Library
Universal Adaptive Tracking🙏🏻 Behold, this is UAT (Universal Adaptive Tracker) , with less words imma proceed how it compares with alternatives:
^^ comparison with non-adaptive quadratic regression (purple line), that has higher overshoots, less precision
^^ comparison with JMA and its adaptive gain. JMA’s gain is heavily limited, while UAT’s negative and positive gains are soft-saturated with p-order Möbius transform
This drop is inspired by, dedicated to, and made will all love towards Jurik Research , who retired in October 2k21. When some1 steps out, some1 has to step in, and that time it’s me (again xd). But there’s some history u gotta know:
Some history u gotta know:
In ~2008 dudes from forexfactory reverse engineered Jurik Moving Average
In late 1990s dudes from Jurik Research approximated the best possible adaptive tracking filter for evolution of prices via engineering miracles
Today in 2k26, me I'm gonna present to you the real mathematical objects/entities behind JMA top-edge engineered approximates. You will prolly be even more happy now then all the dem together back then.
Why all this?
When we talk about object tracking stuff, e.g. air defense, drones, missiles, projectiles, prices, etc, it all comes down to adaptive control and (Position & Velocity & Acceleration) aka PVA state space models (the real stuff many of you count as DSP ).
Why? Cuz while position (P) : (mean), or position & velocity (PV) : (linear regression) are stable enough in dem own ways, Position & Velocity & Acceleration (PVA) : (quadratic regression+) require adaptivity do be stable. And real world stuff needs PVA, due to non-linearity for starters.
So that’s why. If your goal is Really smoothing and no lag, u gotta go there. I see a lot of folks are crazy with it and want it, so here is it, for y’all. And good news, this is perfect for your favorite Moving Windows.
How to use it
The upper study:
The final filter (main state): just as you use other fast smoothers, MAs, etc, you know better than me here
You can also turn in volatility bands in script’s style settings, these do not require any adjustments
Finally, you can turn on, in the same place, separate trackers each based on negative and positive volatility exclusively. When both are almost equal, that indicates stability & persistence in markets. May sound like it’s nothing important, but I've never seen anything like it before. Also, if you'd allow your our inner mental gym hero gloriously arise, you can argue that these 2 separate trackers represent 2 fair prices (one for sellers, one for buyers). All better then 1 imaginary fair price for both (forget about it)
The lower study:
The lower study: you can analyze streams of upward of downward volatilities separately. This is incredibly powerful
You can also turn these off and turn on neg & pos intensities, and use them as trend detector, when each or both cross 1.5 (naturally neutral) threshold.
^^ Upper study with expected typical and maximum volatility bands turned On
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The method explained
What you got in the end is non-linear, adaptive, lighting fast when needed and slow when required price tracking. All built upon real math entities/objects, not a brilliantly engineered approximation of them. No parameters to optimize, data tells it all.
... It all starts from a process model, in our cause this is...
MFPM (Mechanical Feedback Price Model)
Doesn’t make gaussian assumptions like most quant mainstream tech, accepts that innovations are Laplace “at best”, relies in L inf and L0 spaces.
I created this model neither trynna fit non-fitting ARMA / variants, nor trynna be silly assuming that price state evolution and markets are random.
Theory behind it: if no new volume comes, then price evolution would be simply guided by the feedback based on previous trading activity, pushing prices towards the midrange between 2 latest datapoints, being the main force behind so called “pullbacks” and reason why most pullbacks end just a bit past 50% of a move.
This is the Real mechanical feedback based mean reversion, that is always there in the markets no matter what, think of it as a background process that is always there, and fresh new volume deviates prices away from it. Btw, this can also be expressed as AR2 with both phis = 0.5 .
Then I separate positive and negative innovations from this model and process them separately, reflecting the asymmetry between buy and sell forces, smth that most forget. Both of these follow exponential distribution . Each stream has its own memory so here we use recursive operators . We track maximum innovations (differences between real and expected datapoints) with exponentially decaying damping factor, and keep tracking typical innovation, with the same factor.
