Research Article
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Year 2019, Volume: 68 Issue: 2, 1528 - 1542, 01.08.2019
https://doi.org/10.31801/cfsuasmas.543012

Abstract

References

  • Abegaz, F., Gijbels, I. and Veraverbeke, N., Semiparametric estimation of conditional copulas, Journal of Multivariate Analysis, 110, (2012), 43-73.
  • Acar, E.F., Nonparametric estimation and inference for the copula parameter in conditional copulas, Dissertation, University of Toronto, 2010.
  • Acar, E.F., Craiu, R.U. and Yao, F., Dependence calibration in conditional copulas: A nonparametric approach, Biometrics, 67(2), (2011), 445-453.
  • Acar, E.F., Craiu, R.U. and Yao, F., Statistical testing of covariate effects in conditional copula models, Electronic Journal of Statistics, 7, (2013), 2822-2850.
  • Allcroft, D.J. and Glasbey, C.A., A simulation-based method for model evaluation, Statistical Modelling, 3(1), (2003), 1-13.
  • Altınok, Y., Seismic risk estimation of the North Anatolian Faulth Zone Using Semi-Markov model, Jeofizik, 2, (1988), 44-58 (article in Turkish with English abstract).
  • Altınok, Y., Evaluation of earthquake risk in West Anatolia by Semi-Markov model, Jeofizik, 5, (1991), 135-140 (article in Turkish with English abstract).
  • Altınok, Y. and Kolçak, D., An application of the Semi-Markov model for earthquake occurrences in North Anatolia, Turkey, Journal of Balkan Geophysical Society, 2, (1999), 90--99.
  • Bartram, S., Taylor, S. and Wang, Y., The Euro and European financial market dependence, Journal of Banking and Finance, 31, (2007), 1461--1481.
  • Bee, M., Modelling credit default swap spreads by means normal mixtures and copulas, Applied Mathematical Finance, 11, (2004), 125-146.
  • Bhatia, S.C., Kumar, M.R. and Gupta, H.K., A Probabilistic Seismic Hazard Map of India and Adjoining Regions, Annali Di Geofisica , 2(6), (1999), 1153-1164.
  • Breymann, W., Dias, A. and Embrechts, P., Dependence structures for multivariate high-frequency data in finance, Quantitative Finance, 3, (2003), 1-14.
  • Cameron, A.C., Li, T., Trivedi, P.K. and Zimmer, D.M., Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts, The Econometrics Journal, 7, (2004), 566-584.
  • Chen, X., Fan, Y., Pouzo, D. and Ying, Z., Estimation and model selection of semiparametric multivariate survival functions under general censorship, Journal of Econometrics, 157, (2010), 129-142.
  • Clayton, D.G., A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65, (1978), 141-151.
  • Fan, J., Zhang, C. and Zhang, J., Generalized Likelihood Ratio Tests and Wilks Phenomenon, Annals of Statistics, 29(1), (2001), 153-193.
  • Fischbach, P., Copula-Models in the Electric Power Industry, Dissertation, University of St. Gallen, 2010.
  • Frees, E.W. and Valdez, E.A., Understanding relationships using copulas, North American Actuarial Journal, 2, (1998), 1-25.
  • Gijbels, I., Veraverbeke, N. and Omelka, M., Conditional copulas, association measures and their application, Computational Statistics and Data Analysis, 55(5), (2011), 1919-1932.
  • Hougaard, P., A class of multivariate failure time distributions, Biometrika, 73, (1986), 671-678.
  • Internet: Earthquake Katalog, Bogazici University, Kandilli Observatory and Earthquake Research Institute, National Earthquake Monitoring Center. (1901- 2008). URL:http://www.webcitation.org/query?url=http%3A%2F%2F www.koeri.boun.edu.tr%2Fsismo%2FMudim%2Fkatalog.asp&date=2015-12-15, (2015).
  • Internet: 1900-20xx Earthquake Katalog, AFAD. (2008-2014). URL:http://www.webcitation.org/query?url=http%3A%2F%2F www.deprem.gov.tr%2Ftr%2Fdepremkatalogu&date=2015-12-16, (2015).
  • Jondeau, E. and Rockinger, M., The Copula-GARCH model of conditional dependencies: an international stock market application, Journal of International Money and Finance, 25, (2006), 827--853.
  • Klugman, S.A. and Parsa, R., Fitting bivariate loss distributions with copulas, Insurance: Mathematics and Economics, 24, (1999), 139-148.
  • Li, Y., Shi, B. and Zhang, J., Copula joint function and its application in probability seismic hazard analysis, Acta Seismologica Sinica, 21(3), (2008), 296-305.
  • Nelsen, R.B., An introduction to copulas, Springer, New York, 2006.
  • Nikoloulopoulos, A.K. and Karlis, D., Fitting copulas to bivariate eartquake data: The Seismic Gap Hypothesis revisited, Environmetrics, 19, (2008a), 251-269.
  • Nikoloulopoulos, A.K. and Karlis, D., Copula model evaluation based on Parametric Bootstrap, Computational Statistics and Data Analysis, 52, (2008b), 3342-3353.
  • Oakes, D., A model for association in bivariate survival data, Journal of Royal Statistical Society Series B, 44, (1982), 414-422.
  • Palaro, H.P. and Hotta, L.K., Using conditional copula to estimate value at risk, Journal of Data Science, 4, (2006), 93-115.
  • Patton, A.J., Modelling Asymmetric Exchange Rate Dependence, Working paper, University of California, San Diego, 2003.
  • Patton, A.J., Modelling Asymmetric Exchange Rate Dependence, International Economic Review, 47, (2006), 527-556.
  • Sadeghian, R., Forecasting time and place of earthquakes using a Semi-Markov model (with case study in Tehran province), Journal of Industrial Engineering International, 8(20), (2012), 1-7.
  • Shih, J.H. and Louis, T.A., Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, (1995), 1384-1399.
  • Ünal, S., Modelling the earthquakes occuring on Turkey by Markov Chains, Dissertation, Gazi University, Ankara, 2010.
  • Ünal, S. and Çelebioğlu, S., A Markov Chain modelling of the earthquakes occurring in Turkey, Gazi University Journal of Science, 24, (2011), 263--274.
  • Zhang, C., Calibrating the degrees of freedom for automatic data-smoothing and effective curve checking, Journal of the American Statistical Association, 98(463), (2003), 609-628.

