THE DEPENDENCE STRUCTURE BETWEEN THE MONTHLY MINIMUM AND MAXIMUM BAROMETRIC DATA IN IRAN

Yıl 2016, Cilt: 29 Sayı: 3, 593 - 597, 30.09.2016

Vadoud Najjari

Öz

In choosing the right copula, existing methods pose numerous difficulties and none is entirely satisfactory. In this study, the main endeavor is to propose a simple and reliable method to select the right copula family that fits the best to data. In this new method,  standard  goodness of fit test statistic value is posed as a function of copula parameters and then the main problem is to investigate the minimum value of this function. Hereby an estimation of copula parameters are in the minimum point of the mentioned function and also by minimum value of the mentioned function we are able to find the right copula that is the best to data. With an empirical example the new method will be compared with results of the maximum likelihood estimation and also the nonparametric method proposed by Genest and Rivest (1993).

Anahtar Kelimeler

Copulas, generator, goodness of fit test (GOF test), MLE

Kaynakça

• B. Brahimi., A. Necir., A semiparametric estimation of copula models based on the method of moments, Statistical Methodology .9 (2012) 467-477.
• X. Chen., Y. Fan., Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection, La Revue Canadienne de Statistique. 33 (3) (2005) 389-414.
• S. Çelebioğlu., Archimedean copulas and an application, Selcuk University Journal of Science, 22 (2003) 43-52.
• J. Dobric., F. Schmidt., Testing goodness of fıt for parametric families of copulas application to fınancial data. Seminar of economic and social statistics, University of Cologne. 2004.
• V. Durrleman., A. Nikeghbali., T. Roncalli., Which copula is the right one? Working document, Groupe de Recherche Operationnelle, Credit Lyonnais, 2000.
• C. Genest., Frank's family of bivariate distributions, Biometrika, 74 (1987) 549-555. [7] C. Genest., K. Ghoudi., semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82 (1995) 543-552. L.P. Rivest., A
• C. Genest., L. P. Rivest., Statistical Inference Procedures for Bivariate Archimedean copulas, Journal of the American Statistical Association, 88:423(1993) 1034-1043.
• H. Joe Multivariate Models and Dependence Concepts, Chapman - Hall, London, 1997.
• H. Joe., Asymptotic efficiency of the two-stage estimation method for copula based models, J. Multivariate Anal, 94 (2005) 401-419.
• M. Kendall., A. Stuart., The Advanced Theory of Statistics, fourth ed. Oxford University Press, New York, vol 2, 1983.
• G. Kim., M.J. Silvapulle., P. Silvapulle., Comparison of semiparametric and parametric methods for estimating copulas, Comm. Statist. Simulation Comp., 51 (2007) 2836-2850.
• Kojadinovic., J. Yan., Tests of serial independence for continuous multivariate time series based on a Mobius decomposition empirical copula process, Ann. Inst. Stat. Math, 2010. the independence
• V. Najjari., T. Bacigal., H. Bal., An Archimedean Copula Generator, International Journal of Uncertainty, Fuzziness 22(5):(2014) 761-768. Cotangent and
• Knowledge-Based Systems,
• V. Najjari., M. G. Ünsal., An Application of Archimedean Copulas for Meteorological Data, G. U. Journal of Science, 25:2 (2012) 301-306.
• R. B. Nelsen., An introduction to copulas, Springer, New York, Second edition, 2006.
• D. Pollard., General chi-square goodness-of-fıt tests with data-dependent cells. Z. Wahrscheinlich keitstheorie und verwandte Gebiete, 50 (1979) 317- 331.
• A.Sklar., Fonctions de rèpartition á n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8 (1959) 229-231.
• S. T. Şahin Tekin., V. Najjari., H. H. Örkcü., Simulation Communications in Mathematical Analysis, 1(2) (2014) 55-63. copulas, Sahand
• H. Tsukahara., Semiparametric estimation in copula models, Canad. J. Statist, 33 (2005) 357-375.
• J. Yan., Enjoy the joy of copulas: with a package copula, J. Stat. Software, 21(4) (2007) 1-21.