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arXiv · 1604.01472

Conjugate Processes: Theory and Application to Risk Forecasting

Eduardo Horta·Flavio Ziegelmann
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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.

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Eduardo Horta, Flavio Ziegelmann. 2016-04-06. Conjugate Processes: Theory and Application to Risk Forecasting. https://arxiv.org/abs/1604.01472

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