Maximum Entropy Models for Time-Varying Moments applied to Daily Financial Returns

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[Jaynes, 1957a] and [Jaynes, 1957b]'s principle of maximum entropy gives a consistent framework for the motivation of assumptions on distributions. [Rockinger & Jondeau, 2002] introduced maximum entropy distributions for the analysis of motion in higher moments of nancial returns. Their approach has inspired this work as it turned out that it allows a simpler presentation of time series processes and motivates new generalizations in several directions. These generalizations again allow for some popular nancial return models to nd a maximum entropy or generalized maximum entropy interpretation. Both approaches allow for further extensions. The exibility of this approach rivals that of all known parametric classes of distributions, yet it often relies on simpler assumptions. The aim of this work is to give a formulation of the maximum entropy and generalized maximum entropy principle suitable for time series processes and nancial market return models, to show its exibility, and to give some empirical evidence withillustrative data. Contrary to parametric approaches maximum entropy approaches allow explicit modeling of time-variability of higher moments.