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# PFE: Polarized Fractal Efficiency
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Dynamic |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 10), `smoothPeriod` (default 5) |
| **Outputs** | Single series (Pfe) |
| **Output range** | Varies (see docs) |
| **Warmup** | `period + 1` bars |
### TL;DR
- Polarized Fractal Efficiency (PFE) quantifies trend strength by comparing the Euclidean distance a price series actually travels bar-to-bar against...
- Parameterized by `period` (default 10), `smoothperiod` (default 5).
- Output range: Varies (see docs).
- Requires `period + 1` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The shortest distance between two points is a straight line. The market never takes the shortest distance. PFE measures how badly it misses."
Polarized Fractal Efficiency (PFE) quantifies trend strength by comparing the Euclidean distance a price series actually travels bar-to-bar against the straight-line distance between the endpoints over the same window. The ratio, scaled to [-100, +100] and smoothed with an EMA, distinguishes efficient trending motion (values near ±100) from fractal, self-similar noise (values near 0). Created by Hans Hannula and published in *Technical Analysis of Stocks & Commodities* (January 1994), PFE applies fractal geometry to price action without requiring Hurst exponent estimation or rescaled-range analysis. With default parameters (period=10, smooth=5), the indicator needs 11 close values for the first raw reading plus 5 bars of EMA convergence, totaling ~16 bars of warmup. The core loop executes $N$ square roots per bar, making it $O(N)$ per update in streaming mode.