Then we calculate what’s called in lovely audio engineering as “ crest factor ”, the difference is we don’t do RMS and stuff. But hey again we work with laplace innovations, so we keep things in L0 and L inf spirit. Then we go a couple of steps further, making this crest factor truly relative (resolution agnostic), and then, most importantly, we apply a natural saturation on it based on p-order Möbius transform, but not with arbitrary p and L, but guided by informational limits of the data. These final "intensity" parameters are what we need next to make our object tracking adaptive.
Extended Beta(2, 2) Window
This is imo the main part of this. Looking at tapering windows in DSP and how wavelets are made from derivatives of PDF functions of probability distributions, I figured that why use just one derivative? That made me come up with Universal Moving Average , that combines PDF and CDF of Beta(2, 2) distribution . And that is fine for P (position) tracking model.
Here we need PVA (position & velocity & acceleration). We can realize that everything starts from PDF, and by adding derivatives and anti-derivatives of it as factors of final window weights, we can create smth truly unique, a weightset that is non-arbitrary and naturally provides response alike quadratic regression does, But, naturally smoothed.
Why do I consider this a discovery, a primordial math object? Because x^2 itself and Beta(2, 2) based on it are the only primitives, esp out of all these dozens of DSP tapering windows, that provide you a finite amount of derivatives. You can keep differentiating Hann window until the kingdom f come, while Welch window aka Beta(2, 2) has a natural stopping point, because the 3rd derivative is 0, so we can’t use it. Symmetrically, we do 2 steps up from PDF, getting 1st and second anti-derivatives. What’s lovely, symmetrically, 3rd antiderivative even tho exist, it stops making any sense. 2nd one still makes sense, it’s smth like “potential” of probability distribution, not really discussed in mainstream open access sources.
Finally, the last part is to introduce adaptivity using these intensity exponents we’ve calculated with MFPM. We do 2 separate trackers, one using the negative intensity exponent, another one uses positive intensity exponent.
And at the end, even tho using both together is cool, the final state estimate is calculated simply as the state which intensity has higher.
^^ impulse response of our final kernel with fixed (non adaptive) intensity exponents: 1 (blue) and 2 (red). You see it's all about phase
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And that’s all folks.
…
Actually no …
Last, not least, is the ability to add additional innovation weight to the kernel:
^^ Weighting by innovations “On”. Provides incredible tracking precision, paid with smoothness. I think this screenshot, showing what happened after the gap, and how the tracker managed to react, explains it all.
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Live Long and Prosper, all good PulseWire
∞ Indicator
IIR One-Pole Price Filter [BackQuant]IIR One-Pole Price Filter
A lightweight, mathematically grounded smoothing filter derived from signal processing theory, designed to denoise price data while maintaining minimal lag. It provides a refined alternative to the classic Exponential Moving Average (EMA) by directly controlling the filter’s responsiveness through three interchangeable alpha modes: EMA-Length , Half-Life , and Cutoff-Period .
Concept overview
An IIR (Infinite Impulse Response) filter is a type of recursive filter that blends current and past input values to produce a smooth, continuous output. The "one-pole" version is its simplest form, consisting of a single recursive feedback loop that exponentially decays older price information. This makes it both memory-efficient and responsive , ideal for traders seeking a precise balance between noise reduction and reaction speed.
Unlike standard moving averages, the IIR filter can be tuned in physically meaningful terms (such as half-life or cutoff frequency) rather than just arbitrary periods. This allows the trader to think about responsiveness in the same way an engineer or physicist would interpret signal smoothing.
Why use it
Filters out market noise without introducing heavy lag like higher-order smoothers.
Adapts to various trading speeds and time horizons by changing how alpha (responsiveness) is parameterized.
Provides consistent and mathematically interpretable control of smoothing, suitable for both discretionary and algorithmic systems.
