PFE Pass Node

Polarized Fractal Efficiency — Series Input

MomentumFractalPass

Overview

The PFE Pass Node computes the Polarized Fractal Efficiency (PFE) on a series input. PFE measures how efficiently price moves by comparing the straight-line distance to the actual path taken — values near +100 indicate efficient upward trending; values near −100 indicate efficient downward trending; values near 0 indicate choppy, inefficient movement.

PFE is based on fractal geometry: a perfectly efficient trend has a fractal dimension of 1 (straight line), while random noise has a dimension near 2. PFE normalizes this into an oscillator and applies EMA smoothing to reduce noise.

Formula

straightLine = √(period² + (close[i] − close[i−period])²)

pathLength = Σ √(1 + (close[j] − close[j−1])²) for j = i−period+1 to i

rawPFE = (straightLine / pathLength) × 100 × sign(close[i] − close[i−period])

PFE[i] = EMA(rawPFE, smoothPeriod)

Output range: [−100, +100]. Warm-up: period + smoothPeriod bars.

Parameters

Parameter	Default	Description
period	10	Lookback period for fractal efficiency calculation
smoothPeriod	5	EMA period for smoothing the raw PFE output

Inputs & Outputs

Slot	Direction	Type	Description
input	Input	{ values, timestamps }	Price or any numeric series
values	Output	(number \| null)[]	PFE values in [−100, +100]; nulls during warm-up
timestamps	Output	number[]	Unix timestamps aligned to input

Use Cases

Trend Quality Filter

When |PFE| > 50, the market is trending efficiently — apply trend-following systems. When |PFE| < 25, the market is chopping — switch to mean-reversion or stay flat.

Directional Confirmation

PFE sign confirms direction: positive values confirm upward trend efficiency, negative values confirm downward trend efficiency. Combine with ADX or VHF for multi-indicator confirmation.

Regime Detection

Track PFE over time to identify regime shifts — sustained high PFE indicates a trend regime; consistently low PFE indicates range-bound conditions. Switch strategy modes accordingly.

Tips & Best Practices

Use Absolute Value

For trend strength (ignoring direction), use |PFE|. Values > 50 indicate strong trending regardless of direction. Values near 0 indicate maximum inefficiency (chop).

Period Affects Sensitivity

Shorter periods (5–8) make PFE very reactive to local moves. Longer periods (15–20) focus on sustained trend efficiency. Default period=10 balances responsiveness with stability.

Compare with VHF

PFE and VHF both measure trend efficiency but use different approaches. When both agree on trend vs. chop regime, the signal is more reliable than either alone.