Fractal Retracement [Jamallo](2025)
Intro
FRAMA is a moving average that adapts its speed based on fractal geometry — specifically, the fractal dimension (D) of recent price action. When price is trending strongly (low fractal dimension), it moves fast. When price is choppy/ranging (high fractal dimension), it slows down. This makes it far more responsive than a standard EMA or SMA.
Breakdown:
The indicator wraps this with a continuous range logic layer: the filtered line = k only moves if price breaks beyond the FRAMA ± ATR-based range, creating a stepped/ratcheting effect that filters out noise.
Two sets of bands are plotted around the filtered line, scaled by ATR multiplied by user-defined multipliers (tight at 0.5×, medium at 1.0×). They're smoothed with a short EMA to reduce jitter, and filled with gradient colors for visual clarity.
Direction is simply determined by whether k is rising or falling, and colors everything green (uptrend) or pink/red (downtrend).
END
In short, it's a noise-filtered trend indicator useful for identifying trend direction, dynamic support/resistance , and gauging how far price has retraced from the trend baseline. Indicator
Adaptive Centric Moving Average [LuxAlgo]The Adaptive Centric Moving Average indicator provides a dynamic smoothing tool that adjusts its reactivity based on where the price sits relative to its recent trading range midpoint.
🔶 USAGE
The Adaptive Centric Moving Average (AMA) is designed to filter out noise during periods of consolidation while remaining highly responsive during trending moves. When the price is near the center of its recent high-low range, the indicator becomes flatter and less prone to "whipsaws." As price moves toward the extremes of its range, the indicator accelerates to catch the emerging trend.
Users can utilize the AMA for trend identification and trailing stop-loss levels. The visual gradient fill between the source price and the AMA line helps traders quickly identify the current trend strength and the distance between price and the smoothed average.
🔶 DETAILS
The core logic of the script relies on a normalized relative position (similar to a Stochastic calculation) to determine how far the price is from its range midpoint.
🔹 Adaptive Smoothing Logic
The indicator calculates a smoothing factor (alpha) based on the absolute distance from the 50% level of the range.
When price is at the midpoint (50%), the alpha is zero, causing the moving average to stay flat.
As price moves toward the upper or lower boundaries (0% or 100%), the alpha increases, making the average more reactive.
🔹 The Centric Calculation
Unlike standard moving averages that track the source price directly, this indicator centers its target around the range midpoint. The Attenuation Factor scales the distance between the source and the midpoint, while the Power Factor applies an exponent to the smoothing factor, allowing for non-linear reactivity.
🔶 SETTINGS
🔹 Price Settings
Source: The price series used for calculations (default is Close).
Length: The window size used for pre-smoothing the source and determining the highest highs and lowest lows for the range.
🔹 Adaptive Settings
Attenuation Factor: Controls the intensity of the price input relative to the midpoint. Lower values increase reactivity, while higher values provide a more stable, base smoothing speed.
Power Factor: Exponents the smoothing factor. Higher values make the moving average significantly flatter when the price is near the range midpoint, requiring stronger moves to trigger a reaction.
🔹 Colors
AMA Color: The color of the main Adaptive Centric Moving Average line.
Bullish Fill: The color used for the gradient fill when the price is above the AMA.
Bearish Fill: The color used for the gradient fill when the price is below the AMA.
Indicator
Weighted Fourier Transform: Spectral Gating & Main Frequency🙏🏻 This drop has 2 purposes:
1) to inform every1 who'd ever see it that Weighted Fourier Tranform does exist, while being available nowhere online, not even in papers, yet there's nothing incredibly complicated about it, and it can/should be used in certain cases;
2) to show PulseWire users how they can use it now in dem endevours, to show em what spectral filtering is, and what can they do with all of it in diy mode.
... so we gonna have 2 sections in the description
Section 1: Weighted Fourier Transform
It's quite easy to include weights in Fourier analysis: you just premultiply each datapoint by its corresponding weight -> feed to direct Fourier Transform, and then divide by weights after inverse Fourier transform. Alternatevely, in direct transform you just multiply contributions of each data point to the real and imaginary parts of the Fourier transform by corresponding weights (in accumulation phase), and in inverse transform you divide by weights instead during the accumulation phase. Everything else stays the same just like in non-weighted version.
If you're from the first target group let's say, you prolly know a thing or deux about how to code & about Fourier Transform, so you can just check lines of code to see the implementation of Weighted Discrete version of Fourier Transform, and port it to to any technology you desire. Pine Script is a developing technology that is incredibly comfortable in use for quant-related tasks and anything involving time series in general. While also using Python for research and C++ for development, every time I can do what I want in Pine Script, I reach for it and never touch matlab, python, R, or anything else.
Weighted version allows you to explicetly include order/time information into the operation, which is essential with every time series, although not widely used in mainstream just as many other obvious and right things. If you think deeply, you'll understand that you can apply a usual non-weighted Fourier to any 2d+ data you can (even if none of these dimensions represent time), because this is a geometric tool in essence. By applying linearly decaying weights inside Fourier transform, you're explicetly saying, "one of these dimensions is Time, and weights represent the order". And obviously you can combine multiple weightings, eg time and another characteristic of each datum, allows you to include another non-spatial dimension in your model.
