Chapter

Advances in Directional and Linear Statistics

pp 173-188

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Innovation Processes in Logically Constrained Time Series

  • Christoph MöllerAffiliated withDepartment of Statistics, Econometrics and Mathematical Finance, School of Economicsand Business Engineering, University of Karlsruhe and KIT Email author 
  • , Svetlozar T. Rachev
  • , Young S. Kim
  • , Frank J. Fabozzi

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Abstract

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.