Support and Resistance LevelsDetecting Support and Resistance Levels
Description:
Support & Resistance levels are essential for every trader to define the decision points of the markets. If you are long and the market falls below the previous support level, you most probably have got the wrong position and better exit.
This script uses the first and second deviation of a curve to find the turning points and extremes of the price curve.
The deviation of a curve is nothing else than the momentum of a curve (and inertia is another name for momentum). It defines the slope of the curve. If the slope of a curve is zero, you have found a local extreme. The curve will change from rising to falling or the other way round.
The second deviation, or the momentum of momentum, shows you the turning points of the first deviation. This is important, as at this point the original curve will switch from acceleration to break mode.
Using the logic laid out above the support&resistance indicator will show the turning points of the market in a timely manner. Depending on level of market-smoothing it will show the long term or short term turning points.
This script first calculates the first and second deviation of the smoothed market, and in a second step runs the turning point detection.
Style tags: Trend Following, Trend Analysis
Asset class: Equities, Futures, ETFs, Currencies and Commodities
Dataset: FX Minutes/Hours/Days
Cari dalam skrip untuk "curve"
ErrorFunctionsLibrary "ErrorFunctions"
A collection of functions used to approximate the area beneath a Gaussian curve.
Because an ERF (Error Function) is an integral, there is no closed-form solution to calculating the area beneath the curve. Meaning all ERFs are approximations; precisely wrong, but mostly accurate. How close you need to get to the actual area depends entirely on your use case, with more precision being less efficient.
The internal precision of floats in Pine Script is 1e-16 (16 decimals, aka. double precision). This library adapts well known algorithms designed to efficiently reach double precision. Single precision alternates are also included. All of them were made free to use, modify, and distribute by their original authors.
HASTINGS
Adaptation of a single precision ERF by Cecil Hastings Jr, published through Princeton University in 1955. It was later documented by Abramowitz and Stegun as equation 7.1.26 in their 1972 Handbook of Mathematical Functions. Fast, efficient, and ideal when precision beyond a few decimals is unnecessary.
GILES
Adaptation of a single precision Inverse ERF by Michael Giles, published through the University of Oxford in 2012. It reverses the ERF, estimating an X coordinate from an area. It too is fast, efficient, and ideal when precision beyond a few decimals is unnecessary.
LIBC
Adaptation of the double precision ERF & ERFC in the standard C library (aka. libc). It is also the same ERF & ERFC that SciPy uses. While not quite as efficient as the Hastings approximation, it's still very fast and fully maximizes Pines precision.
BOOST
Adaptation of the double precision Inverse ERF & Inverse ERFC in the Boost Math C++ library. SciPy uses these as well. These reverse the ERF & ERFC, estimating an X coordinate from an area. It too isn't quite as efficient as the Giles approximation, but still fast and fully maximizes Pines precision.
While these algorithms are not exported directly, they are available through their exported counterparts.
- - -
ERROR FUNCTIONS
erf(x, precise)
An Error Function estimates the theoretical error of a measurement.
Parameters:
x (float) : (float) Upper limit of the integration.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between -1 and 1.
erfc(x, precise)
A Complementary Error Function estimates the difference between a theoretical error and infinity.
Parameters:
x (float) : (float) Lower limit of the integration.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and 2.
erfinv(x, precise)
An Inverse Error Function reverses the erf() by estimating the original measurement from the theoretical error.
Parameters:
x (float) : (float) Theoretical error.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and ± infinity.
erfcinv(x, precise)
An Inverse Complementary Error Function reverses the erfc() by estimating the original measurement from the difference between the theoretical error and infinity.
Parameters:
x (float) : (float) Difference between the theoretical error and infinity.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and ± infinity.
- - -
DISTRIBUTION FUNCTIONS
pdf(x, m, s)
A Probability Density Function estimates the probability density . For clarity, density is not a probability .
Parameters:
x (float) : (float) X coordinate for which a density will be estimated.
m (float) : (float) Mean
s (float) : (float) Sigma
Returns: (float) Between 0 and ∞.
cdf(z, precise)
A Cumulative Distribution Function estimates the area under a Gaussian curve between negative infinity and the Z Score.
Parameters:
z (float) : (float) Z Score.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and 1.
cdfinv(a, precise)
An Inverse Cumulative Distribution Function reverses the cdf() by estimating the Z Score from an area.
Parameters:
a (float) : (float) Area between 0 and 1.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between -∞ and +∞
cdfab(z1, z2, precise)
A Cumulative Distribution Function from A to B estimates the area under a Gaussian curve between two Z Scores (A and B).
Parameters:
z1 (float) : (float) First Z Score.
z2 (float) : (float) Second Z Score.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and 1.
ttt(z, precise)
A Two-Tailed Test estimates the area under a Gaussian curve between symmetrical ± Z scores and ± infinity.
Parameters:
z (float) : (float) One of the symmetrical Z Scores.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and 1.
tttinv(a, precise)
An Inverse Two-Tailed Test reverses the ttt() by estimating the absolute Z Score from an area.
Parameters:
a (float) : (float) Area between 0 and 1.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and ∞.
ott(z, precise)
A One-Tailed Test estimates the area under a Gaussian curve between an absolute Z Score and infinity.
Parameters:
z (float) : (float) Z Score.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and 1.
ottinv(a, precise)
An Inverse One-Tailed Test Reverses the ott() by estimating the Z Score from a an area.
Parameters:
a (float) : (float) Area between 0 and 1.
precise (bool) : Double precision (true) or single precision (false).
Returns: (float) Between 0 and ∞.
Trailing Management (Zeiierman)█ Overview
The Trailing Management (Zeiierman) indicator is designed for traders who seek an automated and dynamic approach to managing trailing stops. It helps traders make systematic decisions regarding when to enter and exit trades based on the calculated risk-reward ratio. By providing a clear visual representation of trailing stop levels and risk-reward metrics, the indicator is an essential tool for both novice and experienced traders aiming to enhance their trading discipline.
