SAQRID

SVNexus · Dependence

Transfer entropy

Also called: information flow, Schreiber transfer entropy

Transfer entropy measures directed information flow: how much one series' past reduces uncertainty about another's next value, beyond its own past.

Definition

Transfer entropy, introduced by Thomas Schreiber in 2000, quantifies how much knowing the past of series Y reduces uncertainty about the next value of series X, over and above what X's own past already tells you. It is measured in bits or nats.

Unlike correlation, it is directional: transfer entropy from Y to X generally differs from X to Y.

Intuition

If one market tends to move first and another follows, the leader's history carries information about the follower's next move. Transfer entropy captures that lead–lag information without assuming a linear relationship, so it can pick up nonlinear and asymmetric links that correlation or linear regressions miss.

In cross-asset work it is used to map which assets act as information sources and which as sinks.

An illustration of the asymmetry: hourly returns of a large, liquid index future might carry information about the next hour of a smaller regional index, while the reverse link is close to zero. Correlation between the two is one number for both directions; transfer entropy separates them.

How it's calculated

With histories xt(k) and yt(l) of lengths k and l:

TY→X = Σ p(xt+1, xt(k), yt(l)) · log [ p(xt+1 | xt(k), yt(l)) / p(xt+1 | xt(k)) ]

Probabilities are estimated by discretizing returns into bins or symbols, or with nearest-neighbor estimators for continuous data. For jointly Gaussian variables, transfer entropy is equivalent to Granger causality (it equals half the log ratio of the restricted and unrestricted residual variances).

Because estimates are biased upwards in finite samples, significance is tested against surrogate data, for example by shuffling Y to destroy its timing while keeping its distribution; the effective transfer entropy subtracts the shuffled average.

How to read it

Compare TY→X with TX→Y: a clear asymmetry suggests Y leads X at the sampling frequency used. A net value near zero after surrogate correction means no detectable information flow.

Results depend on sampling frequency, bin choice and history lengths. A link found on daily data may vanish or reverse on hourly data.

Common mistakes

  • Reporting raw transfer entropy without bias correction or significance testing.
  • Reading information flow as a causal mechanism.
  • Using non-synchronous closing prices across time zones, which manufactures leads.
  • Choosing many bins for a short sample, which inflates the estimate.

In Saqrid

SVNexus can build its asset network from transfer-entropy links, or from return correlation, DCC correlation, tail dependence or implied-vol spillover.

Pair drill-downs show lead-lag alongside tail risk, regime sync, wavelet coherence and correlation dynamics.

Open SVNexus.

  • Shannon entropy in marketsShannon entropy measures how uncertain a distribution of outcomes is; applied to returns or price patterns, it gauges how disordered a market is.
  • Volatility spilloverVolatility spillover is the transmission of volatility shocks from one asset or market to others, measured with VAR, GARCH or information-flow models.
  • Correlation networksA correlation network represents assets as nodes and their dependence as weighted links, making clusters and central assets visible.
  • Diebold–Yilmaz connectednessThe Diebold–Yilmaz index measures how much of each market's forecast-error variance comes from shocks to other markets, summarized as total connectedness.

Go deeper

Saqrid Institute lesson: Information Flow: Transfer Entropy. Lesson text is open to read without an account.

← All terms