Can serve as the core component in adaptive strategies, volatility normalization, or trend extraction pipelines.
Alpha Modes Explained
EMA-Length : Classic exponential decay with alpha = 2 / (L + 1). Equivalent to a standard EMA but exposed directly for fine control.
Half-Life : Defines the number of bars it takes for the influence of a price input to decay by half. More intuitive for time-domain analysis.
Cutoff-Period : Inspired by analog filter theory, defines the cutoff frequency (in bars) beyond which price oscillations are heavily attenuated. Lower periods = faster response.
Formula in plain terms
Each bar updates as:
yₜ = yₜ₋₁ + alpha × (priceₜ − yₜ₋₁)
Where alpha is the smoothing coefficient derived from your chosen mode.
Smaller alpha → smoother but slower response.
Larger alpha → faster but noisier response.
Practical application
Trend detection : When the filter line rises, momentum is positive; when it falls, momentum is negative.
Signal timing : Use the crossover of the filter vs its previous value (or price) as an entry/exit condition.
Noise suppression : Apply on volatile assets or lower timeframes to remove flicker from raw price data.
Foundation for advanced filters : The one-pole IIR serves as a building block for multi-pole cascades, adaptive smoothers, and spectral filters.
Customization options
Alpha Scale : Multiplies the final alpha to fine-tune aggressiveness without changing the mode’s core math.
Color Painting : Candles can be painted green/red by trend direction for visual clarity.
Line Width & Transparency : Adjust the visual intensity to integrate cleanly with your charting style.
Interpretation tips
A smooth yet reactive line implies optimal tuning — minimal delay with reduced false flips.
A sluggish line suggests alpha is too small (increase responsiveness).
A noisy, twitchy line means alpha is too large (increase smoothing).
Half-life tuning often feels more natural for aligning filter speed with price cycles or bar duration.
Summary
The IIR One-Pole Price Filter is a signal smoother that merges simplicity with mathematical rigor. Whether you’re filtering for entry signals, generating trend overlays, or constructing larger multi-stage systems, this filter delivers stability, clarity, and precision control over noise versus lag, an essential tool for any quantitative or systematic trading approach.
Indicator
ATR RopeATR Rope is inspired by DonovanWall's "Range Filter". It implements a similar concept of filtering out smaller market movements and adjusting only for larger moves. In addition, this indicator goes one step deeper by producing actionable zones to determine market state. (Trend vs. Consolidation)
> Background
When reading up on the Range Filter indicator, it reminded me exactly of a Rope stabilization drawing tool in a program I use frequently. Rope stabilization essentially attaches a fixed length "rope" to your cursor and an anchor point (Brush). As you move your cursor, you are pulling the brush behind it. The cursor (of course) will not pull the brush until the rope is fully extended, this behavior filters out jittery movements and is used to produce smoother drawing curves.
If compared visually side-by-side, you will notice that this indicator bears striking resemblance to its inspiration.
> Goal
Other than simply distinguishing price movements between meaningful and noise, this indicator strives to create a rigid structure to frame market movements and lack-there-of, such as when to anticipate trend, and when to suspect consolidation.
Since the indicator works based on an ATR range, the resulting ATR Channel does well to get reactions from price at its extremes. Naturally, when consolidating, price will remain within the channel, neither pushing the channel significantly up or down. Likewise, when trending, price will continue to push the channel in a single direction.
With the goal of keeping it quick and simple, this indicator does not do any smoothing of data feeds, and is simply based on the deviation of price from the central rope. Adjusting the rope when price extends past the threshold created by +/- ATR from the rope.
> Features & Behaviors
- ATR Rope
ATR Rope is displayed as a 3 color single line.
This can be considered the center line, or the directional line, whichever you'd prefer.
The main point of the Rope display is to indicate direction, however it also is factually the center of the current working range.
