A Simple Adaptive Method for Time-Series Forecasting

Many financial time series look erratic and their evolution is notoriously hard to forecast. Most if not all economist do not see financial markets as being governed by some low-dimensional system of deterministic equations. Rather, it is generally accepted that financial variables evolve under the influence of a high number of factors. Therefore, it appears sensible to model such systems within a stochastic framework. In this paper we present an information- theoretic approach to the problem of estimating an adaptive stochastic model for forecasting the short-term evolution of ``difficult discrete time sequences. As the estimation of the model parameters is very fast, the time scale may be very short. The model is adaptive in the sense that both the set of past data, used for forecasting the next value, as well as their probability masses are automatically adjusted at each step. By ``difficult time sequence we understand that the conditional probability density of every new value conditioned on the knowledge of past data is near to the uniform distribution. In other words, there is a lot of uncertainty in the relation between the newest value and past data.