@article {4991,
	title = {Conjugate processes: Theory and application to risk forecasting},
	journal = {Stochastic Processes and their Applications},
	volume = {128},
	year = {2018},
	pages = {727-755},
	abstract = {<p>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 {\textendash} called conjugate processes {\textendash} 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.</p>
},
	author = {Horta, Eduardo and Flavio Ziegelmann}
}