- ATR Rope Color
When the rope's value moves up, it changes to green (uptrend), when down, red (downtrend).
When the source crosses the rope, it turns blue (flat).
With these simple rules, we've formed a structure to view market movements.
- Consolidation Zones
Consolidation Zones generate from "Flat" areas, and extend into subsequent trend areas. Consolidation is simply areas where price has crossed the Rope and remains inside the range. Over these periods, the upper and lower values are accumulated and averaged together to form the "Consolidation Zone" values. These zones are draw live, so values are averaged as the flat areas progress and don't repaint, so all values seen historically are as they would appear live.
- ATR Channel
ATR Channel displays the upper and lower bounds of the working range.
When the source moves beyond this range, the rope is adjusted based on the distance from the source to the channel. This range can be extremely useful to view, but by default it is hidden.
> Application
This indicator is not created to provide signals, or serve as a "complete" system.
(People who didn't read this far will still comment for signals. :) )
This is created to be used alongside manual interpretation and intuition. This indicator is not meant to constrain any users into a box, and I would actually encourage an open mind and idea generation, as the application of this indicator can take various forms.
> Examples
As you would probably already know, price movement can be fast impulses, and movement can be slow bleeds. In the screenshot below, we are using movements from and to consolidation zones to classify weak trend and strong trend. As you can see, there are also areas of consolidation which get broken out of and confirmed for the larger moves.
Author's Note: In each of these examples, I have outlined the start and end of each session. These examples come from 1 Min Future charts, and have specifically been framed with day trading in mind.
"Breakout Retest" or "Support/Resistance Flips" or "Structure Retests" are all generally the same thing, with different traders referring to them by different names, all of which can be seen throughout these examples.
In the next example, we have a day which started with an early reversal leading into long, slow, trend. Notice how each area throughout the trend essentially moves slightly higher, then consolidates while holding support of the previous zone. This day had a few sharp movements, however there was a large amount of neutrality throughout this day with continuous higher lows.
In contrast to the previous example, next up, we have a very choppy day. Throughout which we see a significant amount of retests before fast directional movements. We also see a few examples of places where previous zones remained relevant into the future. While the zones only display into the resulting trend area, they do not become immediately meaningless once they stop drawing.
> Abstract
In the screenshot below, I have stacked 2 of these indicators, using the high as the source for one and the low as the source for the other. I've hidden lines of the high and low channels to create a 4 lined channel based on the wicks of price.
This is not necessary to use the indicator, but should help provide an idea of creative ways the simple indicator could be used to produce more complicated analysis.
If you've made it this far, I would hope it's clear to you how this indicator could provide value to your trading.
Thank you to DonovonWall for the inspiration.
Enjoy! Indicator
[GYTS] Filters ToolkitFilters Toolkit indicator
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
The GYTS Filters Toolkit indicator is an advanced, interactive interface built atop the high‐performance, curated functions provided by the FiltersToolkit library . It allows traders to experiment with different combinations of filtering methods -— from smoothing low-pass filters to aggressive detrenders. With this toolkit, you can build custom indicators tailored to your specific trading strategy, whether you're looking for trend following, mean reversion, or cycle identification approaches.
🌸 --------- 2. FILTER METHODS AND TYPES --------- 🌸
💮 Filter categories
The available filters fall into four main categories, each marked with a distinct symbol:
🌗 Low Pass Filters (Smoothers)
These filters attenuate high-frequency components (noise) while allowing low-frequency components (trends) to pass through. Examples include:
Ultimate Smoother
Super Smoother (2-pole and 3-pole variants)
MESA Adaptive Moving Average (MAMA) and Following Adaptive Moving Average (FAMA)
BiQuad Low Pass Filter
ADXvma (Adaptive Directional Volatility Moving Average)
A2RMA (Adaptive Autonomous Recursive Moving Average)
Low pass filters are displayed on the price chart by default, as they follow the overall price movement. If they are combined with a high-pass or bandpass filter, they will be displayed in the subgraph.
