MAD Adaptive Trend Score [BackQuant]MAD Adaptive Trend Score
Overview
MAD Adaptive Trend Score is a trend oscillator built from a Median Absolute Deviation-based price filter and a multi-lookback relative-position score.
The indicator first calculates a rolling median and MAD from the selected source. Price deviation from the median is then clipped to a configurable MAD envelope, producing the MAD Adaptive Filter.
The current value of that filtered series is then compared with a range of its previous values. Each comparison contributes either +1 or -1 to a Trend Score.
The result is a bounded directional score that can be used with separate bullish and bearish thresholds to create a persistent trend state.
The script includes:
Exact rolling median and MAD calculations.
MAD-based clipping of source movement.
Configurable multi-lookback Trend Score.
Separate long and short regime thresholds.
Optional filter overlay on the main chart.
Trend candle colouring and signals.
Reference levels and alerts.
MAD Adaptive Filter
The first stage calculates the rolling median of the selected Source over the MAD Length.
It then calculates Median Absolute Deviation:
MAD = Median(|X - Median(X)|)
Raw MAD is multiplied by 1.4826:
Scaled MAD = Raw MAD × 1.4826
with a minimum value based on the instrument's minimum tick.
The 1.4826 factor is commonly used to scale MAD to approximately the same scale as standard deviation when the underlying distribution is normal.
The indicator then measures:
Deviation = Source - Rolling Median
and defines the maximum permitted deviation as:
Maximum Deviation = Scaled MAD × MAD Multiplier
The source deviation is clipped to this range before being added back to the median.
Conceptually:
If Source remains inside the MAD envelope, the filter follows Source.
If Source moves above the envelope, the filter is limited to the upper MAD boundary.
If Source moves below the envelope, the filter is limited to the lower MAD boundary.
The MAD Adaptive Filter is therefore not a conventional moving average. It is a source series whose distance from its rolling median is limited by the current MAD-derived envelope.
MAD Multiplier
MAD Multiplier controls the permitted distance between the filtered value and the rolling median.
Lower values:
Create a tighter envelope.
Clip more of the source movement.
Keep the filter closer to the median.
Higher values:
Create a wider envelope.
Allow more source movement through unchanged.
Make the filter follow price more closely.
Trend Score
The second stage scores the current MAD Filter against several previous values of the same filtered series.
For every lookback between Score Lookback Start and End:
+1 if the current MAD Filter is above the historical MAD Filter.
-1 otherwise.
The final Trend Score is the sum of all comparisons.
If N historical values are being compared, the theoretical score range is:
-N to +N
For the default 1-to-45 range, 45 comparisons are made, so the score can range from -45 to +45.
What the score represents
A high positive score means the current MAD-filtered value is above most of the historical filtered values being compared.
A strongly negative score means it is above very few of them.
For example, with 45 comparisons:
A score near +45 means the current filtered value is above nearly the entire comparison range.
A score near 0 means the comparisons are more evenly divided.
A score near -45 means the current filtered value is below, or equal to, nearly all of them.
The score is therefore best understood as a relative position / trend score of the filtered series.
It is not a return forecast or probability of future direction.
Why use several lookbacks?
Comparing the current filter with only one previous value would effectively reduce the calculation to short-term slope.
Using many previous values instead measures where the current filtered level sits relative to a broader section of its history.
A steadily rising filtered series will generally move toward higher positive scores because the current value becomes greater than an increasing number of historical values.
During sustained weakness, the opposite occurs.
Score Lookback Start and End
These settings define which historical MAD Filter values participate in the score.
For example:
Start = 1
End = 45
compares the current filter against each filtered value from 1 through 45 bars ago.
A shorter range:
Responds more quickly to recent changes.
Creates a smaller score range.
A longer range:
Includes more historical comparisons.
Produces a broader measure of relative trend position.
Usually changes more gradually.
Because the score range depends on the number of comparisons, threshold settings should be chosen with the selected score range in mind.
Trend State
The script converts the Trend Score into a persistent bullish or bearish signal state.
The bullish and bearish rules are deliberately separate.
Bullish condition
The signal becomes bullish when:
Trend Score > Long Threshold
Once bullish, the state remains bullish until a valid bearish condition occurs.
Bearish condition
The signal becomes bearish when the score crosses downward through the Short Threshold:
Previous Score >= Short Threshold
Current Score < Short Threshold
The bearish condition therefore requires an actual downward threshold crossing rather than simply remaining below the level.
Why use separate thresholds?
Using different bullish and bearish levels introduces persistence into the regime.
The signal does not need to reverse whenever the score crosses zero.
For example, with:
Long Threshold = 40
Short Threshold = -6
the score must reach a strongly positive state before the model turns bullish, but the bullish state can persist through a substantial amount of score deterioration before a bearish transition occurs.
This creates a form of threshold hysteresis and reduces rapid switching around a single center level.
The thresholds are fully configurable and do not need to be symmetrical.
Initial state
The signal begins neutral.
A bullish state can be established once the Long Threshold condition is satisfied.
A bearish state requires a valid downward crossing of the Short Threshold.
Signal markers are shown only when an established bullish state changes to bearish or an established bearish state changes to bullish.
The initial transition from neutral does not produce a long/short marker.
Reference Lines
The optional dashed reference lines display the Long and Short Thresholds directly in the oscillator pane.
These levels correspond to the actual regime settings and can be useful when visually tracking how the Trend Score approaches a possible state change.
MAD Filter Overlay
The MAD Adaptive Filter can optionally be plotted directly on the main price chart.
This makes it possible to compare:
Raw price.
The rolling-median/MAD envelope response.
The active trend colour.
The overlay uses the same bullish or bearish state colour as the oscillator.
Trend Candles
Optional chart candles are coloured from the stored trend state:
Bullish state = Long Color.
Bearish state = Short Color.
The colour represents the indicator's trend regime rather than the direction of each individual candle.
Background Colour
An optional transparent background can also display the current trend regime on the main chart.
This is purely visual and does not alter the calculation.
How to interpret it
Strong positive score
The current MAD Filter is above most values in the selected historical comparison range.
This typically accompanies a relatively strong upward position in the filtered trend.
Falling score while still bullish
The filtered trend is losing relative strength, but the Short Threshold has not yet been crossed.
The persistent state therefore remains bullish.
Short Threshold crossing
The score has deteriorated far enough to cross below the selected bearish boundary, changing the stored state to bearish.
Rising score while bearish
The score can recover substantially while the trend remains bearish.
A new bullish state is not established until the score exceeds the Long Threshold.
How to use the indicator
The indicator can be used as:
A directional trend filter.
A persistent bullish/bearish regime indicator.
A way to measure the relative position of a MAD-filtered price series.
A confirmation tool alongside other price or market-structure analysis.
The score itself can also provide additional context beyond the binary trend colour.
