Using Transfer Entropy to Measure Directional Information in Time Series
Summary
The article explains statistical causality in time series and presents transfer entropy as a way to measure whether past information from one series improves understanding of another series’ future. It contrasts this approach with Granger causality, which tests whether lagged values of a source series improve prediction of a target, commonly through autoregressive models and an F-test. Correlation alone cannot establish a causal mechanism, and predictive direction does not prove what physically or economically drives a relationship.
Transfer entropy is framed as conditional information gain, using a divergence between probability distributions to quantify the effect of adding the source series’ past to the target’s past. The article relates it to Granger causality for Gaussian variables and describes linear and nonlinear analysis, with MQL5 implementation examples and demonstrations of lag detection and significance assessment. The examples offer a practical starting point rather than evidence of reliable trading signals. Results depend on model and lag choices, hidden variables may confound inference, and nonlinear calculations can be computationally demanding as the number of lags grows.
Key ideas
- Granger causality tests whether a source series’ past adds predictive information about a target beyond the target’s own past.
- Transfer entropy quantifies directional information gain by conditioning on the target’s history and adding the source’s history.
- A predictive relationship does not establish a definitive causal mechanism because unobserved variables may influence both series.
- Transfer entropy can represent nonlinear dependencies, while autoregressive Granger methods are mainly suited to linear relations.
- Choosing more lags can increase the computational cost of nonlinear transfer entropy analysis.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.