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Conjugate processes: Theory and application to risk forecasting

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  • Horta, Eduardo
  • Ziegelmann, Flavio

Abstract

Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models – called conjugate processes – allowing the sequence of marginal distributions of a cyclic, continuous-time process to evolve stochastically in time. The connection between the two processes is given by a fundamental compatibility equation. Key results include Laws of Large Numbers in the presented framework. We provide a constructive example which illustrates the theory, and give a statistical implementation to risk forecasting in financial data.

Suggested Citation

  • Horta, Eduardo & Ziegelmann, Flavio, 2018. "Conjugate processes: Theory and application to risk forecasting," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 727-755.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:3:p:727-755
    DOI: 10.1016/j.spa.2017.06.002
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