For example, a bullish regime with a score near its maximum is different from a bullish regime whose score has already fallen substantially toward the bearish threshold.
Input Guide
MAD Length
Controls the rolling sample used to calculate the median and Median Absolute Deviation.
Shorter values adapt more quickly.
Longer values produce a broader statistical reference window.
MAD Multiplier
Controls how far the filtered source may move away from its rolling median.
Lower values produce stronger clipping.
Higher values allow the filter to follow Source more closely.
Score Lookback Start / End
Defines the historical MAD Filter values used in the Trend Score comparisons.
Long Threshold
Score level that must be exceeded to establish a bullish state.
Short Threshold
Level that must be crossed downward to establish a bearish state.
Data Window
The script exposes:
Rolling Median.
Raw MAD.
Scaled MAD.
These values can help show how the underlying MAD filter is being constructed.
Limitations
The indicator is reactive rather than predictive.
The score measures the current filtered value relative to historical filtered values; it does not estimate future returns.
Threshold selection can materially change signal frequency and persistence.
A very tight MAD Multiplier can suppress meaningful movement along with noise.
A very wide MAD Multiplier makes the filter increasingly similar to the original Source.
Long score ranges can improve persistence but also delay changes in regime.
Strong trends can keep the score near an extreme for extended periods.
Alerts
The script includes:
MAD Trend Score Long: stored signal changes from bearish to bullish.
MAD Trend Score Short: stored signal changes from bullish to bearish.
Summary
MAD Adaptive Trend Score combines two simple ideas.
First, the selected Source is constrained around a rolling median using Median Absolute Deviation. Source movement inside the MAD envelope passes through normally, while movement beyond the envelope is clipped to the current boundary.
Second, the current filtered value is compared with a configurable range of its own historical values.
Those comparisons are summed into a Trend Score, with positive values indicating that the current filtered level is above more of the historical comparison range and negative values indicating the opposite.
Separate Long and Short Thresholds then convert the score into a persistent bullish or bearish regime.
The result is a MAD-based filtered series and relative-position trend score for experimenting with trend persistence and threshold behaviour. インジケーター
MAD Volatility Trail [BackQuant]MAD Volatility Trail
Overview
MAD Volatility Trail is a robust trend-following overlay built from a rolling median and Median Absolute Deviation rather than a conventional moving average and standard deviation.
The indicator estimates a central price using the rolling median, measures how widely recent prices are distributed around that median using MAD, converts that dispersion into adaptive upper and lower bands, and then transforms those bands into one-sided trailing boundaries.
The result is a persistent bullish or bearish trend regime with:
A robust median-based center.
MAD-derived volatility bands.
Optional ATR minimum band width.
One-sided trailing support and resistance.
Optional median-slope confirmation.
Bullish and bearish regime flips.
Strength-reactive gradient and glow.
Post-flip bloom visualization.
Trend-coloured candles.
Signal and alert support.
The main distinction is statistical.
Most volatility trails rely on:
Means.
Standard deviation.
ATR.
MAD Volatility Trail instead uses:
Median.
Median Absolute Deviation.
Median-based statistics are substantially less sensitive to isolated extreme observations, making the framework useful when the user wants a trend structure that is less influenced by individual spikes or outliers.
Core concept
The indicator separates the problem into four stages:
Estimate a robust rolling center using the median.
Measure robust dispersion around that center using MAD.
Build upper and lower adaptive deviation bands.
Convert those raw bands into persistent trailing trend boundaries.
The resulting trail behaves conceptually like a volatility-aware regime filter, but its volatility estimate comes primarily from the empirical distribution of price around its median.
Why median instead of mean?
A conventional arithmetic mean is calculated by summing all observations and dividing by their count.
Every value directly affects the result.
This makes the mean sensitive to outliers.
Consider a simplified sample:
100
101
101
102
150
The extreme value at 150 pulls the arithmetic mean upward substantially.
The median is simply the middle observation after sorting:
Median = 101
The single extreme observation has much less influence.
This property is called robustness .
In markets, isolated large candles, gaps, liquidation events and temporary price spikes can distort mean-based statistics. Median-based calculations intentionally reduce the influence of those individual observations.
Rolling median
For each bar, the indicator collects the selected Source values across the MAD Lookback.
It then calculates the exact median of the available observations.
For an odd number of observations, the median is the middle sorted value.
For an even number, the median lies between the two central observations according to the median implementation.
The resulting value becomes the statistical center of the trail.
Unlike an EMA or RMA, the median is not recursively smoothed.
It is recomputed from the actual distribution of values inside the current rolling window.
Early-history behaviour
At the beginning of the chart, the script ignores unavailable historical values.
This means the first valid median calculations may use fewer observations than the full MAD Lookback until sufficient chart history has accumulated.
Once the complete lookback is available, the calculation uses the full selected window.
Median Absolute Deviation
After calculating the rolling median, the script measures the absolute distance of every observation from that median:
Absolute Deviation = |Value - Median|
It then takes the median of those absolute deviations:
MAD = Median(|Xi - Median(X)|)
This is the Median Absolute Deviation .
MAD measures the typical distance of observations from the median.
It serves a role similar to standard deviation, but the mathematics and statistical behaviour are different.
Why MAD is robust
Standard deviation squares deviations from the mean.
Large deviations therefore receive disproportionately large influence.
A single extreme observation can:
Move the mean.
Create a very large squared deviation.
Increase the final standard deviation substantially.
MAD does not square deviations.
It calculates absolute distance and then takes another median.
Extreme values therefore have limited ability to change the result unless enough of the underlying sample shifts.
This gives MAD a high resistance to outliers.
In practical chart terms, one unusual wick or shock candle is less likely to inflate the statistical width as dramatically as it could under a standard-deviation model.
MAD versus standard deviation
The two measures answer related but different questions.
Standard deviation
Measures squared dispersion around the arithmetic mean.
MAD
Measures median absolute dispersion around the median.
Standard deviation is highly useful when a mean-and-variance framework is desired.
MAD is useful when robustness to unusual observations is more important.
The indicator does not claim one is universally superior.
It intentionally uses MAD because the purpose is to construct a robust trend boundary.
MAD Scale
Raw MAD is not numerically identical to standard deviation.
Under a normal distribution, MAD is usually multiplied by a consistency factor of approximately 1.4826 when the goal is to make it comparable to standard deviation.
The indicator exposes this scaling directly:
Robust Deviation = Raw MAD × MAD Scale
The script default is 1.4655.
The input remains fully adjustable, so users who want the conventional normal-consistency approximation can set the factor near 1.4826.
This scale does not change the median itself.
It changes only the size of the deviation estimate used to build the bands.
Deviation Factor
After scaling MAD, the indicator applies the Deviation Factor:
MAD Width = Scaled MAD × Deviation Factor
This acts as the main sensitivity control.
Lower values:
Create narrower raw bands.
