Rolling Skewness (SKEW)

Summary

An estimate, from the trailing window, of the skewness of the distribution its values come from: the third standardised moment. An asymmetry measure: above 0 the distribution has a longer tail above its mean, below 0 a longer tail below it, and a symmetric window reads 0. The companion to KURTOSIS, VAR and STDDEV in the same group.

Formula

Adjusted Fisher-Pearson coefficient of skewness, the estimator usually written G1. With window size n, window mean x̄ and population moments mₖ = Σ(x−x̄)ᵏ / n:

g1 = m₃ / m₂^(3/2)

G1 = g1 · √(n(n−1)) / (n−2)

The result is 0 when m₂ = 0, that is when every value in the window is equal: a point mass is symmetric.

optInTimePeriod must be at least 3: the n−2 denominator is undefined below it. The bound is enforced by the parameter range, so a shorter period is refused rather than silently degraded.

Notes

This is G1, the form Excel SKEW, scipy.stats.skew(bias=False) and R e1071::skewness(type = 2) compute. Two other estimators are in circulation, each a constant multiple of g1 rather than a rounding convention: g1 itself (scipy.stats.skew(bias=True)) and b1 = g1 · ((n−1)/n)^(3/2) (type = 3).
One reading apart from n−1 equal ones gives exactly √n, above the rest when the odd one is above and −√n when it is below. That is the largest magnitude a window can reach, so a window dominated by one outlier is legitimately far from 0.

Inputs

inReal — The series to measure

Outputs

outReal — Skewness of the trailing window, or 0 where the window has no spread

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	30	3–100000	Number of trailing values in the window

Properties

Numerical Stability: Start-Independent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1
☐ Display Shift
☐ Uses Transcendental
☐ Input Must Be Positive

Implementation

TA-Lib Definition: skew.c · skew.yaml

Native	File
C	`ta_SKEW.c`
Rust	`skew.rs`
Java	`Core_SKEW.java`
C#	`Core_SKEW.cs`

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Skewness, Sample Skewness, Fisher-Pearson Skewness

References

Joanes, D. N. and Gill, C. A. "Comparing measures of sample skewness and kurtosis." Journal of the Royal Statistical Society: Series D, 47(1), 1998, 183-189 — the g1, G1, b1 family and which is unbiased under which assumption.
NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.11 — the Fisher-Pearson coefficient and its adjusted form.
Microsoft, SKEW function — the G1 form.