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Kaufman Efficiency Ratio (ER)

Summary

Kaufman Efficiency Ratio (also searched as "KER"): Perry Kaufman's noise measure from Smarter Trading (1995) — the net directional movement over the period divided by the total path travelled to get there. 1.0 is a perfectly efficient (straight-line) move; values near 0 are churn.

This is exactly the efficiency ratio KAMA computes internally to set its adaptive smoothing constant, exposed standalone and kept bit-identical to it.

Formula

ER[t] = |close[t] − close[t−P]| / Σ |close[k] − close[k−1]| over the same P bars.

Two guards, both shared with KAMA: a ratio that floating point would nudge just above 1.0 on a straight-line advance is pinned to exactly 1.0, and a dead-flat window (0/0) also reports 1.0 — a flat market therefore reads as "perfectly efficient", which is KAMA's own convention and what keeps the two reconstructible from each other.

The clamp compares against the signed net move, so it only fires on advances: on sustained declines the output may exceed 1.0 by a few ULP. The range is "0..1, may exceed 1 by a few ULP on sustained declines", not a hard bound.

TC2000 documents a signed ×100 variant (−100..+100); the absolute 0..1 form here is the author's, StockCharts', LEAN's, backtrader's and pandas-ta's.

Inputs

  • inReal — Source price/value series (canonically close)

Outputs

  • outReal — Efficiency ratio

Parameters

ParameterTypeDefaultAccepted valuesDescription
optInTimePeriodinteger102–100000Number of one-bar changes in the path sum (KAMA's optInTimePeriod is the same window, under its own default)

Notes

  • First output at index P (P one-bar changes need P+1 prices). No unstable period, not start-dependent.

Properties

Numerical Stability: Start-Independent

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: er.c · er.yaml

NativeFile
Cta_ER.c
Ruster.rs
JavaCore_ER.java

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

Aliases

Efficiency Ratio · Kaufman Efficiency Ratio · KER

See Also

KAMA · MAMA · STDDEV · VHF

References

  • Perry Kaufman, Smarter Trading: Improving Performance in Changing Markets (McGraw-Hill, 1995) — the efficiency ratio and the adaptive moving average built on it
  • Perry Kaufman, Trading Systems and Methods, 6th ed. (Wiley, 2019), the "Efficiency Ratio" section
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