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Journals / Natural Science and Discovery / 2017 / Cilt: 3 Sayı: 2

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

Ayse KARAKAS
Pages
13–24
Publication Date
2017-06-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This values, Akaike information criteria (AIC) and Schwartz information criteria (SIC) are used to determine which copula supplies to suitability to the data set.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Objective: Multivariate GARCH (MGARCH) models are forecasted under normality.
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Key Findings & Data:In this study, for non-elliptically distributed the data set which are generated Weilbull distribution.
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Conclusion & Impact:This values, Akaike information criteria (AIC) and Schwartz information criteria (SIC) are used to determine which copula supplies to suitability to the data set.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Copula Function · GARCH method · Kendall Tau

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.

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Cite This Article

KARAKAS, A. (2017). Dependence structure analysis with copula GARCH method and for data set suitable copula selection. Natural Science and Discovery, Cilt: 3 Sayı: 2, 13–24. https://ajindex.com/articles/1003429

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References (17)

  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]