A Simple Adaptive Method for Time-Series Forecasting

Petr Klán and Georges Darbellay
Institute of Computer Science, Academy of Sciences of the Czech Republic
PKlan@uivt.cas.cz

Abstract

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.

In order to calculate the model parameters, and thus develop a definite algorithm, we use an information-theoretic measure of discrepancy between the probability distribution of the model and the assumed probability density of the value to forecast. We show that this measure of discrepancy can, under certain assumptions, be approximated by the least squares criterion.

We have tested our method on foreign exchange and interest rate data and compared it to the classical approach based on ARMA modelling. A demonstration program for MATLAB will also be included.