Place the trail closer to price.
Produce more frequent regime changes.
Higher values:
Create wider bands.
Require larger movement for reversals.
Produce more persistent trend states.
The MAD Scale and Deviation Factor both affect width, but they represent different concepts.
MAD Scale calibrates the statistical dispersion estimate.
Deviation Factor determines how much of that estimated dispersion is used for the trend envelope.
Raw MAD bands
The raw bands are:
Upper MAD Band = Median + Band Width
Lower MAD Band = Median - Band Width
Before trailing logic is applied, these bands can move freely upward or downward with:
The rolling median.
MAD dispersion.
Any active ATR floor.
These are statistical envelopes around the median.
They are not yet the final trend trail.
ATR Minimum Width
MAD can become extremely small when recent prices are tightly clustered.
In very low-dispersion conditions, this may place the raw bands extremely close to the median.
That can create excessive sensitivity to minor price fluctuations.
The optional ATR Minimum Width provides a secondary floor.
The script calculates:
ATR Floor = ATR(ATR Length) × ATR Floor Multiplier
When enabled:
Band Width = max(MAD Width, ATR Floor)
This means MAD remains the primary volatility model, but the bands cannot contract below the selected ATR-based threshold.
Why use an ATR floor?
MAD and ATR measure different aspects of market behaviour.
MAD measures:
Dispersion of the selected source around its rolling median.
ATR measures:
Bar-to-bar trading range.
Gaps relative to the previous close.
A market can have:
Low median dispersion.
But still produce meaningful intrabar range.
The ATR floor can prevent the trail from becoming unrealistically tight under those conditions.
ATR floor disabled
With ATR Minimum Width disabled, the entire structural width comes from:
MAD × MAD Scale × Deviation Factor
This produces the purest MAD-based version of the indicator.
ATR Length
ATR Length controls the volatility horizon used only for the optional minimum-width calculation.
It does not affect:
The rolling median.
Raw MAD.
Scaled MAD.
Note that the visual glow and bloom later in the script use a fixed ATR(14), separate from this ATR Length input.
Trailing bands
The raw MAD bands are converted into one-sided trails.
This is the stage that turns a statistical envelope into a persistent trend system.
Two independent trails are maintained:
Lower Trail.
Upper Trail.
Lower Trail
When the previous trigger remains above the previous Lower Trail, the new Lower Trail is:
max(Current Raw Lower Band, Previous Lower Trail)
This means the Lower Trail can:
Move upward.
Remain unchanged.
But cannot move downward while the condition remains active.
This creates a ratcheting support structure.
If the trigger falls below the prior Lower Trail, the trail is allowed to reset to the new raw lower band.
Upper Trail
When the previous trigger remains below the previous Upper Trail, the new Upper Trail is:
min(Current Raw Upper Band, Previous Upper Trail)
This means the Upper Trail can:
Move downward.
Remain unchanged.
But cannot move upward while the condition remains active.
This creates a ratcheting resistance structure.
If the trigger rises above the previous Upper Trail, the band can reset to the current raw upper value.
Why trailing the bands matters
A raw median-deviation envelope moves in both directions.
If those raw bands were used directly for trend changes:
The threshold itself could retreat toward price.
Small changes in median or MAD could produce unstable reversals.
The one-sided trail introduces hysteresis .
Hysteresis means that once a trend regime is established, the threshold required to reverse it remains on the opposing side.
This reduces the tendency to flip repeatedly around the rolling median.
Flip Trigger
The user can choose which series is used when evaluating trail breaks:
Close.
Source.
Close
Uses the candle close regardless of which series is used for the MAD calculation.
This is the conventional option.
Source
Uses the selected Source input.
For example, if HLC3 is selected as the Source:
The median is calculated from HLC3.
MAD is calculated from HLC3.
The trail can also be triggered by HLC3.
This keeps the center, dispersion and reversal trigger based on the same source.
Initial trend state
The trend begins in a neutral state.
Once a valid rolling median is available:
Trigger at or above Median = bullish initialization.
Trigger below Median = bearish initialization.
This initial assignment is not treated as a bullish or bearish flip.
Flip signals occur only after the indicator has already established one regime and later transitions into the opposite regime.
Bullish flip
A bullish regime change requires:
Trigger to move above the Upper Trail.
Current trend not already bullish.
Optional bullish median-slope confirmation to pass.
Once confirmed:
Trend becomes bullish.
The Lower Trail becomes the active trend boundary.
A bullish signal can be displayed.
Bearish flip
A bearish regime change requires:
Trigger to move below the Lower Trail.
Current trend not already bearish.
Optional bearish median-slope confirmation to pass.
Once confirmed:
Trend becomes bearish.
The Upper Trail becomes the active boundary.
A bearish signal can be displayed.
Active trend trail
The final displayed trend boundary depends on the regime:
Bullish = Lower Trail.
Bearish = Upper Trail.
This means the line automatically moves to the opposite side of price when a complete regime change occurs.
Median Slope Confirmation
The optional Median Slope Confirmation adds a directional requirement to trend reversals.
For a bullish flip:
Current Median > Median from Slope Lookback bars ago
For a bearish flip:
Current Median < Median from Slope Lookback bars ago
This requires the robust statistical center itself to move in the direction of the proposed new trend.
Why confirm with median slope?
Price can briefly cross a trail while the underlying median remains flat or continues moving in the opposite direction.
Slope confirmation can reject some of these events.
For example:
A bullish trail break with a still-falling median may represent:
A temporary rebound.
A liquidity sweep.
Noise inside a larger bearish structure.
Requiring the median to rise adds another layer of confirmation.
The trade-off is lag.
A genuine reversal may cross the trail before the rolling median has clearly changed direction.
Slope Lookback
Slope Lookback controls how far back the median is compared.
Lower values:
Respond more quickly.
Require only a very local median turn.
Higher values:
Require a broader directional shift.
Produce stronger confirmation.
Can delay reversals.
This same lookback is also used in the visual slope-strength calculation even when slope confirmation itself is disabled.
Break Trail On Flips
When enabled, the displayed trail is temporarily hidden on the actual regime-flip bar.
This creates a visual break between:
The previous regime’s trail.
The new regime’s trail.
Without the break, the plotting engine can draw a connecting segment from one side of the market to the other.
That connection has no analytical meaning.
Break Trail On Flips affects visualization only.
It does not affect:
Trend state.
Raw bands.
Trail calculations.
Signals.
Robust trend structure
The complete structural model can therefore be summarized as:
Rolling Median determines robust center.
MAD determines robust dispersion.
MAD Scale calibrates the dispersion.
Deviation Factor determines band distance.
Optional ATR floor prevents excessive compression.
Raw bands form the initial envelope.
Ratchet logic creates trailing support and resistance.
Opposite-trail breaks determine regime changes.
Optional median slope confirms those reversals.
