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Ties, Time Series, and Regression

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Elements of Copula Modeling with R

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Abstract

This chapter is concerned with more advanced topics in copula modeling such as the handling of ties, time series, and covariates (in a regression-like setting).

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References

  • Abegaz, F., Gijbels, I., & Veraverbeke, N. (2012). Semiparametric estimation of conditional copulas. Journal of Multivariate Analysis, 110, 43–73.

    Article  MathSciNet  MATH  Google Scholar 

  • Acar, E. F., Craiu, R. V., & Yao, Y. (2011). Dependence calibration in conditional copulas: A nonparametric approach. Biometrics, 67, 445–453.

    Article  MathSciNet  MATH  Google Scholar 

  • Acar, E. F., Craiu, R. V., & Yao, Y. (2013). Statistical testing of covariate effects in conditional copula models. Electronic Journal of Statistics, 7, 2822–2850.

    Article  MathSciNet  MATH  Google Scholar 

  • Agresti, A. (2010). Analysis of ordinal categorical data (2nd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Aue, A., & Horváth, L. (2013). Structural breaks in time series. Journal of Time Series Analysis, 34(1), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  • Beare, B. K. (2010). Copulas and temporal dependence. Econometrica, 78(1), 395–410.

    Article  MathSciNet  MATH  Google Scholar 

  • Ben Ghorbal, M., Genest, C., & Nešlehová, J. G. (2009). On the test of Ghoudi, Khoudraji, and Rivest for extreme-value dependence. The Canadian Journal of Statistics, 37(4), 534–552.

    Article  MathSciNet  MATH  Google Scholar 

  • Bücher, A., Fermanian, J.-D., & Kojadinovic, I. (forthcoming). Combining cumulative sum change-point detection tests for assessing the stationarity of continuous univariate time series. Journal of Time Series Analysis.

    Google Scholar 

  • Bücher, A., & Kojadinovic, I. (2015). An overview of nonparametric tests of extreme-value dependence and of some related statistical procedures. In D. Dey & J. Yan (Eds.), Extreme value modeling and risk analysis: Methods and applications (pp. 377–398). Boca Baton, FL: Chapman & Hall/CRC.

    Chapter  MATH  Google Scholar 

  • Bücher, A., & Kojadinovic, I. (2016). A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing. Bernoulli, 22(2), 927–968.

    Article  MathSciNet  MATH  Google Scholar 

  • Bücher, A., Kojadinovic, I., Rohmer, T., & Segers, J. (2014). Detecting changes in cross-sectional dependence in multivariate time series. Journal of Multivariate Analysis, 132, 111–128.

    Article  MathSciNet  MATH  Google Scholar 

  • Canty, A., & Ripley, B. D. (2017). boot: Bootstrap R (S-Plus) functions, R package version 1.3-20. https://CRAN.R-project.org/package=boot

    Google Scholar 

  • Cardinali, A., & Nason, G. P. (2013). Costationarity of locally stationary time series using costat. Journal of Statistical Software, 55(1), 1–22.

    Article  MATH  Google Scholar 

  • Chen, X., & Fan, Y. (2005). Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection. The Canadian Journal of Statistics, 33, 389–414.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, X., & Fan, Y. (2006). Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecifcation. Journal of Econometrics, 135, 125–154.

    Article  MathSciNet  MATH  Google Scholar 

  • Constantine, W., & Percival, D. (2016). fractal: Fractal time series modeling and analysis, R package version 2.0-1. https://CRAN.R-project.org/package=fractal

  • Cormier, E., Genest, C., & Nešlehová, J. G. (2014). Using B-splines for nonparametric inference on bivariate extreme-value copulas. Extremes, 17, 633–659.

    Article  MathSciNet  MATH  Google Scholar 

  • Côté, M.-P., Genest, C., & Abdallah, A. (2016). Rank-based methods for modeling dependence between loss triangles. European Actuarial Journal, 6, 377–408.

    Article  MathSciNet  MATH  Google Scholar 

  • Csörgö, M., & Horváth, L. (1997). Limit theorems in change-point analysis. Chichester: Wiley.

    MATH  Google Scholar 

  • Darsow, W. W. F., Nguyen, B., & Olsen, E. T. (1992). Copulas and Markov processes. Illinois Journal of Mathematics, 36, 600–642.

    MathSciNet  MATH  Google Scholar 

  • Deheuvels, P. (1981). A non parametric test for independence. Publications de l’Institut de Statistique de l’Université de Paris, 26, 29–50.

    MATH  Google Scholar 

  • Dehling, H., Vogel, D., Wendler, M., & Wied, D. (2017). Testing for changes in Kendall’s tau. Econometric Theory, 33(6), 1352–1386.

