Conjugate processes: Theory and application to risk forecasting
- Citation:
- Horta, E., & Ziegelmann F. (2018). Conjugate processes: Theory and application to risk forecasting. Stochastic Processes and their Applications. 128(3), 727-755.
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.
