Concept

UHL Adaptive MA

UHL Adaptive MA is a Trend concept. The Library holds 1 implementation — a working definition you can pull into Quant.

Uhl

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UHL Adaptive MA

Indicator

What is the UHL Adaptive MA?

The UHL Adaptive MA, credited to Andreas Uhl and often published as the corrected moving average (CMA), is an average that updates only when movement is statistically meaningful. Each bar, it compares the variance of price over the lookback with the squared distance between the average's previous value and its new target, typically the current SMA. If that distance sits within the variance, the correction factor is zero and the line simply holds its prior value; the further the distance exceeds the variance, the closer the factor gets to one and the faster the line converges on the target.

Formally it is an exponential-style update with a recomputed gain: the correction factor equals one minus the ratio of lookback variance to squared distance, floored at zero, and the line moves that fraction of the way toward the target. An EMA applies a fixed fraction every bar; the corrected average re-derives its fraction from the variance comparison, so it can sit perfectly still for stretches and then cover most of the distance in a single step.

The practical effect is a stepped average that ignores fluctuations inside the recent noise band and moves decisively once price escapes it. A common two-line form applies the same correction to raw price to get a faster trend-step line and to a slow simple average for the baseline, then reads crossings between the two as the signal version of the concept.

The design answers the oldest complaint about moving averages: a fixed length is too slow in trends or too twitchy in ranges. Adaptive averages attack the trade-off from different angles; an adaptive-lookback MA varies the window itself, while the Uhl correction fixes the window and varies the update size. The reward is an honestly flat line in consolidation, which makes downstream rules such as an MA slope filter or a trend regime label noticeably less noisy. The cost is bluntness: a trend that begins gradually can idle inside the gate for several bars.

How to Read the UHL Adaptive MA on a Chart

Reading it means telling genuine steps from flat holds.

  1. 1Apply the corrected average with a single lookback; that one length drives both the variance estimate and the SMA target.
  2. 2Check an obvious trading range: a correct implementation goes genuinely horizontal there, while an EMA of the same length keeps drifting with every oscillation.
  3. 3Treat the first step after a flat stretch as the event; it fires only when price outruns recent variance, so it often coincides with a breakout from the consolidation.
  4. 4In the two-line form, mark crossings of the fast corrected line built on price and the slow corrected baseline; the flat holds make those crossings sharper than fixed-length crossovers.

How it's calculated

A self-correcting average that moves toward its target only to the extent that the squared distance to the target exceeds the recent variance of price.

SMA⁡t=1n×∑i=0n−1Ct−i\operatorname{SMA}_t = \frac{1}{n} \times \sum_{i=0}^{n-1} C_{t-i}
Var⁡t=mult⁡×1n×∑i=0n−1(Ct−i−SMA⁡t)2\operatorname{Var}_t = \operatorname{mult} \times \frac{1}{n} \times \sum_{i=0}^{n-1} (C_{t-i} - \operatorname{SMA}_t)^2
dt=(CMA⁡t−1−SMA⁡t)2d_t = (\operatorname{CMA}_{t-1} - \operatorname{SMA}_t)^2
at=1−Var⁡tdt if dt>Var⁡t, else at=0a_t = 1 - \frac{\operatorname{Var}_t}{d_t} \text{ if } d_t > \operatorname{Var}_t\text{, else } a_t = 0
CMA⁡t=CMA⁡t−1+at×(SMA⁡t−CMA⁡t−1)\operatorname{CMA}_t = \operatorname{CMA}_{t-1} + a_t \times (\operatorname{SMA}_t - \operatorname{CMA}_{t-1})
et=(CTS⁡t−1−Ct)2e_t = (\operatorname{CTS}_{t-1} - C_t)^2
bt=1−Var⁡tet if et>Var⁡t, else bt=0b_t = 1 - \frac{\operatorname{Var}_t}{e_t} \text{ if } e_t > \operatorname{Var}_t\text{, else } b_t = 0
CTS⁡t=CTS⁡t−1+bt×(Ct−CTS⁡t−1)\operatorname{CTS}_t = \operatorname{CTS}_{t-1} + b_t \times (C_t - \operatorname{CTS}_{t-1})
Trend signal: bullish while CTS⁡t>CMA⁡t, bearish while CTS⁡t<CMA⁡t\text{Trend signal: bullish while } \operatorname{CTS}_t > \operatorname{CMA}_t\text{, bearish while } \operatorname{CTS}_t < \operatorname{CMA}_t
C_t: close of bar t
t: bar index
i: bar offset inside the lookback window
n: lookback length for the SMA and variance (default 100)
SMA_t: simple moving average of close over n bars
Var_t: population variance of close over n bars, scaled by mult
mult: variance multiplier (default 1)
d_t: squared distance between the prior CMA and the current SMA
a_t: correction factor for the CMA, between 0 and 1
CMA_t: corrected moving average, the slow line
e_t: squared distance between the prior CTS and the current close
b_t: correction factor for the CTS, between 0 and 1
CTS_t: corrected trend step, the fast line

