Improving predictability of time series using maximum entropy methods

TL;DR

This paper explores how maximum entropy methods can improve the predictability of empirical time series by efficiently reconstructing underlying Markov processes, especially in low-dimensional, non-stationary contexts.

Contribution

It demonstrates that MaxEnt can outperform traditional frequency sampling in certain low-dimensional cases, offering a more effective forecasting approach with shorter data samples.

Findings

MaxEnt is more efficient than sampling in low-dimensional cases.

Shorter historical data can achieve similar accuracy with MaxEnt.

Application to exchange rate data illustrates practical utility.

Abstract

We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there exists a subset of the space of stochastic matrices for which the MaxEnt method is more efficient than sampling, in the sense that shorter historical samples have to be considered to reach the same accuracy. Considering short samples is of particular interest when modelling smoothly non-stationary processes, for then it provides, under some conditions, a powerful forecasting tool. The method is illustrated for a discretized empirical series of exchange rates.