Optimal Markov Approximations and Generalized Embeddings

TL;DR

This paper introduces an information-theoretic method to determine optimal Markov models for time series, balancing model complexity and statistical accuracy, with applications to improved prediction performance.

Contribution

It presents a novel approach to find optimal Markov approximations using entropy estimates, enhancing modeling and prediction of time series data.

Findings

Effective balance between memory and statistical errors in Markov models.

Improved prediction accuracy demonstrated through examples.

Method based on entropy error estimation for optimal embedding dimension.

Abstract

Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.