IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v12y2008i2n3.html
   My bibliography  Save this article

Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market

Author

Listed:
  • Sun Wei

    (University of Karlsruhe, Karlsruhe Institute of Technology, and GCFD)

  • Rachev Svetlozar

    (University of Karlsruhe, Karlsruhe Institute of Technology and UCSB)

  • Stoyanov Stoyan V.

    (FinAnalytica, Inc.)

  • Fabozzi Frank J.

    (Yale University)

Abstract

Analyzing comovements in equity markets is important for risk diversification in portfolio management. Copulas have several advantages compared to the linear correlation measure in modeling comovement. This paper introduces a copula ARMA-GARCH model for analyzing the comovement of indexes in German equity markets. The model is implemented with an ARMA-GARCH model for the marginal distributions and a copula for the joint distribution. After goodness-of-fit testing, we find that the skewed Student's t copula ARMA(1,1)-GARCH(1,1) model with Lévy fractional stable noise is superior to alternative models investigated in our study where we model the simultaneous comovement of six German equity market indexes. This model is also suitable for capturing the long-range dependence, tail dependence, and asymmetric correlation observed in German equity markets.

Suggested Citation

  • Sun Wei & Rachev Svetlozar & Stoyanov Stoyan V. & Fabozzi Frank J., 2008. "Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-37, May.
    • Handle: RePEc:bpj:sndecm:v:12:y:2008:i:2:n:3
    DOI: 10.2202/1558-3708.1572
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1572
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1572?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. T. Rachev, Svetlozar & Samorodnitsky, Gennady, 2001. "Long strange segments in a long-range-dependent moving average," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 119-148, May.
    2. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    3. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    4. Rachev, S.T (ed.), 2003. "Handbook of Heavy Tailed Distributions in Finance," Elsevier Monographs, Elsevier, edition 1, number 9780444508966.
    5. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    6. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    7. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    8. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    9. Sun, Wei & Rachev, Svetlozar & Fabozzi, Frank J., 2007. "Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns," Journal of Economics and Business, Elsevier, vol. 59(6), pages 575-595.
    10. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    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. Allen, David & Lizieri, Colin & Satchell, Stephen, 2020. "A comparison of non-Gaussian VaR estimation and portfolio construction techniques," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 356-368.
    2. Dong, Zhiliang & An, Haizhong & Liu, Sen & Li, Zhengyang & Yuan, Meng, 2020. "Research on the time-varying network structure evolution of the stock indices of the BRICS countries based on fluctuation correlation," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 63-74.
    3. Indranil Ghosh & Dalton Watts & Subrata Chakraborty, 2022. "Modeling Bivariate Dependency in Insurance Data via Copula: A Brief Study," JRFM, MDPI, vol. 15(8), pages 1-20, July.
    4. Lin, Fu-Lai & Yang, Sheng-Yung & Marsh, Terry & Chen, Yu-Fen, 2018. "Stock and bond return relations and stock market uncertainty: Evidence from wavelet analysis," International Review of Economics & Finance, Elsevier, vol. 55(C), pages 285-294.
    5. Krämer, Walter & van Kampen, Maarten, 2011. "A simple nonparametric test for structural change in joint tail probabilities," Economics Letters, Elsevier, vol. 110(3), pages 245-247, March.
    6. Chen, Mei-Ping & Chen, Wen-Yi & Tseng, Tseng-Chan, 2017. "Co-movements of returns in the health care sectors from the US, UK, and Germany stock markets: Evidence from the continuous wavelet analyses," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 484-498.
    7. Miralles-Quirós, José Luis & Daza-Izquierdo, Julio, 2015. "Do DOW returns really influence the intraday Spanish stock market behavior?," Research in International Business and Finance, Elsevier, vol. 33(C), pages 99-126.
    8. Huang, Hung-Hsi & Lin, Shin-Hung & Wang, Ching-Ping & Chiu, Chia-Yung, 2014. "Adjusting MV-efficient portfolio frontier bias for skewed and non-mesokurtic returns," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 59-83.
    9. Desislava Chetalova & Marcel Wollschlager & Rudi Schafer, 2015. "Dependence structure of market states," Papers 1503.09004, arXiv.org, revised Jul 2015.
    10. Chen, Claire Y.T. & Sun, Edward W. & Miao, Wanyu & Lin, Yi-Bing, 2024. "Reconciling business analytics with graphically initialized subspace clustering for optimal nonlinear pricing," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1086-1107.
    11. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhang, Wei, 2019. "Financial systemic risk measurement based on causal network connectedness analysis," International Review of Economics & Finance, Elsevier, vol. 64(C), pages 290-307.
    12. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    13. Sak, Halis & Başoğlu, İsmail, 2017. "Efficient randomized quasi-Monte Carlo methods for portfolio market risk," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 87-94.
    14. Rehman, Mobeen Ur & Katsiampa, Paraskevi & Zeitun, Rami & Vo, Xuan Vinh, 2023. "Conditional dependence structure and risk spillovers between Bitcoin and fiat currencies," Emerging Markets Review, Elsevier, vol. 55(C).
    15. Silvo Dajcman, 2013. "Dependence between Croatian and European stock markets – A copula GARCH approach," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 31(2), pages 209-232.
    16. Luca Riccetti, 2013. "A copula–GARCH model for macro asset allocation of a portfolio with commodities," Empirical Economics, Springer, vol. 44(3), pages 1315-1336, June.
    17. Marcel Wollschlager & Rudi Schafer, 2015. "Impact of non-stationarity on estimating and modeling empirical copulas of daily stock returns," Papers 1506.08054, arXiv.org.
    18. Maximilian Coblenz & Simon Holz & Hans‐Jörg Bauer & Oliver Grothe & Rainer Koch, 2020. "Modelling fuel injector spray characteristics in jet engines by using vine copulas," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 863-886, August.
    19. Fabozzi Frank J. & Stoyanov Stoyan V. & Rachev Svetlozar T., 2013. "Computational aspects of portfolio risk estimation in volatile markets: a survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 103-120, February.
    20. Sun, Edward W. & Chen, Yi-Ting & Yu, Min-Teh, 2015. "Generalized optimal wavelet decomposing algorithm for big financial data," International Journal of Production Economics, Elsevier, vol. 165(C), pages 194-214.
    21. Almira Biglova & Sergio Ortobelli & Frank J Fabozzi, 2014. "Portfolio selection in the presence of systemic risk," Journal of Asset Management, Palgrave Macmillan, vol. 15(5), pages 285-299, October.