Investigation of the dependence structure in seismic hazard analysis: an application for Turkey

Year 2019, Volume: 68 Issue: 2, 1528 - 1542, 01.08.2019
https://doi.org/10.31801/cfsuasmas.543012

Abstract

In this study, using the earthquake occurrence data (Richter magnitude is equal to 4 or greater than 4 in the years 1901-2014) of the areas limited by 39.5°-42° N latitudes and 26°-45° E longitudes of North Anatolia and 36°-39.5° N latitudes and 26°-31° E longitudes of West Anatolia, it is aimed to model the dependence structure of Semi-Markov model via conditional copulas in which the copula is parametric and its parameter varies as the covariate, based on the assumption that the successive earthquakes in the same structural discontinuity should not be independent events and the occurrence of the earthquakes should be influenced by the elapsed time between them. From the results obtained for these regions with high seismicity, it is seen that the variation in the strength of dependence between the time elapsed from the previous seismic event and the magnitude of the next seismic event at different magnitudes of previous seismic event is highly significant and a usage of the parametric linear form in the copula parameter will be adequately characterized.

References

  • Abegaz, F., Gijbels, I. and Veraverbeke, N., Semiparametric estimation of conditional copulas, Journal of Multivariate Analysis, 110, (2012), 43-73.
  • Acar, E.F., Nonparametric estimation and inference for the copula parameter in conditional copulas, Dissertation, University of Toronto, 2010.
  • Acar, E.F., Craiu, R.U. and Yao, F., Dependence calibration in conditional copulas: A nonparametric approach, Biometrics, 67(2), (2011), 445-453.
  • Acar, E.F., Craiu, R.U. and Yao, F., Statistical testing of covariate effects in conditional copula models, Electronic Journal of Statistics, 7, (2013), 2822-2850.
  • Allcroft, D.J. and Glasbey, C.A., A simulation-based method for model evaluation, Statistical Modelling, 3(1), (2003), 1-13.
  • Altınok, Y., Seismic risk estimation of the North Anatolian Faulth Zone Using Semi-Markov model, Jeofizik, 2, (1988), 44-58 (article in Turkish with English abstract).
  • Altınok, Y., Evaluation of earthquake risk in West Anatolia by Semi-Markov model, Jeofizik, 5, (1991), 135-140 (article in Turkish with English abstract).
  • Altınok, Y. and Kolçak, D., An application of the Semi-Markov model for earthquake occurrences in North Anatolia, Turkey, Journal of Balkan Geophysical Society, 2, (1999), 90--99.
  • Bartram, S., Taylor, S. and Wang, Y., The Euro and European financial market dependence, Journal of Banking and Finance, 31, (2007), 1461--1481.
  • Bee, M., Modelling credit default swap spreads by means normal mixtures and copulas, Applied Mathematical Finance, 11, (2004), 125-146.
  • Bhatia, S.C., Kumar, M.R. and Gupta, H.K., A Probabilistic Seismic Hazard Map of India and Adjoining Regions, Annali Di Geofisica , 2(6), (1999), 1153-1164.
  • Breymann, W., Dias, A. and Embrechts, P., Dependence structures for multivariate high-frequency data in finance, Quantitative Finance, 3, (2003), 1-14.
  • Cameron, A.C., Li, T., Trivedi, P.K. and Zimmer, D.M., Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts, The Econometrics Journal, 7, (2004), 566-584.
  • Chen, X., Fan, Y., Pouzo, D. and Ying, Z., Estimation and model selection of semiparametric multivariate survival functions under general censorship, Journal of Econometrics, 157, (2010), 129-142.