    Article  MathSciNet  MATH  Google Scholar 

  • Derumigny, A., & Fermanian, J.-D. (2017). About tests of the “simplifying” assumption for conditional copulas. Dependence Modeling, 5(1), 154–197.

    Article  MathSciNet  MATH  Google Scholar 

  • Fermanian, J.-D., & Lopez, O. (2018). Single-index copulae. Journal of Multivariate Analysis, 165, 27–55.

    Article  MathSciNet  MATH  Google Scholar 

  • Fermanian, J.-D., & Wegkamp, M. (2012). Time-dependent copulas. Journal of Multivariate Analysis, 110, 19–29.

    Article  MathSciNet  MATH  Google Scholar 

  • Frees, E. W. (2010). Multivariate regression using copulas. University Lecture.

    Google Scholar 

  • Frees, E. W., & Valdez, E. A. (1998). Understanding relationships using copulas. North American Actuarial Journal, 2, 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Genest, C., Nešlehová, J. G., & Rémillard, B. (2014). On the empirical multilinear copula process for count data. Bernoulli, 20, 1344–1371.

    Article  MathSciNet  MATH  Google Scholar 

  • Genest, C., Nešlehová, J. G., & Rémillard, B. (2017). Asymptotic behavior of the empirical multilinear copula process under broad conditions. Journal of Multivariate Analysis, 20, 82–110.

    Article  MathSciNet  MATH  Google Scholar 

  • Genest, C., Nešlehová, J. G., & Ruppert, M. (2011). Comment on the paper by S. Haug, C. Klüppelberg and L. Peng entitled “Statistical models and methods for dependence in insurance data”. Journal of the Korean Statistical Society, 40, 141–148.

    Article  MathSciNet  MATH  Google Scholar 

  • Genest, C., & Rémillard, B. (2004). Tests of independence and randomness based on the empirical copula process. Test, 13(2), 335–369.

    Article  MathSciNet  MATH  Google Scholar 

  • Genest, C., Quessy, J.-F., & Rémillard, B. (2006). Goodness-of-fit procedures for copula models based on the probability integral transformation. Scandinavian Journal of Statistics, 33, 337–366.

    Article  MathSciNet  MATH  Google Scholar 

  • Ghalanos, A. (2017). rugarch: Univariate GARCH models. R package version 1.3-8. https://CRAN.R-project.org/package=rugarch

    Google Scholar 

  • Gijbels, I., Omelka, M., & Veraverbeke, N. (2015). Estimation of a copula when a covariate affects only marginal distributions. Scandinavian Journal of Statistics, 42(4), 1109–1126.

    Article  MathSciNet  MATH  Google Scholar 

  • Gombay, E., & Horváth, L. (1999). Change-points and bootstrap, Environmetrics, 10(6), 725–736.

    Article  Google Scholar 

  • Grégoire, V., Genest, C., & Gendron, M. (2008). Using copulas to model price dependence in energy markets. Energy Risk, 5(5), 58–64.

    Google Scholar 

  • Hofert, M., Kojadinovic, I., Mächler, M., & Yan, J. (2017a). copulaData: Data sets for copula modeling. R package version 0.0-1. https://CRAN.R-project.org/package=copulaData

  • Holmes, M., Kojadinovic, I., & Quessy, J.-F. (2013). Nonparametric tests for change-point detection à la Gombay and Horváth. Journal of Multivariate Analysis, 115, 16–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Ibragimov, R. (2009). Copula based characterizations for higher-order Markov processes. Econometric Theory, 25, 819–846.

    Article  MathSciNet  MATH  Google Scholar 

  • Joe, H. (2014). Dependence modeling with copulas. Boca Raton, FL: Chapman & Hall/CRC.

    Book  MATH  Google Scholar 

  • Jondeau, E., & Rockinger, M. (2006). The Copula–GARCH model of conditional dependencies: An international stock market application. Journal of International Money and Finance, 25, 827–853.

    Article  Google Scholar 

  • Kendall, M. G. (1945). The treatment of ties in rank problems. Biometrika, 3, 239–251.

    Article  MATH  Google Scholar 

  • Kojadinovic, I. (2017a). npcp: Some nonparametric tests for change-point detection in possibly multivariate observations. R package version 0.1-9. https://CRAN.Rproject.org/package=npcp

  • Kojadinovic, I. (2017b). Some copula inference procedures adapted to the presence of ties. Computational Statistics and Data Analysis, 142, 24–41.