This combination is what separates the indicator from simply plotting median ± MAD.
Visual strength model
The script calculates a separate Trend Strength value used only to control the presentation of the gradient and glow.
It does not alter:
Trend direction.
Trail levels.
Flip conditions.
Trend Strength combines:
Price distance from the active trail.
Absolute rolling-median slope.
Distance Strength
The script first measures:
Trail Distance = |Close - Active Trail|
This is normalized by the current band width.
The normalized distance is capped when price reaches twice the active band width away from the trail.
Conceptually:
Close to trail = low distance strength.
Far from trail = high distance strength.
This reflects how separated price is from the current structural boundary.
Slope Strength
The indicator also measures:
|Current Median - Median |
This value is normalized by the current band width and capped at one.
The purpose is to compare median movement against the current statistical width.
A steep median relative to the band width produces stronger visual slope strength.
Combined Trend Strength
The final visual strength is:
70% Distance Strength.
30% Median Slope Strength.
and is capped at one.
The distance component receives greater weight because the visual system places more emphasis on how strongly price is separated from the active trail.
Again, this number is not a probability, forecast or additional signal.
It is a visual intensity measure.
Layered gradient
The area between the active trail and current close is divided into several intermediate levels.
The script creates reference points approximately:
15% of the distance from trail to price.
35%.
60%.
82%.
Then the final segment to price.
These create five layered gradient regions.
The layers become progressively more transparent as they move away from the trail.
This gives the trail visual depth without turning the entire area between price and structure into one solid block.
Gradient direction
The geometry of the gradient is determined by whether close is above or below the active trail.
The colour itself comes from the current bullish or bearish trend regime.
The gradient therefore visualizes:
The active trend colour.
The distance between price and trail.
The relative strength of the trend visualization.
The gradient does not determine the regime.
Trend-strength gradient response
Higher Trend Strength reduces transparency in several layers.
This makes the ribbon more visible when:
Price is strongly separated from the trail.
The rolling median is moving meaningfully.
Lower strength produces a softer appearance.
This allows the visual presentation to communicate more than simple bullish or bearish state.
Flip bloom
The indicator includes a temporary post-flip bloom.
The bloom is derived from the number of bars elapsed since the most recent bullish or bearish transition.
Importantly, in the current implementation the bloom begins after the flip bar:
Flip bar: no bloom boost.
1 bar after flip: maximum bloom.
2 bars after flip: reduced bloom.
3 bars after flip: smaller residual bloom.
Afterward: bloom disappears.
The relative bloom strengths are:
1.00
0.55
0.25
This emphasizes the early bars following a newly confirmed regime change.
Why bloom after the flip?
The flip itself can optionally contain a break in the trail.
Applying the bloom to the following bars emphasizes the newly established active trail rather than drawing a large effect around a temporarily hidden flip point.
The bloom is cosmetic.
It does not modify the underlying calculations.
Trail glow
The active trail can also display a persistent glow.
Glow width is based on:
ATR(14) × a factor that increases with Trend Strength
This ATR(14) is fixed for visualization and is independent of the user-selected ATR Length used by the optional minimum-width floor.
The glow therefore becomes slightly wider as visual trend strength increases.
Two layers are used:
A tighter inner glow.
A broader outer glow.
The inner glow responds more strongly to Trend Strength and post-flip bloom.
Rolling Median display
The rolling median can be displayed independently from the trail.
This is useful for studying the difference between:
The current robust center.
The statistical raw bands.
The ratcheting trend trail.
During a bullish regime, the active Lower Trail can remain below the rolling median.
During a bearish regime, the active Upper Trail can remain above it.
The median is not itself the trend signal.
Raw MAD Bands display
The raw upper and lower MAD bands can also be shown.
These lines make it easier to see how the trailing logic differs from the unrestricted statistical envelope.
Raw bands:
Can move in either direction.
Trailing bands:
Can ratchet in only one direction while their persistence condition remains active.
The gap between raw and trailing levels illustrates the hysteresis introduced by the trend logic.
Trend candles
The script can redraw candles on the main chart using the active trend colour.
Bullish regime:
Uses the selected Bullish colour.
Bearish regime:
Uses the selected Bearish colour.
The candle colour represents the persistent trail regime, not whether each individual candle closed higher or lower.
A bearish candle can therefore remain bullish-coloured while the broader MAD Trail regime remains bullish.
Signal markers
Bullish and bearish markers appear only on complete transitions between established regimes.
A bullish marker requires:
Previous trend = bearish.
Current trend = bullish.
A bearish marker requires:
Previous trend = bullish.
Current trend = bearish.
Initial trend assignment does not generate a flip marker.
How to interpret the indicator
Bullish regime
A bullish state means price has previously broken above the opposing Upper Trail and the Lower Trail is now active.
The Lower Trail can be interpreted as:
Dynamic trend support.
A structural invalidation reference.
A trailing regime boundary.
Bearish regime
A bearish state means price has broken below the opposing Lower Trail and the Upper Trail is active.
The Upper Trail can be interpreted as:
Dynamic resistance.
A bearish invalidation reference.
A trailing regime boundary.
Price close to trail
When price approaches the active trail:
Visual distance strength decreases.
The gradient becomes softer.
The market is closer to the regime boundary.
This does not guarantee a reversal.
A healthy trend can repeatedly retest its active trail.
Price far from trail
When price moves substantially away:
Distance Strength rises.
The visual effect becomes stronger.
This indicates greater separation from the active structural boundary.
It should not automatically be interpreted as a better entry.
A market can be strongly extended and simultaneously close to exhaustion.
Median and trail rising together
During a bullish regime, a rising median combined with a rising Lower Trail indicates:
The robust center is moving upward.
The structural support boundary is also advancing.
This represents cleaner directional alignment.
Median flattening while trail remains bullish
The persistent regime can remain bullish while the median begins flattening.
This indicates:
The trend has not yet been invalidated.
But the robust center is no longer advancing as strongly.
The visual slope-strength component may weaken under this condition.
Raw band expansion
If MAD increases:
Raw bands widen.
Trail reset levels can move farther away.
This means recent source values are becoming more dispersed around the median.
Raw band contraction
If MAD falls:
The raw envelope tightens.
If the ATR floor is disabled, the structure can become substantially narrower.
If the ATR floor is enabled, contraction stops once the selected minimum width is reached.
How to use the indicator
1. Trend regime filter
Use the persistent trail state as directional context:
Bullish trail regime = prioritize long-side setups.
Bearish trail regime = prioritize short-side setups.
The trail does not define a complete trading system by itself.
2. Pullback structure
During a bullish regime, the Lower Trail can provide a dynamic reference for deeper pullbacks.
During a bearish regime, the Upper Trail can provide a reference for rallies.
The farther price moves from the trail, the greater the current structural separation.
3. Regime transitions
Bullish and bearish flips identify moments when price has crossed completely through the opposing robust-deviation trail.
