Indicators: statistics (Hurst, entropy, z-score)
Thirteen statistical studies computed on the loaded bars: linear regression slope and R², price/volume and price/delta correlation, skewness, kurtosis, Hurst R/S, autocorrelation, Shannon entropy, price z-score, percentile rank, efficiency ratio and Higuchi fractal dimension. All of them draw in a separate pane under the chart.
Senzoukria · Documentation · Updated September 2026
Where to find it
- Where
- Chart toolbar → Indicators → groups Momentum and Volatility
- Placement
- Separate pane (all 13), one line per indicator
- Input
- Bar closes only; returns are close differences, not log-returns
What it does
The statistics family measures the shape and memory of the close series rather than its level. Every study is a pure function of the loaded bars: a window of N values ending at the current bar produces one point, and the point is null (the pen is lifted) while the window is not full or when the value is undefined. Nothing is extrapolated and no session reset is applied: these are continuous oscillators.
Returns are defined as close[i] − close[i−1]. This choice is deliberate: skewness, kurtosis, autocorrelation, entropy and the R/S statistic are scale-invariant, so a log-return would not change their reading but would require close > 0 on every bar. Variances and covariances are computed in two passes around the window mean; Pearson correlation divides by two separate square roots to avoid overflow on cumulative volumes.
The regression trio (slope, fitted value, R²) uses a centred least-squares formulation. The fitted value itself is not exposed as an indicator because it duplicates the LSMA of the averages family; only Linear Regression Slope (price per bar) and R-Squared remain.
Settings
| Setting | Default | What it changes |
|---|---|---|
| Linear Regression Slope — Period | 20 (2–500) | Bars in the least-squares window; output is slope in price per bar |
| R-Squared — Period | 20 (2–500) | Window of the fit; null when the window is flat |
| Price/Volume Correlation — Period | 20 (2–500) | Pearson r between closes and bar volumes, clamped to [−1, 1] |
| Price/Delta Correlation — Period | 20 (2–500) | Pearson r between closes and bar deltas |
| Skewness — Period | 50 (3–1000) | Third standardised moment of returns, population convention |
| Kurtosis — Period | 50 (3–1000) | Fourth standardised moment of returns |
| Hurst Exponent (R/S) — Period | 100 (4–2000) | Single-window rescaled range: log(R/S) / log(N) |
| Autocorrelation — Lag / Window | 1 / 50 (1–100 / 2–1000) | Biased Box-Jenkins estimator, bounded in [−1, 1] |
| Shannon Entropy — Bins / Window | 8 / 50 (2–64 / 2–1000) | Entropy in bits of the return histogram over the window |
| Price Z-Score — Period | 20 (2–500) | (close − mean) / population σ; null when σ = 0 |
| Percentile Rank — Period | 100 (2–2000) | Rank of the current close inside the window |
| Efficiency Ratio — Period | 10 (1–500) | Net move divided by the sum of absolute moves |
| Fractal Dimension — Period / k max | 30 / 5 (4–500 / 2–50) | Higuchi estimator; k max is clamped to half the window |
| Color | per indicator | Line colour of the pane series |
How to use it
Open the Indicators panel from the chart toolbar and search by name. Momentum holds the regression trio, the two correlations, autocorrelation, z-score, percentile rank and efficiency ratio; Volatility holds skewness, kurtosis, Hurst, entropy and fractal dimension. Each study has its own pane, so stack only the ones you read.
The Study guide card shown for Hurst states its nature: a single-window rescaled-range estimate, not a regression across multiple scales. Short windows are unstable and the value does not establish predictive edge; treat readings above or below 0.5 as a description of the recent window only.
Limits and pitfalls
- A flat window (zero variance) yields null, never 0: the correlation, z-score, entropy and R/S are undefined there.
- Hurst R/S needs Period returns, so Period + 1 closes; with the default 100 the first defined point sits on the 101st loaded bar.
- Entropy depends on the number of bins: 8 bins cap the value at 3 bits, so compare readings only at equal bin counts.
- Fractal dimension is not clamped to [1, 2]; the estimator reports what the log-log slope says.
- These studies read closes only. They do not know the session, the tick size or the volume source, and they cannot certify data coverage.
Related pages
- Hurst Exponent (R/S)
- Shannon Entropy
- Price Z-Score
- Candle patterns and structure breaks
- Hurst exponent and mean reversion
This page in other languages
Frequently asked questions
- Why does the Hurst indicator show nothing on the first hundred bars?
- The R/S statistic needs a full window of returns. With the default period of 100 it needs 100 returns, so the first defined value lands on the 101st loaded bar; a shorter period reduces the warm-up but increases instability.
- Is the z-score reset at the session open?
- No. Price Z-Score, like every study in this family, is a continuous rolling oscillator. It uses the same population standard deviation convention as delta-zscore and volume-zscore.
- Can I plot these on the price chart instead of a pane?
- No. All thirteen statistics indicators target a dedicated pane because their units (bits, ratios, standardised moments) are not prices.