The Trailing Management (Zeiierman) indicator integrates a Break-Even Curve feature to enhance its utility in trailing stop management and risk-reward optimization. The Break-Even Curve illuminates the precise point at which a trade neither gains nor loses value, offering clarity on the risk-reward landscape. Furthermore, this precise point is calculated based on the required win rate and the risk/reward ratio. This calculation aids traders in understanding the type of strategy they need to employ at any given time to be profitable. In other words, traders can, at any given point, assess the kind of strategy they need to utilize to make money, depending on the price's position within the risk/reward box.
█ How It Works
The indicator operates by computing the highest high and the lowest low over a user-defined period and then applying this information to determine optimal trailing stop levels for both long and short positions.
Directional Bias:
It establishes the direction of the market trend by comparing the index of the highest high and the lowest low within the lookback period.
Bullish
Bearish
Trailing Stop Adjustment:
The trailing stops are adjusted using one of three methods: an automatic calculation based on the median of recent peak differences, pivot points, or a fixed percentage defined by the user.
The Break-Even Curve:
The Break-Even Curve, along with the risk/reward ratio, is determined through the trailing method. This approach utilizes the current closing price as a hypothetical entry point for trades. All calculations, including those for the curve, are based on this current closing price, ensuring real-time accuracy and relevance. As market conditions fluctuate, the curve dynamically adjusts, offering traders a visual benchmark that signifies the break-even point. This real-time adjustment provides traders with an invaluable tool, allowing them to visually track how shifts in the market could impact the point at which their trades neither gain nor lose value.
Example:
Let's say the price is at the midpoint of the risk/reward box; this means that the risk/reward ratio should be 1:1, and the minimum win rate is 50% to break even.
In this example, we can see that the price is near the stop-loss level. If you are about to take a trade in this area and would respect your stop, you only need to have a minimum win rate of 11% to earn money, given the risk/reward ratio, assuming that you hold the trade to the target.
In other words, traders can, at any given point, assess the kind of strategy they need to employ to make money based on the price's position within the risk/reward box.
█ How to Use
Market Bias:
When using the Auto Bias feature, the indicator calculates the underlying market bias and displays it as either bullish or bearish. This helps traders align their trades with the underlying market trend.
Risk Management:
By observing the plotted trailing stops and the risk-reward ratios, traders can make strategic decisions to enter or exit positions, effectively managing the risk.
Strategy selection:
The Break-Even Curve is a powerful tool for managing risk, allowing traders to visualize the relationship between their trailing stops and the market's price movements. By understanding where the break-even point lies, traders can adjust their strategies to either lock in profits or cut losses.
Based on the plotted risk/reward box and the location of the price within this box, traders can easily see the win rate required by their strategy to make money in the long run, given the risk/reward ratio.
Consider this example: The market is bullish, as indicated by the bias, and the indicator suggests looking into long trades. The price is near the top of the risk/reward box, which means entering the market right now carries a huge risk, and the potential reward is very low. To take this trade, traders must have a strategy with a win rate of at least 90%.
█ Settings
Trailing Method:
Auto: The indicator calculates the trailing stop dynamically based on market conditions.
Pivot: The trailing stop is adjusted to the highest high (long positions) or lowest low (short positions) identified within a specified lookback period. This method uses the pivotal points of the market to set the trailing stop.
Percentage: The trailing stop is set at a fixed percentage away from the peak high or low.
Trailing Size (prd):
This setting defines the lookback period for the highest high and lowest low, which affects the sensitivity of the trailing stop to price movements.
Percentage Step (perc):
If the 'Percentage' method is selected, this setting determines the fixed percentage for the trailing stop distance.
Set Bias (bias):
Allows users to set a market bias which can be Bullish, Bearish, or Auto, affecting how the trailing stop is adjusted in relation to the market trend.
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Disclaimer
The information contained in my Scripts/Indicators/Ideas/Algos/Systems does not constitute financial advice or a solicitation to buy or sell any securities of any type. I will not accept liability for any loss or damage, including without limitation any loss of profit, which may arise directly or indirectly from the use of or reliance on such information.
All investments involve risk, and the past performance of a security, industry, sector, market, financial product, trading strategy, backtest, or individual's trading does not guarantee future results or returns. Investors are fully responsible for any investment decisions they make. Such decisions should be based solely on an evaluation of their financial circumstances, investment objectives, risk tolerance, and liquidity needs.
My Scripts/Indicators/Ideas/Algos/Systems are only for educational purposes!
[blackcat] L2 Ehlers Truncated BP FilterLevel: 2
Background
John F. Ehlers introuced Truncated BandPass (BP) Filter in Jul, 2020.
Function
In Dr. Ehlers' article “Truncated Indicators” in Jul, 2020, he introduces a method that can be used to modify some indicators, improving how accurately they are able to track and respond to price action. By limiting the data range, that is, truncating the data, indicators may be able to better handle extreme price events. A reasonable goal, especially during times of high volatility. John Ehlers shows how to improve a bandpass filter’s ability to reflect price by limiting the data range. Filtering out the temporary spikes and price extremes should positively affect the indicator stability. Enter a new indicator ——— the Truncated BandPass (BP) filter.
Cumulative indicators, such as the EMA or MACD, are affected not only by previous candles, but by a theoretically infinite history of candles. Although this effect is often assumed to be negligible, John Ehlers demonstrates in his article that it is not so. Or at least not for a narrow-band bandpass filter.
Bandpass filters are normally used for detecting cycles in price curves. But they do not work well with steep edges in the price curve. Sudden price jumps cause a narrow-band filter to “ring like a bell” and generate artificial cycles that can cause false triggers. As a solution, Ehlers proposes to truncate the candle history of the filter. Limiting the history to 10 bars effectively dampened the filter output and produced a better representation of the cycles in the price curve. For limiting the history of a cumulative indicator, John Ehlers proposes “Truncated Indicators,” John Ehlers takes us aside to look at the impact of sharp price movements on two fundamentally different types of filters: finite impulse response, and infinite impulse response filters. Given recent market conditions, this is a very well timed subject.
