Conjugate processes: Theory and application to risk forecasting

Eduardo Horta and Flavio Ziegelmann

Stochastic Processes and their Applications, 2018, vol. 128, issue 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.

Keywords: Random measure; Covariance operator; Dimension reduction; Functional time series; High frequency financial data; Risk forecasting (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.06.002

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