  • Clayton, D.G., A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65, (1978), 141-151.
  • Fan, J., Zhang, C. and Zhang, J., Generalized Likelihood Ratio Tests and Wilks Phenomenon, Annals of Statistics, 29(1), (2001), 153-193.
  • Fischbach, P., Copula-Models in the Electric Power Industry, Dissertation, University of St. Gallen, 2010.
  • Frees, E.W. and Valdez, E.A., Understanding relationships using copulas, North American Actuarial Journal, 2, (1998), 1-25.
  • Gijbels, I., Veraverbeke, N. and Omelka, M., Conditional copulas, association measures and their application, Computational Statistics and Data Analysis, 55(5), (2011), 1919-1932.
  • Hougaard, P., A class of multivariate failure time distributions, Biometrika, 73, (1986), 671-678.
  • Internet: Earthquake Katalog, Bogazici University, Kandilli Observatory and Earthquake Research Institute, National Earthquake Monitoring Center. (1901- 2008). URL:http://www.webcitation.org/query?url=http%3A%2F%2F www.koeri.boun.edu.tr%2Fsismo%2FMudim%2Fkatalog.asp&date=2015-12-15, (2015).
  • Internet: 1900-20xx Earthquake Katalog, AFAD. (2008-2014). URL:http://www.webcitation.org/query?url=http%3A%2F%2F www.deprem.gov.tr%2Ftr%2Fdepremkatalogu&date=2015-12-16, (2015).
  • Jondeau, E. and Rockinger, M., The Copula-GARCH model of conditional dependencies: an international stock market application, Journal of International Money and Finance, 25, (2006), 827--853.
  • Klugman, S.A. and Parsa, R., Fitting bivariate loss distributions with copulas, Insurance: Mathematics and Economics, 24, (1999), 139-148.
  • Li, Y., Shi, B. and Zhang, J., Copula joint function and its application in probability seismic hazard analysis, Acta Seismologica Sinica, 21(3), (2008), 296-305.
  • Nelsen, R.B., An introduction to copulas, Springer, New York, 2006.
  • Nikoloulopoulos, A.K. and Karlis, D., Fitting copulas to bivariate eartquake data: The Seismic Gap Hypothesis revisited, Environmetrics, 19, (2008a), 251-269.
  • Nikoloulopoulos, A.K. and Karlis, D., Copula model evaluation based on Parametric Bootstrap, Computational Statistics and Data Analysis, 52, (2008b), 3342-3353.
  • Oakes, D., A model for association in bivariate survival data, Journal of Royal Statistical Society Series B, 44, (1982), 414-422.
  • Palaro, H.P. and Hotta, L.K., Using conditional copula to estimate value at risk, Journal of Data Science, 4, (2006), 93-115.
  • Patton, A.J., Modelling Asymmetric Exchange Rate Dependence, Working paper, University of California, San Diego, 2003.
  • Patton, A.J., Modelling Asymmetric Exchange Rate Dependence, International Economic Review, 47, (2006), 527-556.
  • Sadeghian, R., Forecasting time and place of earthquakes using a Semi-Markov model (with case study in Tehran province), Journal of Industrial Engineering International, 8(20), (2012), 1-7.
  • Shih, J.H. and Louis, T.A., Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, (1995), 1384-1399.
  • Ünal, S., Modelling the earthquakes occuring on Turkey by Markov Chains, Dissertation, Gazi University, Ankara, 2010.
  • Ünal, S. and Çelebioğlu, S., A Markov Chain modelling of the earthquakes occurring in Turkey, Gazi University Journal of Science, 24, (2011), 263--274.
  • Zhang, C., Calibrating the degrees of freedom for automatic data-smoothing and effective curve checking, Journal of the American Statistical Association, 98(463), (2003), 609-628.
There are 37 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Serpil Ünal Karaçam 0000-0002-4043-6832