As demostrated in this script, Ehlers suggests “truncation” as an approach to the way the trader calculates filters. He explains why truncation is not appropriate for finite impulse response filters but why truncation can be beneficial to infinite impulse response filters. He then explains how to apply truncation to infinite impulse response filters using his bandpass filter as an example.
Key Signal
BPT --> Truncated BandPass (BP) Filter fast line
Trigger --> Truncated BandPass (BP) Filter slow line
Pros and Cons
100% John F. Ehlers definition translation, even variable names are the same. This help readers who would like to use pine to read his book.
Remarks
The 98th script for Blackcat1402 John F. Ehlers Week publication.
Readme
In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.
The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works.
Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element.
Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level.
Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated.
Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.
Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Polynomial Regression HeatmapPolynomial Regression Heatmap – Advanced Trend & Volatility Visualizer
Overview
The Polynomial Regression Heatmap is a sophisticated trading tool designed for traders who require a clear and precise understanding of market trends and volatility. By applying a second-degree polynomial regression to price data, the indicator generates a smooth trend curve, augmented with adaptive volatility bands and a dynamic heatmap. This framework allows users to instantly recognize trend direction, potential reversals, and areas of market strength or weakness, translating complex price action into a visually intuitive map.
Unlike static trend indicators, the Polynomial Regression Heatmap adapts to changing market conditions. Its visual design—including color-coded candles, regression bands, optional polynomial channels, and breakout markers—ensures that price behavior is easy to interpret. This makes it suitable for scalping, swing trading, and longer-term strategies across multiple asset classes.
How It Works
The core of the indicator relies on fitting a second-degree polynomial to a defined lookback period of price data. This regression curve captures the non-linear nature of market movements, revealing the true trajectory of price beyond the distortions of noise or short-term volatility.
Adaptive upper and lower bands are constructed using ATR-based scaling, surrounding the regression line to reflect periods of high and low volatility. When price moves toward or beyond these bands, it signals areas of potential overextension or support/resistance.
The heatmap colors each candle based on its relative position within the bands. Green shades indicate proximity to the upper band, red shades indicate proximity to the lower band, and neutral tones represent mid-range positioning. This continuous gradient visualization provides immediate feedback on trend strength, market balance, and potential turning points.
Optional polynomial channels can be overlaid around the regression curve. These three-line channels are based on regression residuals and a fixed width multiplier, offering additional reference points for analyzing price deviations, trend continuation, and reversion zones.
Signals and Breakouts
The Polynomial Regression Heatmap includes statistical pivot-based signals to highlight actionable price movements:
Buy Signals – A triangular marker appears below the candle when a pivot low occurs below the lower regression band.
Sell Signals – A triangular marker appears above the candle when a pivot high occurs above the upper regression band.
These markers identify significant deviations from the regression curve while accounting for volatility, providing high-quality visual cues for potential entry points.
The indicator ensures clarity by spacing markers vertically using ATR-based calculations, preventing overlap during periods of high volatility. Users can rely on these signals in combination with heatmap intensity and regression slope for contextual confirmation.
Interpretation
Trend Analysis :
The slope of the polynomial regression line represents trend direction. A rising curve indicates bullish bias, a falling curve indicates bearish bias, and a flat curve indicates consolidation.
Steeper slopes suggest stronger momentum, while gradual slopes indicate more moderate trend conditions.
Volatility Assessment :
Band width provides an instant visual measure of market volatility. Narrow bands correspond to low volatility and potential consolidation, whereas wide bands indicate higher volatility and significant price swings.
Heatmap Coloring :
Candle colors visually represent price position within the bands. This allows traders to quickly identify zones of bullish or bearish pressure without performing complex calculations.
Channel Analysis (Optional) :
The polynomial channel defines zones for evaluating potential overextensions or retracements. Price interacting with these lines may suggest areas where mean-reversion or trend continuation is likely.
Breakout Signals :
Buy and Sell markers highlight pivot points relative to the regression and volatility bands. These are statistical signals, not arbitrary triggers, and should be interpreted in context with trend slope, band width, and heatmap intensity.
Strategy Integration
The Polynomial Regression Heatmap supports multiple trading approaches:
Trend Following – Enter trades in the direction of the regression slope while using the heatmap for momentum confirmation.
Pullback Entries – Use breakouts or deviations from the regression bands as low-risk entry points during trend continuation.
Mean Reversion – Price reaching outer channel boundaries can indicate potential reversal or retracement opportunities.
Multi-Timeframe Alignment – Overlay on higher and lower timeframes to filter noise and improve entry timing.
Stop-loss levels can be set just beyond the opposing regression band, while take-profit targets can be informed by the distance between the bands or the curvature of the polynomial line.
Advanced Techniques
For traders seeking greater precision:
Combine the Polynomial Regression Heatmap with volume, momentum, or volatility indicators to validate signals.
Observe the width and slope of the regression bands over time to anticipate expanding or contracting volatility.
Track sequences of breakout signals in conjunction with heatmap intensity for systematic trade management.
Adjusting regression length allows customization for different assets or timeframes, balancing responsiveness and smoothing. The combination of polynomial curve, adaptive bands, heatmap, and optional channels provides a comprehensive statistical framework for informed decision-making.
Inputs and Customization
Regression Length – Determines the number of bars used for polynomial fitting. Shorter lengths increase responsiveness; longer lengths improve smoothing.
Show Bands – Toggle visibility of the ATR-based regression bands.
Show Channel – Enable or disable the polynomial channel overlay.
Color Settings – Customize bullish, bearish, neutral, and accent colors for clarity and visual preference.
All other internal parameters are fixed to ensure consistent statistical behavior and minimize potential misconfiguration.
Why Use Polynomial Regression Heatmap
The Polynomial Regression Heatmap transforms complex price action into a clear, actionable visual framework. By combining non-linear trend mapping, adaptive volatility bands, heatmap visualization, and breakout signals, it provides a multi-dimensional perspective that is both quantitative and intuitive.
