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Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi

Year 2015, Issue: 7, 53 - 62, 11.07.2016
https://doi.org/10.1501/bsad_0000000020

Abstract

Bu çalışmada, tüketici fiyatlarının on iki aylık ortalamalara göre değişimi (TÜFE) ile dolar kuru arasındaki bağımlılık yapısı iki boyutlu Archimedean kapulalar kullanılarak modellenmiştir. Çalışmanın temel varsayımı, bu iki değişken arasındaki bağımlılığın Archimedean kapula ailesine ait olan Gumbel, Clayton ve Frank kapula fonksiyonlarından biriyle modellenebileceğidir. Bağımlılık yapısını modelleyebilecek iki boyutlu Archimedean kapula fonksiyonun tahmini için Genest ve Rivest (1993) çalışmasında önerilen yöntem kullanılmıştır. Bağımlılığı modelleyecek en uygun kapula fonksiyonu, aday kapula fonksiyonlarından her biri ile ampirik kapula fonksiyonu arasındaki uzaklığı minimum yapacak şekilde seçilmiştir. Bulgulara göre, TÜFE ve dolar kuru arasındaki bağımlılık yapısını modelleyen iki boyutlu Archimedean kapula fonksiyonu Gumbel (θ=100) olarak tahmin edilmiş ve değişkenlerin birlikte artmaya eğilimli oldukları görülmüştür.

References

  • Clayton, D.G. (1978), ‘A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incideince’, Biometrika, 65:141-151.
  • Genest, C., Mackay, J. (1986b), ‘The Joy of Copulas: Bivariate Distributions with Uniform Marginals,’ The American Statistician, 40, 280–283.
  • Genest, C. (1987), ‘Frank’s family of bivariate distributions’, Biometrika, 74:549-555.
  • Genest, C., Rivest, L.P. (1989),’A characterization of Gumbel’s family of extreme value distributions’, Statist Probab Lett, 8:207-211.
  • Genest, C. ,Rivest L.P. (1993), ‘Statistical inference procedures for bivariate archimedean copulas’, Journal of The American Statistical Association Theory and Methods (88), No: 423.
  • Genest, C., Favre, A.C. (2007), ‘Everything You Always Wanted to Know about Copula but Were Afraid to Ask’, Journal of Hydrological Engineering, Vol:12, No:4, 347-368.
  • ‘Fiyat Endeksleri ve Enflasyon’, Sorularla Resmi İstatistikler Dizisi-3, TÜİK
  • Frank, M.J (1979), ‘On the simultaneous associativity of F(x,y) and x+y-F(x,y)’, Aequ. Math, 19 (2-3), 194-226.
  • Frees, W.E., Valdez A.E. (1997), Understanding relationships using copulas. 32nd. Actuarial Research Conference, 6-8 August at University of Calgary, Albert ,Canada.
  • Gumbel, E.J. (1960),’ Distributions des valeurs extremes en plusiers dimensions’, Publ Inst. Statist Univ. Paris, 9:171-173.
  • Hougaard, P. (1986), ‘A class of multivariate failure time distributions’, Biometrika, 73:671-678.
  • Joe H (1997). Multivariate Models and Dependence Concepts. (Chapman & Hall Ltd.) Kimeldorf, G., Sampson, A. (1975b), Uniform representations of bivariate distributions. Communications in Statistics, 4, 617–627 (1975b)
  • Kolev, N., dos Anjos, U., Mendes, B. (2006),Copulas: a review and recent developments. Stoch.Models 22 (4), 617–660
  • Melchiori R. M. (2003),Which archimedean aopula is the right one? YieldCurve.com (eJournal)
  • Naifar N. (2011). Modelling dependence structure with archimedean copulas and applications iTraxx CDS index.Journal of Computational and Applied Mathematics, (235); 2459-2466.
  • Nelsen, R.B. 1986.’ Properties of a one-parameter family of bivariate distributions with specified marginals’, Communications in Statistics—Theory and Methods, 15, 3277–85.
  • Nelsen, R., (1999), ‘An Introduction to Copulas’, NewYork ,Springer.
  • Schweizer, B., Sklar, A. (1983), ‘Probabilistic Metric Spaces’, New York ,NorthHolland,
  • Schweizer, B. (1991),’ Thirty years of copulas’, pp.13-50 in: G. Dall’Aglio, S.Katz and G. Salinetti, eds. Advances in probability distributions with given marginals Math. Appl., vol. 67,pp. 13–50. Kluwer Acad. Publ., Dordrecht
  • Sklar, A. (1959),’ Fonctions de repartition a n dimensions et leurs marges’, Publicationsdel’Institut de Statistique de lUniversite de Paris,8, 229-231.
  • Sklar, A. (1973), ‘Random Variables, Joint Distribution Functions and Copulas.’, Kybernetika, 9:449 460.