Publication Date August 1, 2019
Submission Date December 19, 2017
Acceptance Date September 6, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Ünal Karaçam, S. (2019). Investigation of the dependence structure in seismic hazard analysis: an application for Turkey. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1528-1542. https://doi.org/10.31801/cfsuasmas.543012
AMA Ünal Karaçam S. Investigation of the dependence structure in seismic hazard analysis: an application for Turkey. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1528-1542. doi:10.31801/cfsuasmas.543012
Chicago Ünal Karaçam, Serpil. “Investigation of the Dependence Structure in Seismic Hazard Analysis: An Application for Turkey”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1528-42. https://doi.org/10.31801/cfsuasmas.543012.
EndNote Ünal Karaçam S (August 1, 2019) Investigation of the dependence structure in seismic hazard analysis: an application for Turkey. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1528–1542.
IEEE S. Ünal Karaçam, “Investigation of the dependence structure in seismic hazard analysis: an application for Turkey”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1528–1542, 2019, doi: 10.31801/cfsuasmas.543012.
ISNAD Ünal Karaçam, Serpil. “Investigation of the Dependence Structure in Seismic Hazard Analysis: An Application for Turkey”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1528-1542. https://doi.org/10.31801/cfsuasmas.543012.
JAMA Ünal Karaçam S. Investigation of the dependence structure in seismic hazard analysis: an application for Turkey. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1528–1542.
MLA Ünal Karaçam, Serpil. “Investigation of the Dependence Structure in Seismic Hazard Analysis: An Application for Turkey”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1528-42, doi:10.31801/cfsuasmas.543012.
Vancouver Ünal Karaçam S. Investigation of the dependence structure in seismic hazard analysis: an application for Turkey. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1528-42.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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