This indicator allows traders to focus on execution, interpret market structure at a glance, and evaluate trend strength, overextensions, and potential reversals in real time. Its design is compatible with scalping, swing trading, and long-term strategies, providing a robust tool for disciplined, data-driven trading.
Neural Pulse System [Alpha Extract]Neural Pulse System (NPS)
The Neural Pulse System (NPS) is a custom technical indicator that analyzes price action through a probabilistic lens, offering a dynamic view of bullish and bearish tendencies.
Unlike traditional binary classification models, NPS employs Ordinary Least Squares (OLS) regression with dynamically computed coefficients to produce a smooth probability output ranging from -1 to 1.
Paired with ATR-based bands, this indicator provides an intuitive and volatility-aware approach to trend analysis.
🔶 CALCULATION
The Neural Pulse System utilizes OLS regression to compute probabilities of bullish or bearish price action while incorporating ATR-based bands for volatility context:
Dynamic Coefficients: Coefficients are recalculated in real-time and scaled up to ensure the regression adapts to evolving market conditions.
Ordinary Least Squares (OLS): Uses OLS regression instead of gradient descent for more precise and efficient coefficient estimation.
ATR Bands: Smoothed Average True Range (ATR) bands serve as dynamic boundaries, framing the regression within market volatility.
Probability Output: Instead of a binary result, the output is a continuous probability curve (-1 to 1), helping traders gauge the strength of bullish or bearish momentum.
Formula:
OLS Regression = Line of best fit minimizing squared errors
Probability Signal = Transformed regression output scaled to -1 (bearish) to 1 (bullish)
ATR Bands = Smoothed Average True Range (ATR) to frame price movements within market volatility
🔶 DETAILS
📊 Visual Features:
Probability Curve: Smooth probability signal ranging from -1 (bearish) to 1 (bullish)
ATR Bands: Price action is constrained within volatility bands, preventing extreme deviations
Color-Coded Signals:
Blue to Green: Increasing probability of bullish momentum
Orange to Red: Increasing probability of bearish momentum
Interpretation:
Bullish Bias: Probability output consistently above 0 suggests a bullish trend.
Bearish Bias: Probability output consistently below 0 indicates bearish pressure.
Reversals: Extreme values near -1 or 1, followed by a move toward 0, may signal potential trend reversals.
🔶 EXAMPLES
📌 Trend Identification: Use the probability output to gauge trend direction.
📌Example: On a 1-hour chart, NPS moves from -0.5 to 0.8 as price breaks resistance, signaling a bullish trend.
Reversal Signals: Watch for probability extremes near -1 or 1 followed by a reversal toward 0.
Example: NPS hits 0.9, price touches the upper ATR band, then both retreat—indicating a potential pullback.
📌 Example snapshots:
Volatility Context: ATR bands help assess whether price action aligns with typical market conditions.
Example: During low volatility, the probability signal hovers near 0, and ATR bands tighten, suggesting a potential breakout.
🔶 SETTINGS
Customization Options:
ATR Period – Defines lookback length for ATR calculation (shorter = more responsive, longer = smoother).
ATR Multiplier – Adjusts band width for better volatility capture.
Regression Length – Controls how many bars feed into the coefficient calculation (longer = smoother, shorter = more reactive).
Scaling Factor – Adjusts the strength of regression coefficients.
Output Smoothing – Option to apply a moving average for a cleaner probability curve
Dynamic ALMA with signalsEnhanced ALMA with Signals
This TradingView indicator is designed to enhance your trading strategy by utilizing the Arnaud Legoux Moving Average (ALMA), a unique moving average that provides smoother price action while minimizing lag. The script not only plots the ALMA line but also dynamically adjusts its parameters based on market volatility to adapt to different trading conditions. Additionally, it highlights potential bounce points off the line, as well as breakout points, giving traders clear signals for potential support, resistance levels, and breakouts.
Key Features:
Dynamic ALMA Line with Glow Effect:
The core of this indicator is the ALMA line, which is dynamically adjusted to market volatility, providing more accurate signals in varying conditions. The line adapts to both trending and consolidating markets by adjusting its sensitivity in real time. A glow effect is created by plotting the ALMA line multiple times with increasing transparency, making it visually distinct.
Bounce Detection Signals with Volatility Filter:
The script detects and labels potential support and resistance bounces based on the crossover and crossunder of the price with the ALMA line, further filtered by a volatility condition. This helps in filtering out false signals during low-volatility conditions, making the signals more reliable.
Visual Enhancements:
Custom glow effects and labels for bounce detection enhance chart readability and help traders quickly identify key levels.
Inputs:
Base Window Size: Sets the number of bars used in calculating the ALMA, allowing traders to adjust the sensitivity of the moving average. This parameter is dynamically adjusted based on current market volatility.
Offset: Determines the position of the ALMA curve. Higher values move the curve further away from the price. This value remains constant for stability.
Sigma: Controls the smoothness of the ALMA curve; a higher sigma results in a smoother curve. This value also remains constant.
ATR Period and Threshold Multiplier: Used to calculate the Average True Range (ATR) for the volatility filter, which determines whether the market conditions are sufficiently volatile to consider bounce signals.
How It Works:
Dynamic ALMA Calculation:
The script calculates the ALMA (Arnaud Legoux Moving Average) using the ta.alma function, dynamically adjusting the window size based on market volatility measured by the ATR (Average True Range). This ensures that the ALMA line remains responsive in high-volatility environments and smooth in low-volatility conditions.
Glow Effect:
To create a glow effect around the ALMA line, the script plots the ALMA multiple times with varying degrees of transparency. This visual enhancement helps the ALMA line stand out on the chart.
Bounce Detection with Volatility Filter:
The script uses two conditions to detect potential bounces:
Support Bounce: Detected when the low of the bar crosses above the ALMA line (ta.crossover(low, alma)) and the close is above the ALMA, while the volatility filter confirms sufficient market activity. This suggests potential support at the ALMA line.
Resistance Bounce: Detected when the high of the bar crosses below the ALMA line (ta.crossunder(high, alma)) and the close is below the ALMA, while the volatility filter confirms sufficient market activity. This indicates potential resistance at the ALMA line.
