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Miha Kralj
2026-02-27 07:48:12 -08:00
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# HARMEAN: Harmonic Mean
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Statistic |
| **Inputs** | Source (close) |
| **Parameters** | `period` |
| **Outputs** | Single series (Harmean) |
| **Output range** | Varies (see docs) |
| **Warmup** | `period` bars |
### TL;DR
- The Harmonic Mean computes the reciprocal of the arithmetic mean of reciprocals over a sliding window.
- Parameterized by `period`.
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The harmonic mean is never greater than the geometric mean, which is never greater than the arithmetic mean." - The Mean Inequality, a mathematical fact older than calculus
The Harmonic Mean computes the reciprocal of the arithmetic mean of reciprocals over a sliding window. It is the correct average for quantities defined in terms of rates or ratios (speed, P/E ratios, yield). For financial time series, the harmonic mean gives the largest discount to outliers, making it the most conservative of the three Pythagorean means.