    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. Wei Sun & Svetlozar Rachev & Frank Fabozzi & Petko Kalev, 2009. "A new approach to modeling co-movement of international equity markets: evidence of unconditional copula-based simulation of tail dependence," Empirical Economics, Springer, vol. 36(1), pages 201-229, February.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    3. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    4. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    5. Sun, Wei & Rachev, Svetlozar & Fabozzi, Frank J., 2007. "Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns," Journal of Economics and Business, Elsevier, vol. 59(6), pages 575-595.
    6. Rajan Sruthi & Santhakumar Shijin, 2020. "Investigating liquidity constraints as a channel of contagion: a regime switching approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-21, December.
    7. Wei Sun & Svetlozar Rachev & Frank Fabozzi & Petko Kalev, 2008. "Fractals in trade duration: capturing long-range dependence and heavy tailedness in modeling trade duration," Annals of Finance, Springer, vol. 4(2), pages 217-241, March.
    8. Wei Sun & Svetlozar Rachev & Frank J. Fabozzi, 2009. "A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions," European Financial Management, European Financial Management Association, vol. 15(2), pages 340-361, March.
    9. Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.
    10. Julien Chevallier & Florian Ielpo, 2013. "Volatility spillovers in commodity markets," Applied Economics Letters, Taylor & Francis Journals, vol. 20(13), pages 1211-1227, September.
    11. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    12. Dimic, Nebojsa & Piljak, Vanja & Swinkels, Laurens & Vulanovic, Milos, 2021. "The structure and degree of dependence in government bond markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    13. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    14. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    15. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    16. Lorán Chollete & Andréas Heinen & Alfonso Valdesogo, 2009. "Modeling International Financial Returns with a Multivariate Regime-switching Copula," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 437-480, Fall.
    17. Reboredo, Juan C., 2012. "Do food and oil prices co-move?," Energy Policy, Elsevier, vol. 49(C), pages 456-467.
    18. Rakesh Gupta & Junhao Yang & Thadavillil Jithendranathan, 2017. "Diversification into Emerging Markets – An Australian and the US Perspective Using a Time-varying Approach," Australian Economic Papers, Wiley Blackwell, vol. 56(2), pages 134-162, June.
    19. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    20. Jiangze Du & Xizhuo Chen & Jincheng Gong & Xiao Lin & Kin Keung Lai, 2023. "Analysis of stock markets risk spillover with copula models under the background of Chinese financial opening," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 3997-4019, October.

    More about this item

    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:bpj:sndecm:v:12:y:2008:i:2:n:3. 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.degruyter.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.