Labeling Bounce Points:
When a bounce is detected, the script labels it on the chart:
Support Bounces (S): Labeled with a blue "S" below the bar where a support bounce is detected.
Resistance Bounces (R): Labeled with a white "R" above the bar where a resistance bounce is detected.
Usage:
This enhanced indicator helps traders visualize key support and resistance levels more effectively by dynamically adjusting the ALMA moving average to market conditions. By detecting and labeling potential bounce points and filtering these signals based on volatility, traders can better identify entry and exit points in their trading strategy. The dynamic adjustments and visual enhancements make it easier to spot critical levels quickly and adapt to changing market conditions.
Customize the inputs to fit your trading style, and use this enhanced ALMA indicator to gain a more refined understanding of market trends, potential reversals, and breakouts.
SMIIO + VolumeThis indicator generates long and short signals.
The operation of the indicator is as follows;
First, true strength index is calculated with closing prices. We call this the "ergodic" curve.
Then the average of the ergodic (ema) is calculated to obtain the "signal" curve.
To calculate the "oscillator", the signal is subtracted from ergodic (oscillator = ergodic - signal).
The last variable to be used in the calculation is the average volume, calculated with sma.
Calculation for long signal;
- If the ergodic curve cross up the zero line (ergodic > 0 AND ergodic < 0) and,
- If the current oscillator is greater than the previous oscillator (oscillator > oscillator ) and,
- If the current ergonic is greater than the previous signal (ergonic > signal) and,
- If the current volume is greater than the average volume (volume > averageVolume) and,
- If the current candle closing price is greater than the opening price (close > open)
If all the above conditions are fullfilled, the long input signal is issued with "Buy" label.
Calculation for short signal;
- If the ergodic curve cross down the zero line (ergodic < 0 AND ergodic > 0) and,
- If the current oscillator is smaller than the previous oscillator (oscillator < oscillator ) and,
- If the current ergonic is smaller than the previous signal (ergonic < signal) and,
- If the current volume is greater than the average volume (volume > averageVolume) and,
- If the current candle closing price is smaller than the opening price (close < open)
If all the above conditions are fullfilled, the short input signal is issued with "Sell" label.
Treasury Yields Heatmap [By MUQWISHI]▋ INTRODUCTION :
The “Treasury Yields Heatmap” generates a dynamic heat map table, showing treasury yield bond values corresponding with dates. In the last column, it presents the status of the yield curve, discerning whether it’s in a normal, flat, or inverted configuration, which determined by using Pearson's linear regression coefficient. This tool is built to offer traders essential insights for effectively tracking bond values and monitoring yield curve status, featuring the flexibility to input a starting period, timeframe, and select from a range of major countries' bond data.
_______________________
▋ OVERVIEW:
______________________
▋ YIELD CURVE:
It is determined through Pearson's linear regression coefficient and considered…
R ≥ 0.7 → Normal
0.7 > R ≥ 0.35 → Slight Normal
0.35 > R > -0.35 → Flat
-0.35 ≥ R > -0.7 → Slight Inverted
-0.7 ≥ R → Inverted
_______________________
▋ INDICATOR SETTINGS:
#Section One: Table Setting
#Section Two: Technical Setting
(1) Country: Select country’s treasury yields data
(2) Timeframe: Time interval.
(3) Fetch By:
(3A) Date: Retrieve data by beginning of date.
(3B) Period: Retrieve data by specifying the number of time series back.
Enjoy. Please let me know if you have any questions.
Thank you.
Nonlinear Regression, Zero-lag Moving Average [Loxx]Nonlinear Regression and Zero-lag Moving Average
Technical indicators are widely used in financial markets to analyze price data and make informed trading decisions. This indicator presents an implementation of two popular indicators: Nonlinear Regression and Zero-lag Moving Average (ZLMA). Let's explore the functioning of these indicators and discuss their significance in technical analysis.
Nonlinear Regression
The Nonlinear Regression indicator aims to fit a nonlinear curve to a given set of data points. It calculates the best-fit curve by minimizing the sum of squared errors between the actual data points and the predicted values on the curve. The curve is determined by solving a system of equations derived from the data points.
We define a function "nonLinearRegression" that takes two parameters: "src" (the input data series) and "per" (the period over which the regression is calculated). It calculates the coefficients of the nonlinear curve using the least squares method and returns the predicted value for the current period. The nonlinear regression curve provides insights into the overall trend and potential reversals in the price data.
Zero-lag Moving Average (ZLMA)
Moving averages are widely used to smoothen price data and identify trend directions. However, traditional moving averages introduce a lag due to the inclusion of past data. The Zero-lag Moving Average (ZLMA) overcomes this lag by dynamically adjusting the weights of past values, resulting in a more responsive moving average.
We create a function named "zlma" that calculates the ZLMA. It takes two parameters: "src" (the input data series) and "per" (the period over which the ZLMA is calculated). The ZLMA is computed by first calculating a weighted moving average (LWMA) using a linearly decreasing weight scheme. The LWMA is then used to calculate the ZLMA by applying the same weight scheme again. The ZLMA provides a smoother representation of the price data while reducing lag.
Combining Nonlinear Regression and ZLMA
The ZLMA is applied to the input data series using the function "zlma(src, zlmaper)". The ZLMA values are then passed as input to the "nonLinearRegression" function, along with the specified period for nonlinear regression. The output of the nonlinear regression is stored in the variable "out".
To enhance the visual representation of the indicator, colors are assigned based on the relationship between the nonlinear regression value and a signal value (sig) calculated from the previous period's nonlinear regression value. If the current "out" value is greater than the previous "sig" value, the color is set to green; otherwise, it is set to red.
The indicator also includes optional features such as coloring the bars based on the indicator's values and displaying signals for potential long and short positions. The signals are generated based on the crossover and crossunder of the "out" and "sig" values.
