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Year 2017, Volume: 3 Issue: 2, 13 - 24, 30.06.2017

Ayse Karakas

https://doi.org/10.20863/nsd.302773

Abstract

References

  • [1] A. Sklar. Fonctions de Repartition a n Dimensions et Leurs Marges. Publications de I’lnstitut de Statistique de I’University de Paris. 1959; 8: 229-231.
  • [2] B. Schweitzer, E.F Wolff. On nonparametric measures of dependence for random variables. Annals of Statistics. 1981; 9: 879-885.
  • [3] Chan, N.-H., J. Chen, X. Chen, Y. Fan and L. Peng. Statistical Inference for Multivariate Residual Copula of GARCH Models. Statistica Sinica. 2009; 19: 53-70.
  • [4] Cherubini, U., Luciano, E. Value-at-Risk Trade-off and Capital Allocation with Copulas.Economic Notes. 2001; 30: 235–256.
  • [5] Cyril Caillault, Dominique Guegan. Empirical Estimation of Tail Dependence Using Copulas. Application to Asian Markets. Quantitative Finance, Taylor & Francis. 2005; 5: 489 - 501.
  • [6] Dong Hwan Oha, Andrew J. Pattonb. High-dimensional copula-based distributions with mixed frequency data. Journal of Econometrics. 2016; 193: 349-366.
  • [7] Embrechts, P., A. McNeil, and D. Straumann. Correlation: Pitfalls and Alternatives. ETH Zentrum. 1999.
  • [8] Embrechts, P., A. McNeil and D. Straumann. Correlation and Dependence Properties in Risk Management: Properties and Pitfalls, in M. Dempster, ed., Risk Management: Value at Risk and Beyond. Cambridge University Press. 2002.
  • [9] Eugene F. Fama. Mandelbrot and the Stable Paretıan Hypotesıs. The Journal of Business, 1963; 36: 420-429.
  • [10] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
  • [11] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
  • [12] Genest C., J. MacKay.V. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien. 1986; 40: 280-283.
  • [13] Genest C. L.P. Rivest. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association. 1993; 88: 1034-1043.
  • [14] Genest, C., Favre, A.-C. Everything You Always Wanted to Know About Copula Modelling butWere Afraid to Ask. Journal of Hydrologic Engineering. 2006; 12: 347-368.
  • [15] Genest, C., Gendron, M., Boudeau-Brien, M. The Advent of Copulas in Finance. The European Journal of Finance. 2009; 15: 609-618.
  • [16] Malevergne, Y., Sornette, D. Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Quantitative Finance. 2003; 3: 231-250.
  • [17] Metin A, Çalık S. Copula Function and Application with Economic Data. Turkish Journal of Science and Technology. 2012; 7: 199-204.
  • [18] Pranesh Kumar. Probability Distributions and Estimation of Ali-Mikhail-Haq Copula, Applied Mathematical Sciences. 2010; 4: 657 – 666.
  • [19] Riadh Aloui, MohamedSafouaneBenAïssab, Relationship between oil, stock prices and exchange rates: A vine copula based GARCH method, North American Journal of Economics and Finance 37 (2016), 458-471.
  • [20] R. Nelsen. An Introduction to Copulas.Springer, Verlag. New York. 1999.
  • [21] Rosenberg, J., Schuermann, T. A General Approach to Integrated Risk Management withSkewed, Fat-tailed Risks, Journal of Financial Economics. 2006; 79: 569-614.
  • [22] Shih, J.H., Louis, T.A. Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics. 1995;5: 1384-1399.
  • [23] Quesade-Molina, J.J. A generalization of an identity of Hoeffding and some applications, J.Ital.Stat.Soc. 1992: 3.

Dependence structure analysis with copula GARCH method and for data set suitable copula selection

Year 2017, Volume: 3 Issue: 2, 13 - 24, 30.06.2017

Ayse Karakas

https://doi.org/10.20863/nsd.302773

Abstract

 





Objective:  Multivariate GARCH (MGARCH) models are
forecasted under normality. In this study, for non-elliptically distributed the
data set which are generated Weilbull distribution. Copula-based GARCH
(Copula-GARCH) was used. The aim of the paper is to model GARCH for
non-normal distributions using copulas.


Material and
Methods:  A two-step Copula-GARCH model to analyze the
dependence structure of data sets was used. In the first step, we show data
using univariate GARCH model to get standard residuals and construct marginal
distributions. In this section GARCH (p,q) and GARCH (1,1) method are
introduced. GARCH (1,1) method for data set was used for first step. In the
second step, for dependence structures of the data sets were calculated
Kendall Tau and Spearman Rho values which are nonparametric. Based on this
method, parameters of copula are obtained. 


Results:  A clear advantage of the copula-based model
is that it allows for maximum-likelihood estimation using all available data.


Conclusion:  The aim of the method is basic to find the
parameters that make the likelihood functions get its maximum value. With the
help of the maximum-likelihood estimation method, for copula families obtain
likelihood values. This values, Akaike information criteria (AIC) and
Schwartz information criteria (SIC) are used to determine which copula
supplies to suitability to the data set.