    Article  MathSciNet  MATH  Google Scholar 

  • Kojadinovic, I., & Yan, J. (2010). Modeling multivariate distributions with continuous margins using the copula R package. Journal of Statistical Software, 34(9), 1–20.

    Article  Google Scholar 

  • Kojadinovic, I., & Yan, J. (2011). Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process. Annals of the Institute of Statistical Mathematics, 63, 347–373.

    Article  MathSciNet  MATH  Google Scholar 

  • Lambert, P. (2007). Archimedean copula estimation using Bayesian splines smoothing techniques. Computational Statistics and Data Analysis, 51(12), 6307–6320.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, Y., Li, Y., Qin, Y., & Yan, J. (2016). Copula modeling for data with ties. Tech. Rep., ArXiv E-prints. arxiv:1612.06968.

    Google Scholar 

  • Lindsey, J. K. (1997). Applying generalized linear models. New York: Springer.

    MATH  Google Scholar 

  • McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools (2nd ed.). Princeton, NJ: Princeton University Press.

    MATH  Google Scholar 

  • Nason, G. (2016). locits: Tests of stationarity and localized autocovariance. R package version 1.7.3. https://CRAN.R-project.org/package=locits

  • Nason, G., & Cardinali, A. (2013). costat: Time series costationarity determination. R package version 2.3. http://CRAN.R-project.org/package=costat

  • Nason, G. P. (2013). A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series. Journal of the Royal Statistical Society Series B, 75, 879–904.

    Article  MathSciNet  Google Scholar 

  • Pappadà, R., Durante, F., & Salvadori, G. (2017). Quantification of the environmental structural risk with spoiling ties: Is randomization worthwhile? Stochastic Environmental Research and Risk Assessment, 31, 2483–2497.

    Article  Google Scholar 

  • Patton, A. J. (2006). Modelling asymmetric exchange rate dependence. International Economic Review, 47(2), 527–556.

    Article  MathSciNet  Google Scholar 

  • Patton, A. J. (2012). A review of copula models for economic time series. Journal of Multivariate Analysis, 110, 4–18.

    Article  MathSciNet  MATH  Google Scholar 

  • Patton, A. J. (2013). Copula methods for forecasting multivariate time series. In G. Elliott & A. Timmermann (Eds.), Handbook of economic forecasting (pp. 899–960). New York: Springer.

    Google Scholar 

  • Portier, F., & Segers, J. (2018). On the weak convergence of the empirical conditional copula under a simplifying assumption. Journal of Multivariate Analysis, 166, 160–181.

    Article  MathSciNet  MATH  Google Scholar 

  • Priestley, M. B., & Subba Rao, T. (1969). A test for stationarity of time series. Journal of the Royal Statistical Society Series B, 31, 140–149.

    MathSciNet  MATH  Google Scholar 

  • Quessy, J.-F., Saïd, M., & Favre, A.-C. (2013). Multivariate Kendall’s tau for change-point detection in copulas. The Canadian Journal of Statistics, 41, 65–82.

    Article  MathSciNet  MATH  Google Scholar 

  • Rémillard, B. (2017). Goodness-of-fit tests for copulas of multivariate time series. Econometrics, 5(13), 1–23.

    Google Scholar 

  • Rémillard, B., Papageorgiou, N., & Soustra, F. (2012). Copula-based semiparametric models for multivariate time series. Journal of Multivariate Analysis, 110, 30–42.

    Article  MathSciNet  MATH  Google Scholar 

  • Ryan, J. A., & Ulrich, J. M. (2017). xts: eXtensible Time Series. R package version 0.10-0. http://CRAN.R-project.org/package=xts

  • Sun, J., Frees, E. W., & Rosenberg, M. A. (2008). Heavy-tailed longitudinal data modeling using copulas. Insurance: Mathematics and Economics, 42, 817–830.

    MATH  Google Scholar 

  • Veraverbeke, N., Omelka, M., & Gijbels, I. (2011). Estimation of a conditional copula and association measures. Scandinavian Journal of Statistics, 38, 766–780.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada

    Marius Hofert

  2. Laboratory of Mathematics and its Applications, University of Pau and Pays de l’Adour, Pau, France

    Ivan Kojadinovic

  3. Seminar for Statistics, ETH Zurich, Zurich, Switzerland

    Martin Mächler

  4. Department of Statistics, University of Connecticut, Storrs, Connecticut, USA

    Jun Yan

Authors
  1. Marius Hofert
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  2. Ivan Kojadinovic
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  3. Martin Mächler
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  4. Jun Yan
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Hofert, M., Kojadinovic, I., Mächler, M., Yan, J. (2018). Ties, Time Series, and Regression. In: Elements of Copula Modeling with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-89635-9_6

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