Transfer Entropy

Transfer entropy measures directed information flow from one time series to another as the information that the source's past adds about the target's present beyond the target's own past.

전이 엔트로피는 원천 시계열의 과거가 목표 시계열 자신의 과거를 넘어 목표의 현재값에 대해 추가로 주는 정보량으로, 방향이 있는 정보 흐름을 잽니다.

Does the history of one time series carry information about the next value of another series, even if the link is nonlinear?

한 시계열의 과거가 다른 시계열의 다음 값에 대해 비선형적으로라도 정보를 주는지 알고 싶어요.

Transfer entropy is the conditional mutual information between the target's current value and the source's past, given the target's own past, so it detects directional dependence that need not be linear. Significance is judged against time-shifted surrogate series, and in the linear-Gaussian case the measure equals half the Granger causality statistic.

When to use Transfer Entropy

• Two time series are compared for directional, possibly nonlinear predictive information.
• A Granger causality test is planned but the relationship may be nonlinear.
• Both directions (X to Y and Y to X) should be compared on the same scale.

When to use something else

• The series are short (fewer than about 100 time points); use a linear Granger causality test.
• The question is causal effect size under intervention; use a structural time-series or interrupted time-series design.

Assumptions and requirements

• The series are stationary; difference trending series first.
• Time points are equally spaced and a single unit is observed.
• Binned estimates need enough data for the bins raised to the joint history length.

What the analysis reports

• Transfer entropy in both directions (nats and bits)
• Bias-corrected value (estimate minus surrogate mean)
• Surrogate p-value from circular time shifts
• Linear-Gaussian transfer entropy and Granger likelihood-ratio test

How to report it

Transfer entropy from [X] to [Y] (history length [value], quantile-binned estimator) was [value] nats, surrogate p = [value]; the reverse direction was [value] nats, p = [value].

Related methods

• Granger Causality Test
• Cross-Correlation Function
• k-Nearest-Neighbour Mutual Information (KSG Estimator)

Run Transfer Entropy on Quorant