These may be used as:
Trend-change alerts.
Confirmation for another entry method.
Potential exit conditions.
4. Median confirmation
Users who want more selective signals can enable Median Slope Confirmation.
This can be especially useful when:
The market is choppy.
Price frequently sweeps through statistical boundaries.
5. Pure robust-volatility mode
Disable the ATR Minimum Width to make band width depend only on:
Rolling MAD.
MAD Scale.
Deviation Factor.
This produces the purest version of the model.
6. Hybrid robust-volatility mode
Enable ATR Minimum Width when the MAD channel becomes too narrow for the instrument or timeframe.
This preserves MAD as the primary engine while adding a conventional range-based safety floor.
Input guide
Source
Series used for the rolling median and MAD calculation.
MAD Lookback
Controls the number of observations used for the rolling median and dispersion estimate.
Shorter values adapt faster.
Longer values create a broader and more stable distribution.
MAD Scale
Multiplier applied directly to raw MAD.
The commonly cited normal-distribution consistency factor is approximately 1.4826; the script default is 1.4655.
Deviation Factor
Controls the final width of the MAD envelope.
ATR Minimum Width
Prevents the active band width from falling below an ATR-derived floor.
ATR Length
Controls the ATR used by the optional floor.
ATR Floor
Controls the minimum width as a multiple of ATR.
Median Slope Confirmation
Requires the rolling median to move in the direction of a proposed trend flip.
Slope Lookback
Controls how far back the current median is compared.
It also influences the visual slope-strength calculation.
Flip Trigger
Selects Close or Source for trail-break detection.
Break Trail On Flips
Creates a visual discontinuity on transition bars.
How this differs from a standard Supertrend
A conventional Supertrend generally uses:
A price midpoint such as HL2.
ATR as the full band-width model.
MAD Volatility Trail instead uses:
Rolling median as its center.
Median Absolute Deviation as its primary width.
ATR only as an optional minimum floor.
The trail mechanics are conceptually related, but the statistical foundation is different.
How this differs from Bollinger Bands
Bollinger Bands normally use:
A moving average.
Standard deviation.
Symmetrical raw bands.
MAD Volatility Trail uses:
Rolling median.
Median Absolute Deviation.
One-sided trailing bands.
Persistent trend-state logic.
Bollinger Bands are primarily a statistical envelope.
MAD Volatility Trail converts its robust statistical envelope into a trend-regime system.
How this differs from median ± MAD alone
A simple median-MAD indicator would plot:
Median.
Median + MAD width.
Median - MAD width.
Those bands would move freely.
This indicator adds:
Ratchet logic.
Persistent bullish/bearish state.
Opposite-trail break conditions.
Optional median-slope confirmation.
Signals and alerts.
The raw statistical model is therefore only the first stage.
MAD versus ATR
ATR measures the size of trading ranges.
MAD measures dispersion of the selected source around its median.
They can behave very differently.
For example:
A volatile but mean-reverting market can have large ATR with relatively controlled median dispersion.
A persistent directional displacement can produce increasing MAD even if individual candle ranges are moderate.
The optional floor allows both concepts to coexist without replacing the MAD foundation.
Robust statistics and financial markets
Financial return and price distributions frequently contain:
Outliers.
Large jumps.
Skew.
Fat tails.
Mean-and-standard-deviation models remain extremely useful, but robust alternatives can provide different information when unusual observations are present.
Median and MAD belong to a family of robust statistical tools designed to reduce sensitivity to extreme sample values.
This does not make the resulting indicator immune to market shocks.
If enough of the rolling window moves, the median and MAD will also move.
The advantage is primarily that one isolated observation has less influence.
Strengths
Uses an exact rolling median.
Uses exact Median Absolute Deviation rather than an approximation.
More resistant to isolated outliers than mean/standard-deviation envelopes.
Provides a configurable MAD scale.
Supports a pure MAD or MAD-plus-ATR hybrid width.
Converts robust statistics into persistent trend boundaries.
Uses one-sided trail logic to reduce rapid regime switching.
Provides optional median-direction confirmation.
Separates signal logic from visual strength.
Includes dynamic gradient, glow and post-flip visualization.
Exposes raw MAD, scaled MAD, active band width and Trend Strength in the Data Window.
Limitations
The indicator is reactive rather than predictive.
Robust statistics do not eliminate whipsaws.
A very short MAD Lookback can still react sharply.
A very long lookback can delay adaptation to new regimes.
Median calculations can remain unchanged across several bars and then move discretely as the rolling sample changes.
Higher Deviation Factors reduce reversals but increase confirmation lag.
The ATR floor changes the model from pure MAD dispersion to a hybrid MAD/ATR structure.
Median Slope Confirmation can reject false breaks but also delay genuine reversals.
Extreme readings in the visual-strength system are not probabilities of continuation.
Glow and bloom are cosmetic and should not be treated as separate signals.
Computational considerations
Unlike many moving averages, the exact rolling median and MAD calculations require the script to build and process the values inside the selected window.
For each bar:
The rolling source sample is collected.
Its median is calculated.
Absolute deviations from that median are calculated.
A second median is calculated from those deviations.
Larger MAD Lookbacks therefore require more work than a simple recursive EMA or ATR calculation.
This is the cost of calculating the robust statistics directly.
Causality and live-bar behaviour
The indicator uses current and historical values without intentional future-looking references.
On completed historical bars, the model is causal.
On a live unfinished bar:
The Source can change.
The current rolling median can change.
MAD can change.
Raw bands can change.
A trail break can appear or disappear.
Users who require confirmed regime changes should evaluate signals at bar close.
Data Window
The indicator exposes four useful diagnostic values.
Raw MAD
The unscaled median absolute deviation.
Scaled MAD
Raw MAD multiplied by the selected MAD Scale.
Active Band Width
The actual band width after:
MAD scaling.
Deviation Factor.
Optional ATR minimum floor.
Trend Strength
The visual-strength score expressed from approximately 0 to 100.
This is calculated from trail distance and median movement.
It is not part of the trend-flip logic.
Alerts
The indicator includes:
MAD Trail Bullish: established bearish regime changes to bullish.
MAD Trail Bearish: established bullish regime changes to bearish.
MAD Trail Flip: either regime transition occurs.
Summary
MAD Volatility Trail builds a trend-following regime from robust statistics.
The calculation begins with an exact rolling median of the selected Source.
Rather than measuring dispersion with standard deviation, the script calculates the Median Absolute Deviation:
MAD = Median(|X - Median(X)|)
The raw MAD is scaled and multiplied by a configurable Deviation Factor to create the statistical width around the rolling median.
The resulting raw upper and lower bands are:
Median + Band Width.
Median - Band Width.
An optional ATR minimum floor prevents these bands from becoming excessively narrow during low-dispersion conditions.
The raw envelope is then transformed into one-sided trailing boundaries.
