Concept

Entropy Measures

Entropy Measures, also known as Shannon, approximate, sample, permutation, are Statistics concepts. The Library holds 1 implementation — a working definition you can pull into Quant.

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The top custom implementation, built on the original standard Entropy Measures formula.

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Precision Market Entropy Heatmap preview

Precision Market Entropy Heatmap

Indicator

What are Entropy Measures?

Entropy measures quantify how disordered or unpredictable a series is. The root idea is Claude Shannon's 1948 information theory: bin the data, estimate the probability of each outcome, and sum probability times negative log-probability. The result peaks when every outcome is equally likely and falls to zero when one outcome is certain, so it reads as the average surprise per observation. Applied to returns, it asks how evenly recent outcomes are spread across their range.

Time-series variants ask a sharper question about pattern persistence. Approximate entropy, introduced by Steven Pincus in 1991, and sample entropy, a 2000 refinement by Richman and Moorman that removes its self-matching bias, track how often matching patterns of m consecutive values keep matching at length m+1, scored so that more persistence means a lower reading. Permutation entropy, proposed by Bandt and Pompe in 2002, applies the Shannon formula to ordinal patterns, the rank orderings of consecutive values, which makes it robust to outliers and indifferent to magnitude.

The trading translation: low entropy means repeating structure that trend or cycle logic can grip; high entropy means noise-like behavior where most signals degrade. Entropy is therefore a regime input rather than a signal generator, similar in role to the Hurst exponent and fractal dimension but built from information theory rather than scaling behavior. It also complements autocorrelation: correlation detects only linear dependence at fixed lags, while entropy responds to any repeated structure, linear or not.

Every variant is sensitive to its settings. Bin counts change Shannon readings, embedding length and tolerance change approximate and sample entropy, and window length controls how fast any of them react. Readings therefore only compare under fixed parameters, and most practitioners normalize them, against the theoretical maximum or via a rolling percentile rank, before calling a value high or low. On finite, noisy market data the estimates are themselves noisy, so entropy is usually smoothed and read as a slowly shifting backdrop rather than a bar-by-bar trigger.

How to Identify Entropy Regimes on a Chart

Entropy plots as an indicator pane, so identification means learning what its extremes look like against price:

  1. 1Add an entropy indicator and fix its parameters (window, embedding length, tolerance, or bin count); every comparison that follows assumes they do not move.
  2. 2Establish the local range: note where readings have sat over the past few hundred bars, since raw entropy values have no universal scale.
  3. 3Mark the low-entropy stretches and check price: they should coincide with cleaner trends, steadier cycles, or orderly ranges.
  4. 4Mark the high-entropy stretches: choppy, gappy, or news-driven tape where recent patterns fail to repeat.
  5. 5Watch transitions rather than levels: a fall toward the lower range says structure is emerging; the reverse says an orderly phase is dissolving.

How it's calculated

A family of randomness measures scoring how unpredictable a price or return series is over a lookback window.

Shannon: H=−∑i=1kpi×log⁡2(pi)\text{Shannon: } H = -\sum_{i=1}^{k} p_i \times \log_2(p_i)
Approximate: ApEn⁡(m,r)=Φm(r)−Φm+1(r)\text{Approximate: } \operatorname{ApEn}(m, r) = \Phi_m(r) - \Phi_{m+1}(r)
Sample: SampEn⁡(m,r)=−ln⁡(A/B)\text{Sample: } \operatorname{SampEn}(m, r) = -\ln(A / B)
Permutation: PE⁡m=−∑p(π)×ln⁡(p(π)),summed over the m! ordinal patterns π\text{Permutation: } \operatorname{PE}_m = -\sum p(\pi) \times \ln(p(\pi)), \quad \text{summed over the } m! \text{ ordinal patterns } \pi
H: Shannon entropy of the distribution, in bits
p_i: relative frequency of state or bin i (returns binned into k bins, or mapped to up/down states)
i: state or bin index
k: number of states or bins
ApEn: approximate entropy of the series
SampEn: sample entropy of the series
PE_m: permutation entropy of order m
m: embedding dimension, the compared template or pattern length (commonly 2; 3 to 7 for permutation)
r: match tolerance (commonly 0.2 × the standard deviation of the series)
Φ_m(r): mean over all length-m templates of ln of each template's match fraction, the share of templates within tolerance r of it, self-matches included
A: number of template pairs within tolerance r at length m + 1, self-matches excluded
B: number of template pairs within tolerance r at length m, self-matches excluded
p(π): relative frequency of ordinal pattern π among all length-m windows
π: ordinal pattern, the rank order of m consecutive values

Inputs are usually closes or log returns over a rolling window, commonly 100 to 500 bars.