🌓 High Pass Filters (Detrenders)
These filters do the opposite of low pass filters - they remove low-frequency components (trends) while allowing high-frequency components to pass through. Examples include:
Butterworth High Pass Filter
BiQuad High Pass Filter
High pass filters are displayed as oscillators in the subgraph below the price chart, as they fluctuate around a zero line.
🌑 Band Pass Filters (Cycle Isolators)
These filters combine aspects of both low and high pass filters, isolating specific frequency ranges while attenuating both higher and lower frequencies. Examples include:
Ehlers Bandpass Filter
Cyber Cycle
Relative Vigor Index (RVI)
BiQuad Bandpass Filter
Band pass filters are also displayed as oscillators in a separate panel.
🔮 Predictive Filter
Voss Predictive Filter: A special filter that attempts to predict future values of band-limited signals (only to be used as post-filter). Keep its prediction horizon short (1–3 bars) for reasonable accuracy.
Note that the the library contains elaborate documentation and source material of each filter.
🌸 --------- 3. INDICATOR FEATURES --------- 🌸
💮 Multi-filter configuration
One of the most powerful aspects of this indicator is the ability to configure multiple filters. compare them and observe their combined effects. There are four primary filters, each with its own parameter settings.
💮 Post-filtering
Process a filter’s output through an additional filter by enabling the post-filter option. This creates a filter chain where the output of one filter becomes the input to another. Some powerful combinations include:
Ultimate Smoother → MAMA: Creates an adaptive smoothing effect that responds well to market changes, good for trend-following strategies
Butterworth → Super Smoother → Butterworth: Produces a well-behaved oscillator with minimal phase distortion, John Ehlers also calls a "roofing filter". Great for identifying overbought/oversold conditions with minimal lag.
A bandpass filter → Voss Prediction filter: Attempts to predict future movements of cyclical components, handy to find peaks and troughs of the market cycle.
💮 Aggregate filters
Arguably the coolest feature: aggregating filters allow you to combine multiple filters with different weights. Important notes about aggregation:
You can only aggregate filters that appear on the same chart (price chart or oscillator panel).
The weights are automatically normalised, so only their relative values matter
Setting a weight to 0 (zero) excludes that filter from the aggregation
Filters don't need to be visibly displayed to be included in aggregation
💮 Rich visualisation & alerts
The indicator intelligently determines whether a filter is displayed on the price chart or in the subgraph (as an oscillator) based on its characteristics.
Dynamic colour palettes, adjustable line widths, transparency, and custom fill between any of enabled filters or between oscillators and the zero-line.
A clear legend showing which filters are active and how they're configured
Alerts for direction changes and crossovers of all filters
🌸 --------- 4. ACKNOWLEDGEMENTS --------- 🌸
This toolkit builds on the work of numerous pioneers in technical analysis and digital signal processing:
John Ehlers, whose groundbreaking research forms the foundation of many filters.
Robert Bristow-Johnson for the BiQuad filter formulations.
The PulseWire community, especially @The_Peaceful_Lizard, @alexgrover, and others mentioned in the code of the library.
Everyone who has provided feedback, testing and support!
Indicator
Indicator
PhiSmoother Moving Average Ribbon [ChartPrime]DSP FILTRATION PRIMER:
DSP (Digital Signal Processing) filtration plays a critical role with financial indication analysis, involving the application of digital filters to extract actionable insights from data. Its primary trading purpose is to distinguish and isolate relevant signals separate from market noise, allowing traders to enhance focus on underlying trends and patterns. By smoothing out price data, DSP filters aid with trend detection, facilitating the formulation of more effective trading techniques.
Additionally, DSP filtration can play an impactful role with detecting support and resistance levels within financial movements. By filtering out noise and emphasizing significant price movements, identifying key levels for entry and exit points become more apparent. Furthermore, DSP methods are instrumental in measuring market volatility, enabling traders to assess volatility levels with improved accuracy.
