Past-future Mutual Information Estimation in Sparse Information Conditions

Yuval Shalev, Irad Ben-Gal

Abstract

We introduce the CT-PFMI, a context tree based algorithm that estimates the past-future mutual information (PFMI) between different time series. By applying a pruning phase of the context tree algorithm, uninformative past sequences are removed from PFMI estimation along with their false contributions. In situations where most of the past data is uninformative, the CT-PFMI shows better estimates to the true PFMI than other benchmark methods as demonstrated in a simulated study. By implementing CT-PFMI on real stock prices data we also demonstrate how the algorithm provides useful insights when analyzing the interactions between financial time series.

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