The Lower Trail can ratchet upward while price remains above it, while the Upper Trail can ratchet downward while price remains below it.
These trails create hysteresis and form the actual regime-switching structure.
A bearish regime turns bullish only when the selected trigger breaks above the opposing Upper Trail, optionally while the rolling median itself is rising.
A bullish regime turns bearish only when the trigger breaks below the Lower Trail, optionally while the median is falling.
The active Lower Trail is displayed during bullish regimes and the active Upper Trail during bearish regimes.
A separate visual-strength model measures price-to-trail distance and median slope relative to the active band width. That score controls gradient and glow intensity but does not alter signals.
The result is a robust alternative to conventional mean-, standard-deviation- and ATR-centered trend trails.
Rather than allowing individual extreme prices to dominate its statistical center and dispersion estimate, MAD Volatility Trail uses the median twice: once to define the center of the distribution and again to define the typical absolute distance from that center.
This creates a trend framework designed around robust location, robust dispersion and persistent trailing structure .
インジケーター
Adaptive MAD Supertrend | GForgeAdaptive MAD Supertrend | GForge
The Adaptive MAD Supertrend is a trend-following indicator built on the classic Supertrend framework, but with two core innovations that address well-known weaknesses in the original design: how volatility is measured, and how the indicator behaves across different market conditions.
The Problem With Standard Supertrend
The classic Supertrend uses ATR (Average True Range) as its volatility measure and a fixed multiplier. ATR squares its deviation calculations internally, which means a single spike candle — a news wick, a liquidation cascade — can temporarily blow the bands wide and either trigger a false flip or delay a valid one. On top of that, a fixed multiplier means the indicator behaves identically in a clean trending market and a choppy ranging one. It has no awareness of what the market is actually doing.
Innovation 1 — MAD Replaces ATR
This indicator uses Mean Absolute Deviation as its volatility measure instead of ATR or Standard Deviation.
MAD = mean( |close − mean(close, n)| , n )
The key difference is linearity. Each bar contributes its deviation to the average equally, without squaring. A spike candle influences the band width, but proportionally — it cannot disproportionately dominate the calculation the way it can in ATR or StdDev. The result is a more stable, consistent band width that responds to genuine volatility without overreacting to outlier bars.
An optional EMA smoothing layer can be applied to the raw MAD output before it scales the bands, which further stabilizes band width during volatile periods.
Innovation 2 — Kaufman Efficiency Ratio Scales the Multiplier
The Efficiency Ratio (ER), developed by Perry Kaufman, measures how efficiently price is moving:
ER = |net price change over n bars| / sum(|bar-to-bar changes|, n)
ER → 1.0: price moved efficiently in one direction — a clean trend
ER → 0.0: price moved a lot but went nowhere — chop and noise
The adaptive multiplier uses ER to scale band width dynamically:
adaptive_multiplier = Multiplier_Chop − ER × (Multiplier_Chop − Multiplier_Trend)
During a clean trend, the multiplier contracts toward your Trend setting — bands tighten and the trailing stop follows price closely, capturing more of the move. During choppy conditions, the multiplier expands toward your Chop setting — bands widen and the stop absorbs noise without flipping unnecessarily.
This means the indicator automatically adjusts its sensitivity to what the market is doing, rather than applying the same fixed behaviour to every bar.
Basis MA
The band centre line (basis) is fully configurable. Rather than raw hl2 like the classic Supertrend, any moving average from the menu can serve as the anchor — the band is built outward from it. The default is T3, a Tillson triple-smoothed MA that provides an extremely clean centre line with minimal lag overshoot. Other useful options include DEMA and TEMA for faster response, VWMA for volume-weighted anchoring, or RMA for higher timeframes.
How to Read It
Line colour: green/up colour = bullish trend, red/down colour = bearish trend
Trend fill: shaded area between price and the trailing stop — visual confirmation of which side of the line price is on
Inactive band: the faint dotted line on the opposite side shows where a flip would trigger if price reaches it
Signal diamonds: markers at each trend flip — below bar for long entries, above bar for short/cash exits
Notes
Optimised and tested on Bitcoin 1D. Performs well on trending instruments across higher timeframes (4H and above).
The MAD + ER combination is theoretically complementary: MAD handles what the band width is, ER handles how much of it to apply. They solve orthogonal problems.
As with all trend-following tools, performance degrades in prolonged sideways markets — the Chop multiplier setting mitigates this but does not eliminate it.
⚠️ Disclaimer
This indicator is a technical analysis tool provided for informational and educational purposes only. It is not financial advice, and nothing presented here should be construed as a recommendation to buy, sell, or hold any asset. Past performance does not guarantee future results.
Developed by GForge インジケーター
Ultimate RegimeUltimate Regime | MisinkoMaster
Ultimate Regime is an advanced market environment classification tool designed to identify whether an asset is currently operating in a trending or mean-reverting regime. Instead of focusing on entry signals, the indicator concentrates on answering a more fundamental question: what type of market are we trading right now?
By continuously evaluating market structure, volatility behavior, and directional persistence, the script provides a unified regime view that helps traders adapt strategy selection, risk management, and trade expectations to current conditions.
This makes Ultimate Regime particularly valuable for traders using multiple systems, algorithmic frameworks, or discretionary approaches that perform differently depending on market state.
Core Concept
Markets alternate between expansion phases where directional movement dominates and contraction phases where price oscillates around equilibrium. Strategies built for one condition often underperform in the other.
Ultimate Regime solves this by aggregating several environment measurements into a single regime score that expresses whether the market currently favors:
• Trend continuation strategies
• Breakout participation
• Momentum trading
or instead
• Range trading
• Mean reversion strategies
• Oscillation-based setups
The indicator therefore acts as a decision filter rather than a trade trigger.
Key Features
Unified regime classification combining multiple market characteristics
Automatic detection of trending vs mean-reverting environments
Smooth regime transitions to reduce noise and false flips
Visual histogram representing regime strength
Automatic chart candle coloring based on environment
On-chart regime change labeling for clarity
Configurable lookback and smoothing controls
Works across all timeframes and asset classes
Suitable for discretionary and systematic traders
Designed for integration into multi-indicator workflows
How It Works (Conceptual)
Instead of relying on a single measurement, Ultimate Regime evaluates several dimensions of market behavior simultaneously, such as:
• Price expansion versus contraction
• Volatility shifts
• Directional persistence
• Structural movement characteristics
These components are normalized and combined into a composite regime value. The result is then smoothed to ensure regime changes reflect genuine environment shifts rather than short-term fluctuations.
When the combined regime value turns positive, the market is considered to favor directional movement. When it turns negative, price behavior favors oscillation and mean reversion.
The internal weighting and transformation methods remain proprietary in the invite-only version.
Regime States Explained
Trending Regime
Indicates directional dominance where price tends to move persistently in one direction. Momentum and breakout systems typically perform better under these conditions.
