Bitlis İlindeki Günlük Maksimum ve Minumum Sıcaklık Değişimlerinin Copula Metodu ile Modellenmesi

Year 2018, , 268 - 275, 28.12.2018

Ayşe Metin Karakaş

https://doi.org/10.17798/bitlisfen.423871

Abstract

Bu makalenin amacı Bitlisin 2012-2017 yılları
arasındaki günlük maksimum ve minumum sıcaklıkları arasındaki ilişkiyi Copula
methodu ile açıklamaktır. İlişkiyi açıklamak için çeşitli copula aileleri
kullanılmıştır. Bunlar; Gumbel, Clayton,
Frank,  Joe, Gaussian ve Survival Claytondur.
Bağımlılık yapısını açıklamak ve
Gumbel, Clayton, Frank,  Joe, Gaussian ve
Survival Clayton copula ailelerinin parametrelerini belirlemek için parametrik olmayan metod olan Kendall
Tau ve Spearman Rho değerleri hesaplanmıştır. Uyum iyiliği testleri Kolmogorov
Smirnov,  Cramer on Mises, maksimum
oalabilirlik metodu, Akaike blgi kriteri ve Bayes bilgi kriteri yardımıyla veri
seti için uygun copula ailesi bulunmuştur. Sonuçlar Bitlisin 2012 yılı ile 2017
yılları arasında günlük maksimum ve minumum sıcaklık değişimleri için güçlü bir
bağımlılık olduğunu göstermiştir.

Keywords

Copula Fonksiyonları, Kendall Tau, Spearman Rho, Akaike bilgi kriteri, Uyum iyiliği Testi

With Copula Method Modeling of daily maximum and minimum temperature changes in Bitlis province

Abstract

This
paper aims to examine the relationship between  daily maximum and minimum temperatures of  Bitlis in Turkey between 2012-2017 years with
Copula method. To present the relationship between the variables, we use copula
families such as; Gumbel, Clayton, Frank, 
Joe, Gaussian and Survival Clayton copula.  To explain dependence structures of the data
set and to determine parameters of  Gumbel,
Clayton, Frank,  Joe, Gaussian and
Survival Clayton copula families, we calculate Kendall Tau and Spearman Rho
values which are nonparametric. With he help of  Kolmogorov Smirnov, Cramer Von Mises which are
goodness of  fit test, Maximum likelihood
method, Akaike information Criteria ad Bayes information criteria, we find the
suitable copula family for this data set. 
The results show that there is a strong dependence between daily maximum
and minimum temperatures of Bitlis between 2012-2017 years. 

Keywords

Copula functions, Kendall Tau, Spearman Rho, Goodness of fit test, Akaike information criteria

References

• 1. Sklar 1973. A. Random variables, joint distribution functions, and copulas. Kybernetika, 1973 9(6), 449-460.2. Genest 1986. C., & MacKay, J. The joy of copulas: Bivariate distributions with uniform marginal. The American Statistician, 40(4), 280-283.3. Genest, C., & Rivest, L. 1993. P. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88(423), 1034-10434. Justel, A., Peña, D., & Zamar, R. 1997. A multivariate Kolmogorov-Smirnov test of goodness of & Probability Letters Statistics, 35(3), 251-259.5. Nelsen 1999. R. B. Introduction. An Introduction to Copulas, Springer New York.6. Bouyé, E., Durrleman, V., Nikeghbali, A., Riboulet, G., & Roncelli, T. 2000. Copulas for finance-a reading guide and some applications.7. Frey, J. D. R., McNeil, A. J., Nyfeler, M. 2001. Copulas and credit models. Risk, 10(111114.10).8. Kim, G., Silvapulle, M. J., & Silvapulle, P. 2007. Comparison of semiparametric and parametric methods estimating copulas. Computational Statistics & Data Analysis, 51(6), 2836-2850.9. Genest, C., & Favre, A. C. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of hydrologic engineering, 12(4), 347-368.10. Salvadori, G., De Michele, C., Kottegoda, N. T., & Rosso, R. 2007. Extremes in nature: an approach using copulas, Springer Science & Business Media.11. Berg, Daniel 2009. Copula goodness-of-fit testing: an overview and power comparison. The European Journal of Finance., 15, 675-701.12. Fermanian 2005. J. D. Goodness-of-fit tests for copulas. Journal of multivariate analysis, 95(1), 119-152.13. Genest, C., & Rémillard, B. 2008. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. In Annals de l'Institut Henri Poincaré, Probabilities et Statistiques, 44(6), 1096-1127.14. Genest, C., Rémillard, B., Beaudoin, D. 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and economics, 44(2), 199-213.15. Huard, D., Évin, G., Favre, A. C. 2006. Bayesian copula selection. Computational Statistics & Data in Analysis, 51(2), 809-822.16. Jordanger, L. A., & Tjostheim, D. 2014. Model selection of copulas: AIC versus a cross validation copula information criterion. Statistics & Probability Letters, 92, 249-255.17. Kojadinovic, I., Yan, J., & Holmes, M. 2011. Fast large-sample goodness-of-fit tests for copulas. Statistica Sinica, 841-871.18. Kojadinovic, I., & Yan, J. 2011. A goodness-of-fit test for multivariate multipara meter copulas based on a multiplier central limit theorems, Statistics and Computing, 21(1), 17-30.