IDEAS home Printed from https://ideas.repec.org/a/vrs/demode/v3y2015i1p24n5.html
   My bibliography  Save this article

Forecasting time series with multivariate copulas

Author

Listed:
  • Simard Clarence

    (Department of Mathematics and Statistics, Université de Montréal)

  • Rémillard Bruno

    (Department of Decision Sciences, HEC Montréal)

Abstract

In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.

Suggested Citation

  • Simard Clarence & Rémillard Bruno, 2015. "Forecasting time series with multivariate copulas," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-24, May.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:24:n:5
    DOI: 10.1515/demo-2015-0005
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/demo-2015-0005
    Download Restriction: no
    File URL: https://libkey.io/10.1515/demo-2015-0005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    4. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    7. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    8. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    9. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    10. Busch, Thomas & Jesper Christensen, Bent & Orregaard Nielsen, Morten, 2008. "The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets," Queen's Economics Department Working Papers 273658, Queen's University - Department of Economics.
    11. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    12. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    13. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
    14. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    15. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    16. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    17. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    18. Christian Genest & Michel Gendron & Michaël Bourdeau-Brien, 2009. "The Advent of Copulas in Finance," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 609-618.
    19. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    20. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    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. Amar, Amine & Antonio, Ronald Jeremy S. & Okou, Cyrille Guei & Pede, Valerien O., 2025. "Stochastic modelling of food insecurity risk in Africa: Use of Vine Copulas and cointegration approaches," 2025 AAEA & WAEA Joint Annual Meeting, July 27-29, 2025, Denver, CO 360696, Agricultural and Applied Economics Association.

    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. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    2. 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.
    3. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    4. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    5. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    6. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    7. Nagler, Thomas & Krüger, Daniel & Min, Aleksey, 2022. "Stationary vine copula models for multivariate time series," Journal of Econometrics, Elsevier, vol. 227(2), pages 305-324.
    8. Czado, Claudia & Ivanov, Eugen & Okhrin, Yarema, 2019. "Modelling temporal dependence of realized variances with vines," Econometrics and Statistics, Elsevier, vol. 12(C), pages 198-216.
    9. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    10. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    11. Jorge V. Pérez-Rodríguez, 2020. "Another look at the implied and realised volatility relation: a copula-based approach," Risk Management, Palgrave Macmillan, vol. 22(1), pages 38-64, March.
    12. 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.
    13. Pyun, Sungjune, 2019. "Variance risk in aggregate stock returns and time-varying return predictability," Journal of Financial Economics, Elsevier, vol. 132(1), pages 150-174.
    14. Richard T. Baillie & Fabio Calonaci & Dooyeon Cho & Seunghwa Rho, 2019. "Long Memory, Realized Volatility and HAR Models," Working Papers 881, Queen Mary University of London, School of Economics and Finance.
    15. Degiannakis, Stavros & Filis, George, 2017. "Forecasting oil price realized volatility using information channels from other asset classes," Journal of International Money and Finance, Elsevier, vol. 76(C), pages 28-49.
    16. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    17. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    18. Martin Magris, 2019. "A Vine-copula extension for the HAR model," Papers 1907.08522, arXiv.org.
    19. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2014. "Realized volatility models and alternative Value-at-Risk prediction strategies," Economic Modelling, Elsevier, vol. 40(C), pages 101-116.
    20. Liu, Yi & Liu, Huifang & Zhang, Lei, 2019. "Modeling and forecasting return jumps using realized variation measures," Economic Modelling, Elsevier, vol. 76(C), pages 63-80.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    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:vrs:demode:v:3:y:2015:i:1:p:24:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    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.