In summary, DSP filtration techniques are versatile tools for traders and analysts, enhancing decision-making processes in financial markets. By mitigating noise and highlighting relevant signals, DSP filtration improves the overall quality of trading analysis, ultimately leading to better conclusions for market participants.
APPLYING FIR FILTERS:
FIR (Finite Impulse Response) filters are indispensable tools in the realm of financial analysis, particularly for trend identification and characterization within market data. These filters effectively smooth out price fluctuations and noise, enabling traders to discern underlying trends with greater fidelity. By applying FIR filters to price data, robust trading strategies can be developed with grounded trend-following principles, enhancing their ability to capitalize on market movements.
Moreover, FIR filter applications extend into wide-ranging utility within various fields, one being vital for informed decision-making in analysis. These filters help identify critical price levels where assets may tend to stall or reverse direction, providing traders with valuable insights to aid with identification of optimal entry and exit points within their indicator arsenal. FIRs are undoubtedly a cornerstone to modern trading innovation.
Additionally, FIR filters aid in volatility measurement and analysis, allowing traders to gauge market volatility accurately and adjust their risk management approaches accordingly. By incorporating FIR filters into their analytical arsenal, traders can improve the quality of their decision-making processes and achieve better trading outcomes when contending with highly dynamic market conditions.
INTRODUCTORY DEBUT:
ChartPrime's " PhiSmoother Moving Average Ribbon " indicator aims to mark a significant advancement in technical analysis methodology by removing unwanted fluctuations and disturbances while minimizing phase disturbance and lag. This indicator introduces PhiSmoother, a powerful FIR filter in it's own right comparable to Ehlers' SuperSmoother.
PhiSmoother leverages a custom tailored FIR filter to smooth out price fluctuations by mitigating aliasing noise problematic to identification of underlying trends with accuracy. With adjustable parameters such as phase control, traders can fine-tune the indicator to suit their specific analytical needs, providing a flexible and customizable solution.
Mathemagically, PhiSmoother incorporates various color coding preferences, enabling traders to visualize trends more effectively on a volatile landscape. Whether utilizing progression, chameleon, or binary color schemes, you can more fluidly interpret market dynamics and make informed visual decisions regarding entry and exit points based on color-coded plotting.
The indicator's alert system further enhances its utility by providing notifications of specifically chosen filter crossings. Traders can customize alert modes and messages while ensuring they stay informed about potential opportunities aligned with their trading style.
Overall, the "PhiSmoother Moving Average Ribbon" visually stands out as a revolutionary mechanism for technical analysis, offering traders a comprehensive solution for trend identification, visualization, and alerting within financial markets to achieve advantageous outcomes.
NOTEWORTHY SETTINGS FEATURES:
Price Source Selection - The indicator offers flexibility in choosing the price source for analysis. Traders can select from multiple options.
Phase Control Parameter - One of the notable standout features of this indicator is the phase control parameter. Traders can fine-tune the phase or lag of the indicator to adapt it to different market conditions or timeframes. This feature enables optimization of the indicator's responsiveness to price movements and align it with their specific trading tactics.
Coloring Preferences - Another magical setting is the coloring features, one being "Chameleon Color Magic". Traders can customize the color scheme of the indicator based on their visual preferences or to improve interpretation. The indicator offers options such as progression, chameleon, or binary color schemes, all having versatility to dynamically visualize market trends and patterns. Two colors may be specifically chosen to reduce overlay indicator interference while also contrasting for your visual acuity.
Alert Controls - The indicator provides diverse alert controls to manage alerts for specific market events, depending on their trading preferences.
Alertable Crossings: Receive an alert based on selectable predefined crossovers between moving average neighbors
Customizable Alert Messages: Traders can personalize alert messages with preferred information details
Alert Frequency Control: The frequency of alerts is adjustable for maximum control of timely notifications
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