Higher readings mean a less predictable series, lower readings more regularity.

Permutation entropy is often normalized by ln(m!); Shannon entropy uses log2 for bits, and natural-log versions differ only by a constant factor.

How traders use it

  • As a tradability filter: high-entropy stretches argue for standing aside or reducing size, while falling entropy suggests structure is emerging and pattern or trend signals have better footing.
  • As an input to adaptive parameterization: smoothing lengths and signal thresholds scale with measured entropy so tools slow down in noise and speed up in order, the role measurement noise plays in a Kalman filter.
  • For cross-sectional comparison: ranking instruments or timeframes by entropy to direct attention toward the most structured ones.
  • As a gate on periodic tools: outputs from dominant cycle measurement or FFT/spectral analysis are trusted only when entropy is low enough for a cyclic read to be meaningful.
  • As a multi-window view: entropy computed over several lookbacks at once and color-coded, so shifts in structure show up across scales.

Entropy Measures vs related concepts

Fractal Dimension: Both grade order versus noise, but fractal dimension measures how jagged the price path is through its scaling behavior, while entropy measures how unpredictable the sequence of outcomes is. A smooth but erratic series and a jagged but repetitive one can score differently on each.

Autocorrelation: Autocorrelation detects linear dependence at specific lags and carries a sign, so it distinguishes trending from mean-reverting behavior. Entropy is unsigned and blind to direction: it says how much structure exists, not what kind.

Distribution-of-returns Profiling: Profiling examines the shape of the return distribution: skew, tails, modes. Entropy compresses predictability into one number, and its pattern-based variants care about the ordering of values, which a distribution ignores entirely.

Concept family

Statistics

46 concepts mapped · 46 in the Library

Entropy Measures FAQ

What does high entropy mean on a price chart?

That recent behavior is close to random: patterns of consecutive moves are not repeating, and outcomes are spread evenly rather than concentrated. Practically it warns that trend-following and pattern signals are operating in their worst environment. It does not predict direction; it describes how predictable the series has been over the measurement window, and it changes as that window rolls.

Which entropy measure works best for market data?

There is no consensus best. Sample entropy is generally preferred over approximate entropy on short, noisy series because it removes self-matching bias. Permutation entropy is robust to outliers and cheap to compute but discards magnitude information. Shannon entropy on binned returns is simplest but depends heavily on bin choices. Comparing several measures under fixed settings is safer than trusting one.

Is entropy the same as volatility?

No. Volatility measures the size of moves; entropy measures their predictability. A strong, steady trend can be volatile yet relatively low-entropy because its pattern repeats, while a quiet range can score high if its small moves are effectively random. The two often rise together in stressed markets, but they answer different questions.

What settings do approximate and sample entropy typically use?

Conventions carried over from the physiology literature: an embedding length m of 2 or 3 and a tolerance r around 0.1 to 0.25 of the window's standard deviation, computed over at least a few hundred points. Markets have no agreed defaults, so the safer practice is to fix values, check that readings are stable to small perturbations, and never compare numbers across different settings.

Can entropy predict breakouts?

Not directly. Entropy describes how ordered recent behavior has been, and a falling reading inside a tightening range does suggest coiling structure, but the measure says nothing about direction or timing. Evidence that entropy alone times breakouts is thin; it is better used to decide which signals deserve trust than as a trigger of its own.

How much data do entropy measures need?

More than most indicators. Short windows make the underlying probability estimates unstable, and sample entropy can even be undefined when no patterns match within tolerance. Longer windows stabilize the estimate but lag regime change, so practitioners balance the two, often by smoothing a medium-length window or averaging across several.

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