By doing that, on properly processed (not only stationary but Also centered around zero data), you can get some interesting results that you won't be able to recreate without weights:
^^ A sine wave, centered around zero, period of 16. Gray line made by: DWFT (direct weighted Fourier transform) -> spectral gating -> IWFT (inverse weighted Fourier transform) -> plotting the last value of gated reconstructed data, all applied to expanding window. Look how precisely it follows the original data (the sine wave) with no lag at all. This can't be done by using non-weighted version of Fourier transform.
^^ spectral filtering applied to the whole dataset, calculated on the latest data update
And you should never forget about Fast Fourier Transform, tho it needs recursion...
Section 2: About use cases for quant trading, about this particular implementaion in Pine Script 6 (currently the latest version as of Friday 13, December 2k24).
Given the current state of things, we have certain limits on matrix size on PulseWire (and we need big dope matrixes to calculate polynomial regression -> detrend & center our data before Fourier), and recursion is not yet available in Pine Script, so the script works on short datasets only, and requires some time.
A note on detrending. For quality results, Fourier Transform should be applied to not only stationary but also centered around zero data. The rightest way to do detrending of time series
is to fit Cumulative Weighted Moving Polynomial Regression (known as WLSMA in some narrow circles xD) and calculate the deltas between datapoint at time t and this wonderful fit at time t. That's exactly what you see on the main chart of script description: notice the distances between chart and WLSMA, now look lower and see how it matches the distances between zero and purple line in WFT study. Using residuals of one regression fit of the whole dataset makes less sense in time series context, we break some 'time' and order rules in a way, tho not many understand/cares abouit it in mainstream quant industry.
Two ways of using the script:
Spectral Gating aka Spectral filtering. Frequency domain filtering is quite responsive and for a greater computational cost does not introduce a lag the way it works with time-domain filtering. Works this way: direct Fourier transform your data to get frequency & phase info -> compute power spectrum out of it -> zero out all dem freqs that ain't hit your threshold -> inverse Fourier tranform what's left -> repeat at each datapoint plotting the very first value of reconstructed array*. With this you can watch for zero crossings to make appropriate trading decisions.
^^ plot Freq pass to use the script this way, use Level setting to control the intensity of gating. These 3 only available values: -1, 0 and 1, are the general & natural ones.
* if you turn on labels in script's style settings, you see the gray dots perfectly fitting your data. They get recalculated (for the whole dataset) at each update. You call it repainting, this is for analytical & aesthetic purposes. Included for demonstration only.
Finding main/dominant frequency & period. You can use it to set up Length for your other studies, and for analytical purposes simply to understand the periodicity of your data.
^^ plot main frequency/main period to use the script this way. On the screenshot, you can see the script applied to sine wave of period 16, notice how many datapoints it took the algo to figure out the signal's period quite good in expanding window mode
Now what's the next step? You can try applying signal windowing techniques to make it all less data-driven but your ego-driven, make a weighted periodogram or autocorrelogram (check Wiener-Khinchin Theorem ), and maybe whole shiny spectrogram?
... you decide, choice is yours,
The butterfly reflect the doors ...
∞ Indicator
Indicator
Indicator
Indicator
Indicator
Time_FilterLibrary "Time_Filter"
Time filters for trading strategies.
f_isInWeekDay(_timeZone, _byWeekDay, _byMon, _byTue, _byWed, _byThu, _byFri, _bySat, _bySun)
f_isInWeekDay - Filter by week day or by time delimited session.
Parameters:
_timeZone : - Time zone to use when filter allowed trading by days of the week.
_byWeekDay : - Filter allowed trading time by days of the week.
_byMon : - Is Monday a trading day?
_byTue : - Is Tuesday a trading day?
_byWed : - Is Wednesday a trading day?
_byThu : - Is Thursday a trading day?
_byFri : - Is Friday a trading day?
_bySat : - Is Saturday a trading day?
_bySun : - Is Sunday a trading day?
Returns: series of bool whether or not the time is inside the current day.
f_isInSession(_timeZone, _bySession_1, _timeSession_1, _bySession_2, _timeSession_2)
f_isInSession - Is the current time with in the allowed trading session time.
Parameters:
_timeZone : - Time zone to use when filter allowed trading by days of the week.
_bySession_1 : - Filter allowed trading time with in hours defined in _timeSession_1
_timeSession_1 : - Hours with in trading is allowed.
_bySession_2 : - Filter allowed trading time with in hours defined in _timeSession_2
_timeSession_2 : - Hours with in trading is allowed.
Returns: series of bool whether or not the time is inside selected session.
f_isTradingAllowed(_timeZone, _byWeekDay, _byMon, _byTue, _byWed, _byThu, _byFri, _bySat, _bySun, _bySession_1, _timeSession_1, _bySession_2, _timeSession_2)
f_isTradingAllowed - Is the current time with in the allowed.
Parameters:
_timeZone : - Time zone to use when filter allowed trading by days of the week.
_byWeekDay : - Filter allowed trading time by days of the week.
_byMon : - Is Monday a trading day?
_byTue : - Is Tuesday a trading day?
_byWed : - Is Wednesday a trading day?
_byThu : - Is Thursday a trading day?
_byFri : - Is Friday a trading day?
_bySat : - Is Saturday a trading day?
_bySun : - Is Sunday a trading day?
_bySession_1 : - Filter allowed trading time with in hours defined in _timeSession_1
_timeSession_1 : - Hours with in trading is allowed.
_bySession_2 : - Filter allowed trading time with in hours defined in _timeSession_2
_timeSession_2 : - Hours with in trading is allowed.
Returns: series of bool whether or not trading is allowed at the current time. Library
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
Indicator