Modelling the Relationship between Dollar Exchange Rate and Consumer Price Index via Archimedean Copula

Year 2015, Issue: 7, 53 - 62, 11.07.2016
https://doi.org/10.1501/bsad_0000000020

Abstract

In this paper, the dependence structure between rate of change in twelve months for consumer price indeks
(CPI) and dollar exchange rate is modelled. The main assumption of this study is the dependence structure
between of these two variables can be modelled by one of Gumbel, Clayton and Frank copula functions
that belong to Archimedean copula family. The method that is suggested by Genest anad Rivest (1993) is
used to estimate the bivariate Archimedean copula function that describe dependence structure. The copula
function that provides most approriate fit to data is selected by minimizing the distance between considered
copula function and the emprical copula function. The results show that bivariate Archimedean copula
function that model the dependence structure between CPI and dollar Exchange rate is estimated to be
Gumbel (
ˆ
  100
). Consequently, the variables tend to be increasing together can be said

References

  • Clayton, D.G. (1978), ‘A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incideince’, Biometrika, 65:141-151.
  • Genest, C., Mackay, J. (1986b), ‘The Joy of Copulas: Bivariate Distributions with Uniform Marginals,’ The American Statistician, 40, 280–283.
  • Genest, C. (1987), ‘Frank’s family of bivariate distributions’, Biometrika, 74:549-555.
  • Genest, C., Rivest, L.P. (1989),’A characterization of Gumbel’s family of extreme value distributions’, Statist Probab Lett, 8:207-211.
  • Genest, C. ,Rivest L.P. (1993), ‘Statistical inference procedures for bivariate archimedean copulas’, Journal of The American Statistical Association Theory and Methods (88), No: 423.
  • Genest, C., Favre, A.C. (2007), ‘Everything You Always Wanted to Know about Copula but Were Afraid to Ask’, Journal of Hydrological Engineering, Vol:12, No:4, 347-368.
  • ‘Fiyat Endeksleri ve Enflasyon’, Sorularla Resmi İstatistikler Dizisi-3, TÜİK
  • Frank, M.J (1979), ‘On the simultaneous associativity of F(x,y) and x+y-F(x,y)’, Aequ. Math, 19 (2-3), 194-226.
  • Frees, W.E., Valdez A.E. (1997), Understanding relationships using copulas. 32nd. Actuarial Research Conference, 6-8 August at University of Calgary, Albert ,Canada.
  • Gumbel, E.J. (1960),’ Distributions des valeurs extremes en plusiers dimensions’, Publ Inst. Statist Univ. Paris, 9:171-173.
  • Hougaard, P. (1986), ‘A class of multivariate failure time distributions’, Biometrika, 73:671-678.
  • Joe H (1997). Multivariate Models and Dependence Concepts. (Chapman & Hall Ltd.) Kimeldorf, G., Sampson, A. (1975b), Uniform representations of bivariate distributions. Communications in Statistics, 4, 617–627 (1975b)
  • Kolev, N., dos Anjos, U., Mendes, B. (2006),Copulas: a review and recent developments. Stoch.Models 22 (4), 617–660
  • Melchiori R. M. (2003),Which archimedean aopula is the right one? YieldCurve.com (eJournal)
  • Naifar N. (2011). Modelling dependence structure with archimedean copulas and applications iTraxx CDS index.Journal of Computational and Applied Mathematics, (235); 2459-2466.
  • Nelsen, R.B. 1986.’ Properties of a one-parameter family of bivariate distributions with specified marginals’, Communications in Statistics—Theory and Methods, 15, 3277–85.
  • Nelsen, R., (1999), ‘An Introduction to Copulas’, NewYork ,Springer.
  • Schweizer, B., Sklar, A. (1983), ‘Probabilistic Metric Spaces’, New York ,NorthHolland,
  • Schweizer, B. (1991),’ Thirty years of copulas’, pp.13-50 in: G. Dall’Aglio, S.Katz and G. Salinetti, eds. Advances in probability distributions with given marginals Math. Appl., vol. 67,pp. 13–50. Kluwer Acad. Publ., Dordrecht
  • Sklar, A. (1959),’ Fonctions de repartition a n dimensions et leurs marges’, Publicationsdel’Institut de Statistique de lUniversite de Paris,8, 229-231.
  • Sklar, A. (1973), ‘Random Variables, Joint Distribution Functions and Copulas.’, Kybernetika, 9:449 460.
There are 21 citations in total.

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Other ID JA44KY57BF
Journal Section Articles
Authors

Çiğdem Topçu Gülöksüz This is me

Publication Date July 11, 2016
Published in Issue Year 2015 Issue: 7

Cite

APA Gülöksüz, Ç. T. (2016). Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi. Bankacılık Ve Sigortacılık Araştırmaları Dergisi, 2(7), 53-62. https://doi.org/10.1501/bsad_0000000020
AMA Gülöksüz ÇT. Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi. BSAD. July 2016;2(7):53-62. doi:10.1501/bsad_0000000020
Chicago Gülöksüz, Çiğdem Topçu. “Dolar Kuru Ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula Ile Modellenmesi”. Bankacılık Ve Sigortacılık Araştırmaları Dergisi 2, no. 7 (July 2016): 53-62. https://doi.org/10.1501/bsad_0000000020.
EndNote Gülöksüz ÇT (July 1, 2016) Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi. Bankacılık ve Sigortacılık Araştırmaları Dergisi 2 7 53–62.
IEEE Ç. T. Gülöksüz, “Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi”, BSAD, vol. 2, no. 7, pp. 53–62, 2016, doi: 10.1501/bsad_0000000020.
ISNAD Gülöksüz, Çiğdem Topçu. “Dolar Kuru Ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula Ile Modellenmesi”. Bankacılık ve Sigortacılık Araştırmaları Dergisi 2/7 (July 2016), 53-62. https://doi.org/10.1501/bsad_0000000020.
JAMA Gülöksüz ÇT. Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi. BSAD. 2016;2:53–62.
MLA Gülöksüz, Çiğdem Topçu. “Dolar Kuru Ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula Ile Modellenmesi”. Bankacılık Ve Sigortacılık Araştırmaları Dergisi, vol. 2, no. 7, 2016, pp. 53-62, doi:10.1501/bsad_0000000020.
Vancouver Gülöksüz ÇT. Dolar Kuru ile Tüketici Fiyat Endeksi Arasındaki İlişkinin Archimedean Kapula ile Modellenmesi. BSAD. 2016;2(7):53-62.