Mean Reverting Regime
Indicates oscillatory behavior where price frequently returns toward equilibrium zones. Range strategies and reversal setups often become more effective.
Neutral Transitions
Short transition periods may occur during regime changes as the environment reorganizes before committing to a dominant state.
Visual Components
Regime Histogram
A histogram displays regime strength and direction, making it easy to gauge whether trending or reverting behavior dominates.
Colored Candles
Price candles automatically change color according to regime classification, allowing instant environment recognition directly on the chart.
Regime Change Labels
Labels appear when regime shifts occur, helping traders visually track transitions between trending and mean-reverting phases.
Reference Thresholds
Visual guide levels help users understand regime extremes and neutral zones.
Inputs Overview
Source
Selects the price data used for regime analysis.
High-Low Difference Lookback
Controls how far back structural price expansion is evaluated.
ATR Lookback
Adjusts how volatility expansion or contraction is measured.
Standard Deviation Lookback
Defines the evaluation window for statistical price dispersion.
ADX Lookback
Controls directional persistence measurement sensitivity.
Smoothing Period
Applies smoothing to regime calculations, balancing responsiveness and stability.
Higher smoothing reduces noise but delays regime changes. Lower smoothing reacts faster but may increase regime flipping.
Usage Guidelines
Use Ultimate Regime as a strategy filter rather than a direct entry signal.
Trending regime environments generally favor:
• Breakout systems
• Momentum entries
• Trend-following approaches
• Pullback continuation trades
Mean-reverting environments generally favor:
• Range trading
• Support and resistance reversals
• Oscillation strategies
• Counter-trend setups
Regime analysis works best when combined with entry and risk tools rather than used standalone.
Practical Applications
Strategy selection switching between trend and range systems
Position sizing adjustments based on environment strength
Filtering trades that conflict with prevailing market behavior
Algorithmic system optimization
Portfolio regime monitoring
Timeframe alignment analysis
Parameter Tuning Notes
Lower lookback values increase responsiveness but may produce faster regime changes.
Higher lookback values stabilize regime detection for swing or position trading.
Short smoothing periods work better for intraday trading.
Longer smoothing periods help long-term traders avoid noise.
Optimal settings vary by asset volatility and timeframe.
Best Practices
Combine regime detection with price structure and confirmation tools.
Avoid forcing trend systems in reverting environments and vice versa.
Use regime awareness to improve trade selection discipline.
Backtest strategies separately for trending and mean-reverting periods.
Summary
Ultimate Regime provides a structured and adaptive view of market conditions by classifying whether the environment favors trend continuation or mean reversion. By separating environment analysis from trade signals, traders gain clarity in strategy selection and improve consistency across changing market conditions.
The invite-only version preserves proprietary calculation methods while delivering a robust regime detection framework suitable for discretionary traders, system developers, and algorithmic strategies alike. インジケーター
インジケーター
SMA MAD SuperTrend | OquantThe SMA MAD SuperTrend | Oquant is an trend-following indicator designed to help traders identify potential trend directions and reversals using a unique combination of a Simple Moving Average (SMA), Mean Absolute Deviation (MAD), and a SuperTrend mechanism. This script aims to provide clear visual signals for trend entries and exits, making it suitable for traders looking to capture trends.
This indicator innovatively combines the smoothing properties of an SMA with the volatility-adaptive qualities of MAD to create dynamic SuperTrend bands. Unlike traditional SuperTrend indicators that rely on Average True Range (ATR) for volatility, this script uses Mean Absolute Deviation(MAD) to measure the average absolute deviation from the mean price, providing a different perspective on price volatility. The result is a SuperTrend system that adapts to market conditions with a focus on price deviation, offering a unique tool for trend detection.
Components and Calculations
Simple Moving Average (SMA):
The SMA is a widely used indicator that calculates the average of a specified number of closing prices. It smooths price data to identify the overall trend direction. In this script, the SMA serves as the baseline for calculating dynamic upper and lower bands.
Mean Absolute Deviation (MAD):
MAD measures the average absolute deviation of the price from its mean. It quantifies volatility by calculating how far prices deviate from the mean price, offering an alternative to ATR.
SuperTrend Mechanism:
This SuperTrend indicator generates dynamic upper and lower bands around the Simple Moving Average (SMA) using mean absolute deviation as measure of volatility.
It tracks trend direction by comparing the close price to the bands:
If the price crosses above the upper band, the trend turns bullish, and the SuperTrend follows the lower band.
If the price crosses below the lower band, the trend turns bearish, and the SuperTrend follows the upper band.
The bands adjust based on their previous values, updating only when the price crosses a band or the band shifts in the correct direction, reducing false signals and ensuring stable trend detection.
How to Use the Indicator
Trend Signals:
Green Line: Indicates a bullish trend (price above the SuperTrend line).
Purple Line: Indicates a bearish trend (price below the SuperTrend line).
Bar and Candle Coloring: Bars and candles are colored green for bullish trends and purple for bearish trends, making it easy to visualize trend direction.
Filled Areas: The area between the price and the SuperTrend line is filled with transparent colors (green for bullish, purple for bearish) to highlight trend.
Inputs:
Source: Choose the price data for calculations.
SMA Length: Adjust the period for the SMA. Longer periods smooth the trend further.
MAD Length: Set the period for MAD calculation. Shorter periods make the MAD more sensitive.
Factor: Control the distance of the SuperTrend bands from the SMA. Higher values widen the bands, reducing sensitivity to price fluctuations.
Alerts:
The script includes alert conditions for trend changes:
SMA MAD SuperTrend Long: Triggered when the trend turns bullish.
SMA MAD SuperTrend Short: Triggered when the trend turns bearish.
Set up alerts in TradingView to receive notifications for these conditions.
Why Use This Script?
The SMA MAD SuperTrend | Oquant offers a fresh take on trend-following by integrating SMA as baseline and MAD for volatility measurement, providing an alternative to ATR-based SuperTrend indicators. Its clear visual signals, customizable inputs, and alert conditions make it versatile for traders of all levels.
⚠️ Disclaimer: This indicator is intended for educational and informational purposes only. Trading/investing involves risk, and past performance does not guarantee future results. Always test and evaluate indicators/strategies before applying them in live markets. Use at your own risk.
インジケーター
Inter-Exchanges Crypto Price Spread Deviation (Tartigradia)Measures the deviation of price metrics between various exchanges. It's a kind of realized volatility indicator, as the idea is that in times of high volatility (high emotions, fear, uncertainty), it's more likely that market inefficiencies will appear for the same asset between different market makers, ie, the price can temporarily differ a lot. This indicator will catch these instants of high differences between exchanges, even if they lasted only an instant (because we use high and low values).
Both standard deviation and median absolute deviation (more robust to outliers, ie, exchanges with a very different price from others won't influence the median absolute deviation, but the standard deviation yes).
