Statistical inference of lead-lag at various timescales between asynchronous time series from p-values of transfer entropy

TL;DR

This paper develops a statistical framework for inferring lead-lag relationships across multiple timescales in asynchronous time series using transfer entropy, enabling efficient network inference without intensive bootstrapping.

Contribution

It derives the asymptotic distribution of transfer entropy tests, introduces a method to measure information transfer timescales, and applies these to financial data for validated network inference.

Findings

Asymptotic distribution enables faster statistical testing.

Transfer entropy peaks at specific timescales indicating maximum information transfer.

Validated networks reveal non-trivial lead-lag relationships among stocks.

Abstract

Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks.