Step Generalized Moving Average [BackQuant]Step Generalized Moving Average
Overview
Step Generalized Moving Average (StepGMA) is a trend-structure moving average designed to solve two common problems with classic MAs:
They overreact to noise in chop, causing constant micro-flips.
They lag too much when you smooth them enough to stop that noise.
StepGMA tackles this by combining two layers:
A Generalized Moving Average (GMA) that increases responsiveness without simply shortening length.
A Step Filter that converts the MA into discrete “steps” sized by ATR, suppressing insignificant movement and only updating when the move is meaningful.
The output is a trend line that behaves more like market structure: it holds its level through noise, then “reprices” in chunks when volatility-adjusted movement is large enough.
What the indicator is trying to represent
Instead of showing every tiny MA wiggle, StepGMA tries to represent the idea that:
Most price movement is noise relative to volatility.
Trend only matters when it advances by a meaningful amount.
A good trend line should stay stable until the market forces it to move.
That makes this indicator useful as:
A regime filter (trend vs chop).
A trend-following bias line.
A structure-like dynamic S/R reference.
A signal generator with fewer low-quality flips.
Component 1: Moving Average engine (selectable)
The base smoothing is not fixed. You can choose between multiple MA types:
SMA, EMA, WMA, VWMA: classic smoothing families.
DEMA, TEMA: reduced-lag EMA variants.
T3: smooth yet responsive, good for trend.
HMA: very low lag, can be twitchy without filtering.
ALMA: center-weighted smoothing, often “cleaner” visually.
KAMA: adaptive smoothing based on efficiency ratio, good in mixed regimes.
LSMA: regression-based, tends to track trend direction well.
McGinley: dynamic smoothing designed to reduce lag during fast moves.
This matters because the StepGMA is not “one MA.” It is a framework that lets you pick the underlying smoothing behavior, then applies the generalization and step logic on top.
Component 2: Generalized Moving Average (GMA)
Where the idea comes from
Generalized MA here is essentially a form of two-stage smoothing compensation . A common trick in signal processing and technical analysis is:
Apply a smoother once (MA1).
Apply it again (MA2).
Use MA2 as a “lag reference,” then combine MA1 and MA2 to reduce lag while keeping smoothness.
This is related in spirit to reduced-lag filters (like DEMA/TEMA) and “zero-lag” style constructions that subtract part of the lag component. You are not magically removing lag, you are biasing the output toward the first-pass MA while subtracting some of the second-pass smoothing that represents delayed response.
How this script does it
It computes:
ma1 = MA(src, len)
ma2 = MA(ma1, len)
Then combines them using a volume factor (vf):
generalized = ma1 * (1 + vf) - ma2 * vf
Interpretation:
ma2 is a “more delayed” version of ma1.
Subtracting vf * ma2 and adding (1+vf) * ma1 pushes the output toward responsiveness.
vf controls how aggressive that push is.
Volume Factor (vf) is really an aggressiveness knob
The script clamps vf between 0.01 and 1.0 to keep it stable. Conceptually:
Low vf: behaves closer to a normal MA1, smoother, more lag.
High vf: more compensation, faster response, more risk of overshoot or noise sensitivity (which is then handled by the step filter).
So the GMA stage tries to give you a cleaner, faster trend estimate without just shrinking the MA period.
Component 3: Step Filter (the key behavior)
What a step filter is
A step filter turns a continuous signal (here, the generalized MA) into a discrete “staircase” signal. Instead of updating every bar, it updates only when the input has moved far enough to justify a new step.
This is conceptually similar to:
A quantizer in signal processing (rounding changes to discrete increments).
A volatility threshold filter (ignore changes smaller than X).
Market structure logic where levels matter more than micro movement.
How it works in this script
The filter maintains a persistent value: stepped .
Each bar:
diff = src - stepped
If |diff| < stepSize, do nothing (hold the level).
If |diff| >= stepSize, move stepped by a number of step increments.
The step increment size is:
stepSize = (stepMult / 100) * ATR(atrPeriod)
This is critical:
In higher volatility, ATR is larger, so steps are larger, fewer updates, more stability.
In lower volatility, ATR is smaller, so steps are smaller, more updates, more sensitivity.
So the step behavior automatically adapts to volatility.
Multiple-step catching behavior
If price jumps far beyond one step, the script does not move only one step. It moves by:
floor(|diff| / stepSize) * stepSize
So it “catches up” in discrete blocks, preserving the stepped character without lagging massively after large moves.
Direction and regime
Direction is determined by the stepped line, not the raw MA:
direction = +1 if steppedMA is rising
direction = -1 if steppedMA is falling
otherwise direction stays the same
Signals only trigger on direction state changes:
Long when direction flips to +1
Short when direction flips to -1
This matters because it prevents repeated signals while the trend remains intact. You only get a signal when the market has moved enough (in ATR terms) to justify a structural step in the opposite direction.
Secondary line and gradient fill
The script also plots a secondary “slow MA” (length 25, same MA type). This is not the core logic, it is a visual context layer:
StepGMA is the structure line (discrete, regime-driven).
Slow MA is a smoother reference for the underlying drift.
The gradient fill highlights separation and dominance.
When StepGMA sits above the slow MA, the fill reinforces bullish bias. When below, it reinforces bearish bias. It is basically a “trend pressure” visual, not a separate signal.
How to interpret it
1) StepGMA as trend structure
Flat steps mean price is not making enough volatility-adjusted progress to move structure.
Up-steps mean the market has advanced enough to reprice the trend line upward.
Down-steps mean deterioration significant enough to reprice structure downward.
2) Direction is a regime, not a tick-by-tick call
Because direction is derived from step changes, it is naturally a regime filter:
Fewer flips in chop.
Clearer regime transitions.
Signals tend to occur later than ultra-fast tools, but with better confirmation quality.
3) Step size controls noise rejection
StepMult is the main “anti-chop” control:
Higher stepMult = bigger ATR steps = fewer updates, fewer signals, more confirmation, slower to react.
Lower stepMult = smaller steps = more updates, more signals, more sensitivity, more chop risk.
4) Generalization controls responsiveness of the underlying trend estimate
vf controls how “fast” the MA tries to be before stepping:
Higher vf makes the MA respond faster to new price information.
Lower vf makes the MA smoother and more conservative.
The step filter then decides whether that change is meaningful enough to matter.
Practical use cases
Trend filter for entries
Only take longs when direction is bullish.
Only take shorts when direction is bearish.
Avoid trades when StepGMA is flat for long periods, market is not repricing meaningfully.
Dynamic support and resistance
Because the line holds levels, it often behaves like structure:
In uptrends it can act as a rising support reference.
In downtrends it can act as falling resistance.
Signal quality layer
The step-based flip signals tend to be higher quality than basic MA crossovers because they require:
A meaningful volatility-adjusted move.
A confirmed direction change in the stepped trend structure.
Trade management
Use StepGMA as a trailing invalidation reference.
Use direction flips as “hard” regime exits.
Use separation vs slow MA as a “pressure” gauge for scaling decisions.
Tuning guidelines
MA Type
Pick based on the character you want:
T3, ALMA, KAMA are usually good defaults for clean trend representation.
HMA/LSMA are faster but may need larger stepMult to avoid twitch.
SMA is slow and stable but can be too laggy unless vf is increased.
MA Period
Sets the base smoothing horizon. Longer periods give “macro trend,” shorter periods give “tactical trend.”
Volume Factor (vf)
Sets responsiveness compensation:
0.05–0.25 is usually sensible.
Higher than that can get aggressive, step filter will save you, but your steps may fire more often.
ATR Period and StepMult
These define your structure sensitivity:
ATR Period controls how stable the volatility estimate is.
StepMult controls how large a move must be to change structure.
If you want fewer flips, increase StepMult or ATR Period. If you want quicker reaction, lower StepMult or ATR Period.
What this indicator is and is not
It is:
A trend structure MA that ignores sub-threshold noise.
A regime tool that uses volatility-adjusted repricing logic.
A configurable framework that works across assets and timeframes.
It is not:
A predictive reversal tool.
A scalping signal machine.
A replacement for risk management.
Summary
Step Generalized Moving Average combines a lag-compensated moving average (generalization via MA1/MA2 blending) with a volatility-scaled step filter (ATR-based quantization). The result is a stable, structure-like trend line that updates only when price movement is meaningful relative to volatility, producing cleaner regimes, fewer chop flips, and clearer trend bias than conventional moving averages.