Keywords

Copula Function GARCH method Kendall Tau Spearman Rho Akaike information criteria

References

  • [1] A. Sklar. Fonctions de Repartition a n Dimensions et Leurs Marges. Publications de I’lnstitut de Statistique de I’University de Paris. 1959; 8: 229-231.
  • [2] B. Schweitzer, E.F Wolff. On nonparametric measures of dependence for random variables. Annals of Statistics. 1981; 9: 879-885.
  • [3] Chan, N.-H., J. Chen, X. Chen, Y. Fan and L. Peng. Statistical Inference for Multivariate Residual Copula of GARCH Models. Statistica Sinica. 2009; 19: 53-70.
  • [4] Cherubini, U., Luciano, E. Value-at-Risk Trade-off and Capital Allocation with Copulas.Economic Notes. 2001; 30: 235–256.
  • [5] Cyril Caillault, Dominique Guegan. Empirical Estimation of Tail Dependence Using Copulas. Application to Asian Markets. Quantitative Finance, Taylor & Francis. 2005; 5: 489 - 501.
  • [6] Dong Hwan Oha, Andrew J. Pattonb. High-dimensional copula-based distributions with mixed frequency data. Journal of Econometrics. 2016; 193: 349-366.
  • [7] Embrechts, P., A. McNeil, and D. Straumann. Correlation: Pitfalls and Alternatives. ETH Zentrum. 1999.
  • [8] Embrechts, P., A. McNeil and D. Straumann. Correlation and Dependence Properties in Risk Management: Properties and Pitfalls, in M. Dempster, ed., Risk Management: Value at Risk and Beyond. Cambridge University Press. 2002.
  • [9] Eugene F. Fama. Mandelbrot and the Stable Paretıan Hypotesıs. The Journal of Business, 1963; 36: 420-429.
  • [10] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
  • [11] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
  • [12] Genest C., J. MacKay.V. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien. 1986; 40: 280-283.
  • [13] Genest C. L.P. Rivest. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association. 1993; 88: 1034-1043.
  • [14] Genest, C., Favre, A.-C. Everything You Always Wanted to Know About Copula Modelling butWere Afraid to Ask. Journal of Hydrologic Engineering. 2006; 12: 347-368.
  • [15] Genest, C., Gendron, M., Boudeau-Brien, M. The Advent of Copulas in Finance. The European Journal of Finance. 2009; 15: 609-618.
  • [16] Malevergne, Y., Sornette, D. Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Quantitative Finance. 2003; 3: 231-250.
  • [17] Metin A, Çalık S. Copula Function and Application with Economic Data. Turkish Journal of Science and Technology. 2012; 7: 199-204.
  • [18] Pranesh Kumar. Probability Distributions and Estimation of Ali-Mikhail-Haq Copula, Applied Mathematical Sciences. 2010; 4: 657 – 666.
  • [19] Riadh Aloui, MohamedSafouaneBenAïssab, Relationship between oil, stock prices and exchange rates: A vine copula based GARCH method, North American Journal of Economics and Finance 37 (2016), 458-471.
  • [20] R. Nelsen. An Introduction to Copulas.Springer, Verlag. New York. 1999.
  • [21] Rosenberg, J., Schuermann, T. A General Approach to Integrated Risk Management withSkewed, Fat-tailed Risks, Journal of Financial Economics. 2006; 79: 569-614.
  • [22] Shih, J.H., Louis, T.A. Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics. 1995;5: 1384-1399.
  • [23] Quesade-Molina, J.J. A generalization of an identity of Hoeffding and some applications, J.Ital.Stat.Soc. 1992: 3.
There are 23 citations in total.

Details

Journal Section Original Articles
Authors

Ayse Karakas

Publication Date June 30, 2017
Published in Issue Year 2017 Volume: 3 Issue: 2

Cite

APA Karakas, A. (2017). Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Natural Science and Discovery, 3(2), 13-24. https://doi.org/10.20863/nsd.302773
AMA Karakas A. Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Nat Sci Discov. June 2017;3(2):13-24. doi:10.20863/nsd.302773
Chicago Karakas, Ayse. “Dependence Structure Analysis With Copula GARCH Method and for Data Set Suitable Copula Selection”. Natural Science and Discovery 3, no. 2 (June 2017): 13-24. https://doi.org/10.20863/nsd.302773.
EndNote Karakas A (June 1, 2017) Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Natural Science and Discovery 3 2 13–24.
IEEE A. Karakas, “Dependence structure analysis with copula GARCH method and for data set suitable copula selection”, Nat Sci Discov, vol. 3, no. 2, pp. 13–24, 2017, doi: 10.20863/nsd.302773.
ISNAD Karakas, Ayse. “Dependence Structure Analysis With Copula GARCH Method and for Data Set Suitable Copula Selection”. Natural Science and Discovery 3/2 (June 2017), 13-24. https://doi.org/10.20863/nsd.302773.
JAMA Karakas A. Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Nat Sci Discov. 2017;3:13–24.
MLA Karakas, Ayse. “Dependence Structure Analysis With Copula GARCH Method and for Data Set Suitable Copula Selection”. Natural Science and Discovery, vol. 3, no. 2, 2017, pp. 13-24, doi:10.20863/nsd.302773.
Vancouver Karakas A. Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Nat Sci Discov. 2017;3(2):13-24.
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