Wrapping Up
This indicator combines two important concepts: Nonlinear Regression and Zero-lag Moving Average indicators, which are valuable tools for technical analysis in financial markets. These indicators help traders identify trends, potential reversals, and generate trading signals. By combining the nonlinear regression curve with the zero-lag moving average, this indicator provides a comprehensive view of the price dynamics. Traders can customize the indicator's settings and use it in conjunction with other analysis techniques to make well-informed trading decisions.
Crude Oil: Backwardation Vs ContangoCrude Oil, CL
Plots Futures Curve: Futures contract prices over the next 3.5 years; to easily visualize Backwardation Vs Contango(carrying charge) markets.
Carrying charge (contract prices increasing into the future) = normal, representing the costs of carrying/storage of a commodity. When this is flipped to Backwardation(As the above; contract prices decreasing into the future): it's a bullish sign: Buyers want this commodity, and they want it NOW.
Note: indicator does not map to time axis in the same way as price; it simply plots the progression of contract months out into the future; left to right; so timeframe DOESN'T MATTER for this plot
TO UPDATE (every year or so): in REQUEST CONTRACTS section, delete old contracts (top) and add new ones (bottom). Then in PLOTTING section, Delete old contract labels (bottom); add new contract labels (top); adjust the X in 'bar_index-(X+_historical)' numbers accordingly
This is one of several similar Futures Curve indicators: Meats | Metals | Grains | VIX | Crude Oil
If you want to build from this; to work on other commodities; be aware that Tradingview limits the number of contract calls to 40 (hence the multiple indicators)
Tips:
-Right click and reset chart if you can't see the plot; or if you have trouble with the scaling.
-Right click and add to new scale if you prefer this not to overlay directly on price. Or move to new pane below.
-If this takes too long to load (due to so many security calls); comment out the more distant future half of the contracts; and their respective labels. Or comment out every other contract and every other label if you prefer.
--Added historical input: input days back in time; to see the historical shape of the Futures curve via selecting 'days back' snapshot
updated 20th June 2022
© twingall
Moving Average Delta (Deviation = Absolute/Pips Simple MA)MAD stands for Moving Average Delta, it calculates the difference between moving average and price. The curve shows the difference in Pips.
By calculating the delta between two points we can see more small changes in the direction of the moving average curve which are normally hard to see. You can see the MAD curve as look through the microscope at a simple moving average curve. It may help predicting a trend change before it happens, the sample shows a beginning trend change from long to short.
Interpretation:
If the MAD curve is bigger than 0, the moving average is above the price
conversely;
If the MAD curve is smaller than 0, the moving average is below the price
Before a trend change, the moving average gets flatter, the MAD curve points to towards the zero
We can see what is the maximum rising/falling of the difference and predict an upcomming trend change
Usage:
Moving Average Delta Indicator by KIVANC fr3762Description:
MAD stands for Moving Average Delta, it calculates the difference between moving average and price. The curve shows the difference in Pips.
By calculating the delta between two points we can see more small changes in the direction of the moving average curve which are normally hard to see. You can see the MAD curve as look through the microscope at a simple moving average curve. It may help predicting a trend change before it happens, the sample shows a beginning trend change from long to short.
Interpretation:
If the MAD curve is bigger than 0, the moving average is above the price
conversely;
If the MAD curve is smaller than 0, the moving average is below the price
Before a trend change, the moving average gets flatter, the MAD curve points to towards the zero
We can see what is the maximum rising/falling of the difference and predict an upcomming trend change
Usage:
Drop a simple moving average to a chart and set the period in a way that it best fits the movements. There is no "magic" settings for the moving average period, you may double click the MA line to set it to a different period.
Drop the MAD indicator to the cart and give it the same period as your simple moving average .
Any Oscillator Underlay [TTF]We are proud to release a new indicator that has been a while in the making - the Any Oscillator Underlay (AOU) !
Note: There is a lot to discuss regarding this indicator, including its intent and some of how it operates, so please be sure to read this entire description before using this indicator to help ensure you understand both the intent and some limitations with this tool.
Our intent for building this indicator was to accomplish the following:
Combine all of the oscillators that we like to use into a single indicator
Take up a bit less screen space for the underlay indicators for strategies that utilize multiple oscillators
Provide a tool for newer traders to be able to leverage multiple oscillators in a single indicator
Features:
Includes 8 separate, fully-functional indicators combined into one
Ability to easily enable/disable and configure each included indicator independently
Clearly named plots to support user customization of color and styling, as well as manual creation of alerts
Ability to customize sub-indicator title position and color
Ability to customize sub-indicator divider lines style and color
Indicators that are included in this initial release:
TSI
2x RSIs (dubbed the Twin RSI )
Stochastic RSI
Stochastic
Ultimate Oscillator
Awesome Oscillator
MACD
Outback RSI (Color-coding only)
Quick note on OB/OS:
Before we get into covering each included indicator, we first need to cover a core concept for how we're defining OB and OS levels. To help illustrate this, we will use the TSI as an example.
The TSI by default has a mid-point of 0 and a range of -100 to 100. As a result, a common practice is to place lines on the -30 and +30 levels to represent OS and OB zones, respectively. Most people tend to view these levels as distance from the edges/outer bounds or as absolute levels, but we feel a more way to frame the OB/OS concept is to instead define it as distance ("offset") from the mid-line. In keeping with the -30 and +30 levels in our example, the offset in this case would be "30".
Taking this a step further, let's say we decided we wanted an offset of 25. Since the mid-point is 0, we'd then calculate the OB level as 0 + 25 (+25), and the OS level as 0 - 25 (-25).
Now that we've covered the concept of how we approach defining OB and OS levels (based on offset/distance from the mid-line), and since we did apply some transformations, rescaling, and/or repositioning to all of the indicators noted above, we are going to discuss each component indicator to detail both how it was modified from the original to fit the stacked-indicator model, as well as the various major components that the indicator contains.
TSI:
This indicator contains the following major elements:
TSI and TSI Signal Line
Color-coded fill for the TSI/TSI Signal lines
Moving Average for the TSI
TSI Histogram
Mid-line and OB/OS lines
Default TSI fill color coding:
Green : TSI is above the signal line
Red : TSI is below the signal line
Note: The TSI traditionally has a range of -100 to +100 with a mid-point of 0 (range of 200). To fit into our stacking model, we first shrunk the range to 100 (-50 to +50 - cut it in half), then repositioned it to have a mid-point of 50. Since this is the "bottom" of our indicator-stack, no additional repositioning is necessary.
