Transfer Entropy for Directional Nonlinear Market Information Flow

Summary

This article introduces Granger causality and transfer entropy as ways to study directional predictive relationships in time series. Granger causality tests whether a source series improves forecasts of a target beyond the target’s own history, commonly using a vector autoregression. Transfer entropy measures the additional information about a target’s future contained in the source’s past, without requiring a specified linear functional form. The article also describes net information flow as the difference between the two directional transfer entropies, and notes their equivalence to linear Granger causality under joint Gaussian assumptions.

Applications include pairwise analysis of international equity indices over a historical sample and cited research on social media signals and stock returns. The reported analysis finds substantial cross-market information links, with US-to-UK flow highest, and cites evidence that nonlinear analysis identifies relationships missed by a linear model. These are observational, sample-dependent results; transfer entropy quantifies predictive information and does not by itself prove structural causation. The article also omits mathematical expressions in places, limiting reproducibility from the text alone.

Key ideas

• Granger causality asks whether a series improves forecasts of another series after accounting for the target’s own history.
• Transfer entropy measures directional predictive information without imposing a particular functional form.
• Net information flow compares transfer entropy in both directions to identify the dominant direction of predictive information.
• The article reports strong links among sampled international equity indices, especially between US and UK markets.
• Cited social media research finds nonlinear relationships that a linear Granger analysis may miss, though predictive information alone does not prove causation.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.