Generalized
Quick scan for signal🙏🏻 Hey TV, this is QSFS, following:
^^ Quick scan for drift (QSFD)
^^ Quick scan for cycles (QSFC)
As mentioned before, ML trading is all about spotting any kind of non-randomness, and this metric (along with 2 previously posted) gonna help ya'll do it fast. This one will show you whether your time series possibly exhibits mean-reverting / consistent / noisy behavior, that can be later confirmed or denied by more sophisticated tools. This metric is O(n) in windowed mode and O(1) if calculated incrementally on each data update, so you can scan Ks of datasets w/o worrying about melting da ice.
^^ windowed mode
Now the post will be divided into several sections, and a couple of things I guess you’ve never seen or thought about in your life:
1) About Efficiency Ratios posted there on TV;
Some of you might say this is the Efficiency Ratio you’ve seen in Perry's book. Firstly, I can assure you that neither me nor Perry, just as X amount of quants all over the world and who knows who else, would say smth like, "I invented it," lol. This is just a thing you R&D when you need it. Secondly, I invite you (and mods & admin as well) to take a lil glimpse at the following screenshot:
^^ not cool...
So basically, all the Efficiency Ratios that were copypasted to our platform suffer the same bug: dudes don’t know how indexing works in Pine Script. I mean, it’s ok, I been doing the same mistakes as well, but loxx, cmon bro, you... If you guys ever read it, the lines 20 and 22 in da code are dedicated to you xD
2) About the metric;
This supports both moving window mode when Length > 0 and all-data expanding window mode when Length < 1, calculating incrementally from the very first data point in the series: O(n) on history, O(1) on live updates.
Now, why do I SQRT transform the result? This is a natural action since the metric (being a ratio in essence) is bounded between 0 and 1, so it can be modeled with a beta distribution. When you SQRT transform it, it still stays beta (think what happens when you apply a square root to 0.01 or 0.99), but it becomes symmetric around its typical value and starts to follow a bell-shaped curve. This can be easily checked with a normality test or by applying a set of percentiles and seeing the distances between them are almost equal.
Then I noticed that on different moving window sizes, the typical value of the metric seems to slide: higher window sizes lead to lower typical values across the moving windows. Turned out this can be modeled the same way confidence intervals are made. Lines 34 and 35 explain it all, I guess. You can see smth alike on an autocorrelogram. These two match the mean & mean + 1 stdev applied to the metric. This way, we’ve just magically received data to estimate alpha and beta parameters of the beta distribution using the method of moments. Having alpha and beta, we can now estimate everything further. Btw, there’s an alternative parameterization for beta distributions based on data length.
Now what you’ll see next is... u guys actually have no idea how deep and unrealistically minimalistic the underlying math principles are here.
I’m sure I’m not the only one in the universe who figured it out, but the thing is, it’s nowhere online or offline. By calculating higher-order moments & combining them, you can find natural adaptive thresholds that can later be used for anomaly detection/control applications for any data. No hardcoded thresholds, purely data-driven. Imma come back to this in one of the next drops, but the truest ones can already see it in this code. This way we get dem thresholds.
Your main thresholds are: basis, upper, and lower deviations. You can follow the common logic I’ve described in my previous scripts on how to use them. You just register an event when the metric goes higher/lower than a certain threshold based on what you’re looking for. Then you take the time series and confirm a certain behavior you were looking for by using an appropriate stat test. Or just run a certain strategy.
To avoid numerous triggers when the metric jitters around a threshold, you can follow this logic: forget about one threshold if touched, until another threshold is touched.
In general, when the metric gets higher than certain thresholds, like upper deviation, it means the signal is stronger than noise. You confirm it with a more sophisticated tool & run momentum strategies if drift is in place, or volatility strategies if there’s no drift in place. Otherwise, you confirm & run ~ mean-reverting strategies, regardless of whether there’s drift or not. Just don’t operate against the trend—hedge otherwise.
3) Flex;
Extension and limit thresholds based on distribution moments gonna be discussed properly later, but now you can see this:
^^ magic
Look at the thresholds—adaptive and dynamic. Do you see any optimizations? No ML, no DL, closed-form solution, but how? Just a formula based on a couple of variables? Maybe it’s just how the Universe works, but how can you know if you don’t understand how fundamentally numbers 3 and 15 are related to the normal distribution? Hm, why do they always say 3 sigmas but can’t say why? Maybe you can be different and say why?
This is the primordial power of statistical modeling.
4) Thanks;
I really wanna dedicate this to Charlotte de Witte & Marion Di Napoli, and their new track "Sanctum." It really gets you connected to the Source—I had it in my soul when I was doing all this ∞