Compared to other inter-exchanges spread indicators, this one offers two major features:
* The symbol automatically adapts to the symbol currently selected in user's chart. Hence, switching between tickers does not require the user to modify any option, everything is dynamically updated behind the scenes.
* It's easy to add more exchanges (requires some code editing because PineScript v5 does not allow dynamical request.security() calls).
Limitations/things to know:
* History is limited to what the ticker itself display. Ie, even if the exchanges specified in this indicator have more data than the ticker currently displayed in the user's chart, the indicator will show only a timeperiod as long as the chart.
* The indicator can manage multiple exchanges of different historical length (ie, some exchanges having more data going way earlier in the past than others), in which case they will simply be ignored from calculations when far back in the past. Hence, you should be aware that the further you go in the past, the less exchanges will have such data, and hence the less accurate the measures will be (because the deviation will be calculated from less sources than more recent bars). This is thanks to how the array.* math functions behave in case of na values, they simply skip them from calculations, contrary to math.* functions. インジケーター
Variety N-Tuple Moving Averages w/ Variety Stepping [Loxx]Variety N-Tuple Moving Averages w/ Variety Stepping is a moving average indicator that allows you to create 1- 30 tuple moving average types; i.e., Double-MA, Triple-MA, Quadruple-MA, Quintuple-MA, ... N-tuple-MA. This version contains 2 different moving average types. For example, using "50" as the depth will give you Quinquagintuple Moving Average. If you'd like to find the name of the moving average type you create with the depth input with this indicator, you can find a list of tuples here: Tuples extrapolated
Due to the coding required to adapt a moving average to fit into this indicator, additional moving average types will be added as they are created to fit into this unique use case. Since this is a work in process, there will be many future updates of this indicator. For now, you can choose from either EMA or RMA.
This indicator is also considered one of the top 10 forex indicators. See details here: forex-station.com
Additionally, this indicator is a computationally faster, more streamlined version of the following indicators with the addition of 6 stepping functions and 6 different bands/channels types.
STD-Stepped, Variety N-Tuple Moving Averages
STD-Stepped, Variety N-Tuple Moving Averages is the standard deviation stepped/filtered indicator of the following indicator
Last but not least, a big shoutout to @lejmer for his help in formulating a looping solution for this streamlined version. this indicator is speedy even at 50 orders deep. You can find his scripts here: www.tradingview.com
How this works
Step 1: Run factorial calculation on the depth value,
Step 2: Calculate weights of nested moving averages
factorial(depth) / (factorial(depth - k) * factorial(k); where depth is the depth and k is the weight position
Examples of coefficient outputs:
6 Depth: 6 15 20 15 6
7 Depth: 7 21 35 35 21 7
8 Depth: 8 28 56 70 56 28 8
9 Depth: 9 36 34 84 126 126 84 36 9
10 Depth: 10 45 120 210 252 210 120 45 10
11 Depth: 11 55 165 330 462 462 330 165 55 11
12 Depth: 12 66 220 495 792 924 792 495 220 66 12
13 Depth: 13 78 286 715 1287 1716 1716 1287 715 286 78 13
Step 3: Apply coefficient to each moving average
For QEMA, which is 5 depth EMA , the calculation is as follows
ema1 = ta. ema ( src , length)
ema2 = ta. ema (ema1, length)
ema3 = ta. ema (ema2, length)
ema4 = ta. ema (ema3, length)
ema5 = ta. ema (ema4, length)
In this new streamlined version, these MA calculations are packed into an array inside loop so Pine doesn't have to keep all possible series information in memory. This is handled with the following code:
temp = array.get(workarr, k + 1) + alpha * (array.get(workarr, k) - array.get(workarr, k + 1))
array.set(workarr, k + 1, temp)
After we pack the array, we apply the coefficients to derive the NTMA:
qema = 5 * ema1 - 10 * ema2 + 10 * ema3 - 5 * ema4 + ema5
Stepping calculations
First off, you can filter by both price and/or MA output. Both price and MA output can be filtered/stepped in their own way. You'll see two selectors in the input settings. Default is ATR ATR. Here's how stepping works in simple terms: if the price/MA output doesn't move by X deviations, then revert to the price/MA output one bar back.
ATR
The average true range (ATR) is a technical analysis indicator, introduced by market technician J. Welles Wilder Jr. in his book New Concepts in Technical Trading Systems, that measures market volatility by decomposing the entire range of an asset price for that period.
Standard Deviation
Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.
Adaptive Deviation
By definition, the Standard Deviation (STD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. In technical analysis we usually use it to measure the level of current volatility .
Standard Deviation is based on Simple Moving Average calculation for mean value. This version of standard deviation uses the properties of EMA to calculate what can be called a new type of deviation, and since it is based on EMA , we can call it EMA deviation. And added to that, Perry Kaufman's efficiency ratio is used to make it adaptive (since all EMA type calculations are nearly perfect for adapting).
The difference when compared to standard is significant--not just because of EMA usage, but the efficiency ratio makes it a "bit more logical" in very volatile market conditions.
See how this compares to Standard Devaition here:
Adaptive Deviation
Median Absolute Deviation
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it. In the MAD, the deviations of a small number of outliers are irrelevant.
Because the MAD is a more robust estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution.
For this indicator, I used a manual recreation of the quantile function in Pine Script. This is so users have a full inside view into how this is calculated.
Efficiency-Ratio Adaptive ATR
Average True Range (ATR) is widely used indicator in many occasions for technical analysis . It is calculated as the RMA of true range. This version adds a "twist": it uses Perry Kaufman's Efficiency Ratio to calculate adaptive true range
See how this compares to ATR here:
ER-Adaptive ATR
Mean Absolute Deviation
The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between observations and their mean. MAD uses the original units of the data, which simplifies interpretation. Larger values signify that the data points spread out further from the average. Conversely, lower values correspond to data points bunching closer to it. The mean absolute deviation is also known as the mean deviation and average absolute deviation.
This definition of the mean absolute deviation sounds similar to the standard deviation (SD). While both measure variability, they have different calculations. In recent years, some proponents of MAD have suggested that it replace the SD as the primary measure because it is a simpler concept that better fits real life.
For Pine Coders, this is equivalent of using ta.dev()
Bands/Channels
See the information above for how bands/channels are calculated. After the one of the above deviations is calculated, the channels are calculated as output +/- deviation * multiplier
Signals
Green is uptrend, red is downtrend, yellow "L" signal is Long, fuchsia "S" signal is short.
Included:
Alerts
Loxx's Expanded Source Types
Bar coloring
Signals
6 bands/channels types
6 stepping types
Related indicators
3-Pole Super Smoother w/ EMA-Deviation-Corrected Stepping
STD-Stepped Fast Cosine Transform Moving Average
ATR-Stepped PDF MA
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