. Bladt, Martin & McNeil, Alexander J., 2022. "Time series copula models using d-vines and v-transforms," Econometrics and Statistics, Elsevier, vol. 24(C), pages 27-48.
    4. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    5. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    6. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.
    7. Owusu Junior, Peterson & Tiwari, Aviral Kumar & Tweneboah, George & Asafo-Adjei, Emmanuel, 2022. "GAS and GARCH based value-at-risk modeling of precious metals," Resources Policy, Elsevier, vol. 75(C).
    8. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    9. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    10. Wu, Qi & Yan, Xing, 2019. "Capturing deep tail risk via sequential learning of quantile dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    11. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    12. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    13. Benjamin Beckers & Helmut Herwartz & Moritz Seidel, 2017. "Risk forecasting in (T)GARCH models with uncorrelated dependent innovations," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 121-137, January.
    14. repec:cdl:ucsdec:qt31f8500p is not listed on IDEAS
    15. Abdinardo Moreira Barreto Oliveira & Anandadeep Mandal & Gabriel J. Power, 2024. "Impact of COVID-19 on Stock Indices Volatility: Long-Memory Persistence, Structural Breaks, or Both?," Annals of Data Science, Springer, vol. 11(2), pages 619-646, April.
    16. Fan, Yanqin & Han, Fang & Park, Hyeonseok, 2023. "Estimation and inference in a high-dimensional semiparametric Gaussian copula vector autoregressive model," Journal of Econometrics, Elsevier, vol. 237(1).
    17. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    18. Karmakar, Madhusudan & Shukla, Girja K., 2015. "Managing extreme risk in some major stock markets: An extreme value approach," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 1-25.
    19. Gianna Figà-Talamanca & Marco Patacca, 2024. "An explorative analysis of sentiment impact on S&P 500 components returns, volatility and downside risk," Annals of Operations Research, Springer, vol. 342(3), pages 2095-2117, November.
    20. Wang, Yudong & Liu, Li & Ma, Feng & Wu, Chongfeng, 2016. "What the investors need to know about forecasting oil futures return volatility," Energy Economics, Elsevier, vol. 57(C), pages 128-139.
    21. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.

    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:2002.10135. 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.