Twin RSI:
This indicator contains the following major elements:
Fast RSI (useful if you want to leverage 2x RSIs as it makes it easier to see the overlaps and crosses - can be disabled if desired)
Slow RSI (primary RSI)
Color-coded fill for the Fast/Slow RSI lines (if Fast RSI is enabled and configured)
Moving Average for the Slow RSI
Mid-line and OB/OS lines
Default Twin RSI fill color coding:
Dark Red : Fast RSI below Slow RSI and Slow RSI below Slow RSI MA
Light Red : Fast RSI below Slow RSI and Slow RSI above Slow RSI MA
Dark Green : Fast RSI above Slow RSI and Slow RSI below Slow RSI MA
Light Green : Fast RSI above Slow RSI and Slow RSI above Slow RSI MA
Note: The RSI naturally has a range of 0 to 100 with a mid-point of 50, so no rescaling or transformation is done on this indicator. The only manipulation done is to properly position it in the indicator-stack based on which other indicators are also enabled.
Stochastic and Stochastic RSI:
These indicators contain the following major elements:
Configurable lengths for the RSI (for the Stochastic RSI only), K, and D values
Configurable base price source
Mid-line and OB/OS lines
Note: The Stochastic and Stochastic RSI both have a normal range of 0 to 100 with a mid-point of 50, so no rescaling or transformations are done on either of these indicators. The only manipulation done is to properly position it in the indicator-stack based on which other indicators are also enabled.
Ultimate Oscillator (UO):
This indicator contains the following major elements:
Configurable lengths for the Fast, Middle, and Slow BP/TR components
Mid-line and OB/OS lines
Moving Average for the UO
Color-coded fill for the UO/UO MA lines (if UO MA is enabled and configured)
Default UO fill color coding:
Green : UO is above the moving average line
Red : UO is below the moving average line
Note: The UO naturally has a range of 0 to 100 with a mid-point of 50, so no rescaling or transformation is done on this indicator. The only manipulation done is to properly position it in the indicator-stack based on which other indicators are also enabled.
Awesome Oscillator (AO):
This indicator contains the following major elements:
Configurable lengths for the Fast and Slow moving averages used in the AO calculation
Configurable price source for the moving averages used in the AO calculation
Mid-line
Option to display the AO as a line or pseudo-histogram
Moving Average for the AO
Color-coded fill for the AO/AO MA lines (if AO MA is enabled and configured)
Default AO fill color coding (Note: Fill was disabled in the image above to improve clarity):
Green : AO is above the moving average line
Red : AO is below the moving average line
Note: The AO is technically has an infinite (unbound) range - -∞ to ∞ - and the effective range is bound to the underlying security price (e.g. BTC will have a wider range than SP500, and SP500 will have a wider range than EUR/USD). We employed some special techniques to rescale this indicator into our desired range of 100 (-50 to 50), and then repositioned it to have a midpoint of 50 (range of 0 to 100) to meet the constraints of our stacking model. We then do one final repositioning to place it in the correct position the indicator-stack based on which other indicators are also enabled. For more details on how we accomplished this, read our section "Binding Infinity" below.
MACD:
This indicator contains the following major elements:
Configurable lengths for the Fast and Slow moving averages used in the MACD calculation
Configurable price source for the moving averages used in the MACD calculation
Configurable length and calculation method for the MACD Signal Line calculation
Mid-line
Note: Like the AO, the MACD also technically has an infinite (unbound) range. We employed the same principles here as we did with the AO to rescale and reposition this indicator as well. For more details on how we accomplished this, read our section "Binding Infinity" below.
Outback RSI (ORSI):
This is a stripped-down version of the Outback RSI indicator (linked above) that only includes the color-coding background (suffice it to say that it was not technically feasible to attempt to rescale the other components in a way that could consistently be clearly seen on-chart). As this component is a bit of a niche/special-purpose sub-indicator, it is disabled by default, and we suggest it remain disabled unless you have some pre-defined strategy that leverages the color-coding element of the Outback RSI that you wish to use.
Binding Infinity - How We Incorporated the AO and MACD (Warning - Math Talk Ahead!)
Note: This applies only to the AO and MACD at time of original publication. If any other indicators are added in the future that also fall into the category of "binding an infinite-range oscillator", we will make that clear in the release notes when that new addition is published.
To help set the stage for this discussion, it's important to note that the broader challenge of "equalizing inputs" is nothing new. In fact, it's a key element in many of the most popular fields of data science, such as AI and Machine Learning. They need to take a diverse set of inputs with a wide variety of ranges and seemingly-random inputs (referred to as "features"), and build a mathematical or computational model in order to work. But, when the raw inputs can vary significantly from one another, there is an inherent need to do some pre-processing to those inputs so that one doesn't overwhelm another simply due to the difference in raw values between them. This is where feature scaling comes into play.
With this in mind, we implemented 2 of the most common methods of Feature Scaling - Min-Max Normalization (which we call "Normalization" in our settings), and Z-Score Normalization (which we call "Standardization" in our settings). Let's take a look at each of those methods as they have been implemented in this script.
Min-Max Normalization (Normalization)
This is one of the most common - and most basic - methods of feature scaling. The basic formula is: y = (x - min)/(max - min) - where x is the current data sample, min is the lowest value in the dataset, and max is the highest value in the dataset. In this transformation, the max would evaluate to 1, and the min would evaluate to 0, and any value in between the min and the max would evaluate somewhere between 0 and 1.
The key benefits of this method are:
It can be used to transform datasets of any range into a new dataset with a consistent and known range (0 to 1).
It has no dependency on the "shape" of the raw input dataset (i.e. does not assume the input dataset can be approximated to a normal distribution).
But there are a couple of "gotchas" with this technique...