The corrected moving average is credited to Andreas Uhl of Salzburg University: while the move sits inside recent variance the correction factor is 0 and the line holds perfectly flat, then converges quickly once price escapes the noise band.

CMA corrects toward the SMA and acts as the slow line, CTS corrects toward raw closes and acts as the fast line; raising mult makes both lines harder to move.

Both recursive lines need a seed; published ports start them at the first close or SMA value.

How traders use it

  • As a range-resistant trend filter: because the correction factor is zero while price oscillates inside recent variance, the line stays genuinely flat in consolidation, and slope changes only appear when movement outruns noise.
  • As a crossover system: the fast corrected line (applied to price) crossing the slow corrected line (applied to a long simple average) defines bullish and bearish states, typically with fewer flip-flops than fixed-length moving average crossovers, though signals still lag turns.
  • As a general smoothing stage: the variance-gated update can be applied to inputs other than price, giving any noisy series a version that only moves when change outruns the recent variance.
  • As a dynamic support and resistance reference: because the line holds its level instead of chasing price, trend pullbacks tend to meet it in the same place repeatedly, a cleaner basis for dynamic S/R via MA tactics than a drifting average.
  • As a quieter baseline inside larger systems: traders swap it in for the average in price-versus-baseline rules or Supertrend-style trailing logic, specifically to cut range churn.

UHL Adaptive MA vs Other Smoothers

EMA: An EMA moves every bar by a fixed fraction of its gap to price, so it drifts even in dead ranges. The Uhl correction recomputes that fraction from a variance test and zeroes it inside the noise band, trading response at slow turns for flatness.

Adaptive-lookback MA: Adaptive-lookback designs shorten or lengthen the window as conditions change, so the line always moves, at varying speed. The Uhl approach fixes the window and gates the update itself, producing steps and holds rather than a continuously bending curve.

Ehlers SuperSmoother: The SuperSmoother comes from filter theory and strips high-frequency noise with minimal lag, but it still updates every bar. The Uhl line is piecewise flat instead, which suits regime detection better and curve-following worse.

Concept family

Trend

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UHL Adaptive MA FAQ

How does the UHL Adaptive MA decide when to move?

Through a variance test. The correction factor equals one minus the ratio of the lookback variance to the squared gap between the previous average and the new target, floored at zero. A gap smaller than the variance means no update at all; a gap several times the variance pushes the factor toward one, so the line jumps most of the way to the target.

Is the UHL Adaptive MA better than KAMA?

Neither dominates; they gate adaptation differently. KAMA scales smoothing continuously with the efficiency ratio, so it always creeps toward price. The Uhl correction is closer to a hard gate: literally zero movement inside the noise band, then rapid convergence outside it. That makes it flatter in ranges but blunter at trend starts, so test both on your market rather than assuming.

What lookback should the UHL Adaptive MA use?

There is no universal setting. One length controls both the variance window and the SMA target: longer lookbacks widen the noise band, giving flatter lines and later, larger steps; shorter ones step more often. Match it to your holding period.

Does the UHL Adaptive MA repaint?

Standard implementations do not. Each value is built from the previous corrected value, closed-bar variance, and the current target, so history is fixed once bars close; only the live bar keeps updating until it completes, as with any average.

Is the UHL Adaptive MA useful in ranging markets?

Ranges are its specialty in one narrow sense: it refuses to generate slope inside them, suppressing the false crossovers fixed averages produce. It will not predict how the range resolves; it stays quiet until a genuine reversal or escape carries price beyond recent variance.

Can the UHL correction be applied to averages other than the SMA?

Yes. The gate needs only a previous value, a target, and a variance estimate, so the target can be a weighted, volume-weighted, or quadratic average instead of the simple one; the library's Corrected QWMA does exactly that.

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