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Flexible and Dynamic Modeling of Dependencies via Copulas

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Modeling and Stochastic Learning for Forecasting in High Dimensions

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 217))

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Abstract

In this chapter we first review recent developments in the use of copulas for studying dependence structures between variables. We discuss and illustrate the concepts of unconditional and conditional copulas and association measures, in a bivariate setting. Statistical inference for conditional and unconditional copulas is discussed, in various modeling settings. Modeling the dynamics in a dependence structure between time series is of particular interest. For this we present a semiparametric approach using local polynomial approximation for the dynamic time parameter function. Throughout the chapter we provide some illustrative examples. The use of the proposed dynamical modeling approach is demonstrated in the analysis and forecast of wind speed data.

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Notes

  1. 1.

    Datasets can be obtained from the web site of the Bonneville Power Administration under http://transmission.bpa.gov/Business/Operations/Wind/MetData.aspx.

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Acknowledgements

The authors thank the organizers of the “Second workshop on Industry Practices for Forecasting” (wipfor 2013) for a very simulating meeting. This research is supported by IAP Research Network P7/06 of the Belgian State (Belgian Science Policy), and the project GOA/12/014 of the KU Leuven Research Fund. The third author is Postdoctoral Fellow of the Research Foundation – Flanders, and acknowledges support from the foundation.

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Authors and Affiliations

  1. Department of Mathematics and Leuven Statistics Research Centre (LStat), KU Leuven, Celestijnenlaan 200B, 2400, B-3001, Leuven (Heverlee), Belgium

    Irène Gijbels, Klaus Herrmann & Dominik Sznajder

Authors
  1. Irène Gijbels
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  2. Klaus Herrmann
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  3. Dominik Sznajder
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Correspondence to Irène Gijbels .

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Editors and Affiliations

  1. Department of Statistics, University Joseph Fourier, Grenoble, France

    Anestis Antoniadis

  2. Laboratoire de Mathématiques, Université Paris-Sud, Orsay Cedex, France

    Jean-Michel Poggi

  3. Electricité de France R & D, OSIRIS, Clamart Cedex, France

    Xavier Brossat

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Gijbels, I., Herrmann, K., Sznajder, D. (2015). Flexible and Dynamic Modeling of Dependencies via Copulas. In: Antoniadis, A., Poggi, JM., Brossat, X. (eds) Modeling and Stochastic Learning for Forecasting in High Dimensions. Lecture Notes in Statistics(), vol 217. Springer, Cham. https://doi.org/10.1007/978-3-319-18732-7_7

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