Models for time-varying moments using maximum entropy applied to a generalized measure of volatility

We use an information-theoretic approach to interpret Engle's (1982) and Bollerslev's (1986) GARCH model as a model for the motion in time of the expected conditional second power moment. This interpretation is used to show how these models may be generalized, if we use alternative measures of volatility. We choose one feasible alternative and derive a generalized volatility model. Applying this model to some exemplary market indices, we are able to give some empirical evidence for our method.