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

Main Article Content

Ayse Karakas

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.


 

Article Details

How to Cite
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. Retrieved from https://natscidiscovery.com/index.php/nsd/article/view/47
Section
Research Article

References

[23] Quesade-Molina, J.J. A generalization of an identity of Hoeffding and some applications, J.Ital.Stat.Soc. 1992: 3.
[22] Shih, J.H., Louis, T.A. Inferences on the Association Parameter in Copula Models for Bivariate Survival Data. Biometrics. 1995;5: 1384-1399.
[21] Rosenberg, J., Schuermann, T. A General Approach to Integrated Risk Management withSkewed, Fat-tailed Risks, Journal of Financial Economics. 2006; 79: 569-614.
[20] R. Nelsen. An Introduction to Copulas.Springer, Verlag. New York. 1999.
[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.
[18] Pranesh Kumar. Probability Distributions and Estimation of Ali-Mikhail-Haq Copula, Applied Mathematical Sciences. 2010; 4: 657 – 666.
[17] Metin A, Çalık S. Copula Function and Application with Economic Data. Turkish Journal of Science and Technology. 2012; 7: 199-204.
[16] Malevergne, Y., Sornette, D. Testing the Gaussian Copula Hypothesis for Financial Assets Dependences. Quantitative Finance. 2003; 3: 231-250.
[15] Genest, C., Gendron, M., Boudeau-Brien, M. The Advent of Copulas in Finance. The European Journal of Finance. 2009; 15: 609-618.
[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.
[13] Genest C. L.P. Rivest. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association. 1993; 88: 1034-1043.
[12] Genest C., J. MacKay.V. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien. 1986; 40: 280-283.
[11] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
[10] E.W. Frees, E.A. Valdez. Understanding relationships using copulas. North American Actuarial Journal. 1998; 2:1-25.
[9] Eugene F. Fama. Mandelbrot and the Stable Paretıan Hypotesıs. The Journal of Business, 1963; 36: 420-429.
[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.
[7] Embrechts, P., A. McNeil, and D. Straumann. Correlation: Pitfalls and Alternatives. ETH Zentrum. 1999.
[6] Dong Hwan Oha, Andrew J. Pattonb. High-dimensional copula-based distributions with mixed frequency data. Journal of Econometrics. 2016; 193: 349-366.
[5] Cyril Caillault, Dominique Guegan. Empirical Estimation of Tail Dependence Using Copulas. Application to Asian Markets. Quantitative Finance, Taylor & Francis. 2005; 5: 489 - 501.
[4] Cherubini, U., Luciano, E. Value-at-Risk Trade-off and Capital Allocation with Copulas.Economic Notes. 2001; 30: 235–256.
[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.
[2] B. Schweitzer, E.F Wolff. On nonparametric measures of dependence for random variables. Annals of Statistics. 1981; 9: 879-885.
[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.