Innovation Processes in Logically Constrained Time Series

  • Christoph Möller
  • Svetlozar T. Rachev
  • Young S. Kim
  • Frank J. Fabozzi


Capturing the relevant aspects of phenomena in an econometric model is a fine art. When it comes to the innovation process a trade of between a suitable process and its mathematical implications has to be found.

In many phenomena the likelihood of extreme events plays a crucial role. At the same time, classical extreme value theory is based on assumptions that cannot logically be drawn for the phenomenon in question. In this paper, we exemplify the fitness of tempered stable laws to capture both the probability of extreme events, and the relevant boundary conditions in a back-coupled system, the German balancing energy demand.


Innovation Process Stable Distribution ARIMA Model SARIMA Model Linear Time Series Model 


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Svetlozar T. Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the DFG and the DAAD. The authors thank Prof. Gennady Samorodnitsky for his help in formulating the problem of TID distributions and for his fruitful comments and suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christoph Möller
    • 1
  • Svetlozar T. Rachev
  • Young S. Kim
  • Frank J. Fabozzi
  1. 1.Department of Statistics, Econometrics and Mathematical Finance, School of Economicsand Business EngineeringUniversity of Karlsruhe and KITKarlsruheGermany

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