Improving the autodependogram using the Kulback-Leibler divergence

TL;DR

This paper enhances the autodependogram by replacing chi-square statistics with Kullback-Leibler divergence estimators, improving its ability to detect autodependencies in time series data, demonstrated through simulations and financial data analysis.

Contribution

It introduces a novel autodependogram method using Kullback-Leibler divergence, offering increased power over traditional chi-square-based methods.

Findings

The new autodependogram outperforms the classical version in simulation studies.

It effectively detects autodependencies in various time series models.

Application to financial data confirms its practical usefulness.

Abstract

The autodependogram is a graphical device recently proposed in the literature to analyze autodependencies. It is defined computing the classical Pearson chi-square statistics of independence at various lags in order to point out the presence lag-depedencies. This paper proposes an improvement of this diagram obtained by substituting the chi-square statistics with an estimator of the Kulback-Leibler divergence between the bivariate density of two delayed variables and the product of their marginal distributions. A simulation study, on well-established time series models, shows that this new autodependogram is more powerful than the previous one. An application to financial data is also shown.