Markov Chain Order Estimation and Relative Entropy

TL;DR

This paper introduces a new estimator for determining the order of a Markov chain using relative entropy, and compares its performance with established methods like AIC and BIC through simulations.

Contribution

It proposes a novel estimator based on relative entropy and dependency levels, enhancing Markov chain order estimation techniques.

Findings

The new estimator performs competitively with AIC and BIC.

Simulation results demonstrate the estimator's effectiveness.

The approach provides a new perspective using divergence measures.

Abstract

We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a Markov Chain to be used in the definition of a couple of estimators i.e. the Local Dependency Level and Global Dependency Level for a Markov chain sample. After exploring their properties we propose a new estimator for the Markov chain order. Finally we show a few tables containing numerical simulation results, comparing the performance of the new estimator with the well known and already established AIC and BIC estimators.