tsb — Rolling Extended Statistics

Higher-order rolling window statistics extending the core pandas.Series.rolling() API: sem, skew, kurt, and quantile.

1. rollingSem — Standard Error of the Mean

The standard error of the mean measures how much the sample mean would vary across repeated samples. For a window of n values:

sem = std(ddof=1) / √n

Requires at least 2 valid observations per window.

import { rollingSem, Series } from "tsb";

const s = new Series({ data: [2, 4, 4, 4, 5, 5, 7, 9], name: "x" });
const sem3 = rollingSem(s, 3);
// [null, null, 0.667, 0, 0.577, 0.577, 1.155, 2.082]

2. rollingSkew — Fisher-Pearson Skewness

Skewness measures asymmetry of the distribution in each window. Positive = right tail heavier; negative = left tail heavier. Uses the unbiased Fisher-Pearson formula (same as pandas):

skew = [n/((n-1)(n-2))] × Σ[(xᵢ−x̄)/s]³

Requires ≥ 3 valid observations.

import { rollingSkew, Series } from "tsb";

const s = new Series({ data: [1, 2, 3, 4, 5] });
rollingSkew(s, 3);
// [null, null, 0, 0, 0]   ← symmetric windows → zero skew

3. rollingKurt — Excess Kurtosis

Kurtosis measures how heavy the tails are relative to a normal distribution. The excess kurtosis subtracts 3, so a normal distribution gives 0. Uses the Fisher (1930) unbiased formula:

kurt = [n(n+1)/((n-1)(n-2)(n-3))] × Σ[(xᵢ−x̄)/s]⁴ − 3(n-1)²/((n-2)(n-3))

Requires ≥ 4 valid observations.

import { rollingKurt, Series } from "tsb";

const s = new Series({ data: [1, 2, 3, 4] });
rollingKurt(s, 4);
// [null, null, null, -1.2]   ← uniform distribution has kurt = -1.2

4. rollingQuantile — Rolling Quantile

Computes any quantile within each sliding window using configurable interpolation. When q = 0.5 this is identical to rolling.median().

import { rollingQuantile, Series } from "tsb";

const s = new Series({ data: [1, 2, 3, 4, 5] });

rollingQuantile(s, 0.5, 3);  // rolling median: [null, null, 2, 3, 4]
rollingQuantile(s, 0.25, 3); // [null, null, 1.5, 2.5, 3.5]
rollingQuantile(s, 0.75, 3); // [null, null, 2.5, 3.5, 4.5]

Interpolation methods

Common Options