First, it assumes the input dataset is complete, or an accurate representation of the population via random sampling. While in most situations this is a valid assumption, in trading indicators we don't really have that luxury as we're often limited in what sample data we can access (i.e. number of historical bars available).
Second, this method is highly sensitive to outliers. Since the crux of this transformation is based on the max-min to define the initial range, a single significant outlier can result in skewing the post-transformation dataset (i.e. major price movement as a reaction to a significant news event).
You can potentially mitigate those 2 "gotchas" by using a mechanism or technique to find and discard outliers (e.g. calculate the mean and standard deviation of the input dataset and discard any raw values more than 5 standard deviations from the mean), but if your most recent datapoint is an "outlier" as defined by that algorithm, processing it using the "scrubbed" dataset would result in that new datapoint being outside the intended range of 0 to 1 (e.g. if the new datapoint is greater than the "scrubbed" max, it's post-transformation value would be greater than 1). Even though this is a bit of an edge-case scenario, it is still sure to happen in live markets processing live data, so it's not an ideal solution in our opinion (which is why we chose not to attempt to discard outliers in this manner).
Z-Score Normalization (Standardization)
This method of rescaling is a bit more complex than the Min-Max Normalization method noted above, but it is also a widely used process. The basic formula is: y = (x – μ) / σ - where x is the current data sample, μ is the mean (average) of the input dataset, and σ is the standard deviation of the input dataset. While this transformation still results in a technically-infinite possible range, the output of this transformation has a 2 very significant properties - the mean (average) of the output dataset has a mean (μ) of 0 and a standard deviation (σ) of 1.
The key benefits of this method are:
As it's based on normalizing the mean and standard deviation of the input dataset instead of a linear range conversion, it is far less susceptible to outliers significantly affecting the result (and in fact has the effect of "squishing" outliers).
It can be used to accurately transform disparate sets of data into a similar range regardless of the original dataset's raw/actual range.
But there are a couple of "gotchas" with this technique as well...
First, it still technically does not do any form of range-binding, so it is still technically unbounded (range -∞ to ∞ with a mid-point of 0).
Second, it implicitly assumes that the raw input dataset to be transformed is normally distributed, which won't always be the case in financial markets.
The first "gotcha" is a bit of an annoyance, but isn't a huge issue as we can apply principles of normal distribution to conceptually limit the range by defining a fixed number of standard deviations from the mean. While this doesn't totally solve the "infinite range" problem (a strong enough sudden move can still break out of our "conceptual range" boundaries), the amount of movement needed to achieve that kind of impact will generally be pretty rare.
The bigger challenge is how to deal with the assumption of the input dataset being normally distributed. While most financial markets (and indicators) do tend towards a normal distribution, they are almost never going to match that distribution exactly. So let's dig a bit deeper into distributions are defined and how things like trending markets can affect them.
Skew (skewness): This is a measure of asymmetry of the bell curve, or put another way, how and in what way the bell curve is disfigured when comparing the 2 halves. The easiest way to visualize this is to draw an imaginary vertical line through the apex of the bell curve, then fold the curve in half along that line. If both halves are exactly the same, the skew is 0 (no skew/perfectly symmetrical) - which is what a normal distribution has (skew = 0). Most financial markets tend to have short, medium, and long-term trends, and these trends will cause the distribution curve to skew in one direction or another. Bullish markets tend to skew to the right (positive), and bearish markets to the left (negative).
Kurtosis: This is a measure of the "tail size" of the bell curve. Another way to state this could be how "flat" or "steep" the bell-shape is. If the bell is steep with a strong drop from the apex (like a steep cliff), it has low kurtosis. If the bell has a shallow, more sweeping drop from the apex (like a tall hill), is has high kurtosis. Translating this to financial markets, kurtosis is generally a metric of volatility as the bell shape is largely defined by the strength and frequency of outliers. This is effectively a measure of volatility - volatile markets tend to have a high level of kurtosis (>3), and stable/consolidating markets tend to have a low level of kurtosis (<3). A normal distribution (our reference), has a kurtosis value of 3.
So to try and bring all that back together, here's a quick recap of the Standardization rescaling method:
The Standardization method has an assumption of a normal distribution of input data by using the mean (average) and standard deviation to handle the transformation
Most financial markets do NOT have a normal distribution (as discussed above), and will have varying degrees of skew and kurtosis
Q: Why are we still favoring the Standardization method over the Normalization method, and how are we accounting for the innate skew and/or kurtosis inherent in most financial markets?
A: Well, since we're only trying to rescale oscillators that by-definition have a midpoint of 0, kurtosis isn't a major concern beyond the affect it has on the post-transformation scaling (specifically, the number of standard deviations from the mean we need to include in our "artificially-bound" range definition).
Q: So that answers the question about kurtosis, but what about skew?
A: So - for skew, the answer is in the formula - specifically the mean (average) element. The standard mean calculation assumes a complete dataset and therefore uses a standard (i.e. simple) average, but we're limited by the data history available to us. So we adapted the transformation formula to leverage a moving average that included a weighting element to it so that it favored recent datapoints more heavily than older ones. By making the average component more adaptive, we gained the effect of reducing the skew element by having the average itself be more responsive to recent movements, which significantly reduces the effect historical outliers have on the dataset as a whole. While this is certainly not a perfect solution, we've found that it serves the purpose of rescaling the MACD and AO to a far more well-defined range while still preserving the oscillator behavior and mid-line exceptionally well.
The most difficult parts to compensate for are periods where markets have low volatility for an extended period of time - to the point where the oscillators are hovering around the 0/midline (in the case of the AO), or when the oscillator and signal lines converge and remain close to each other (in the case of the MACD). It's during these periods where even our best attempt at ensuring accurate mirrored-behavior when compared to the original can still occasionally lead or lag by a candle.
Note: If this is a make-or-break situation for you or your strategy, then we recommend you do not use any of the included indicators that leverage this kind of bounding technique (the AO and MACD at time of publication) and instead use the Trandingview built-in versions!
We know this is a lot to read and digest, so please take your time and feel free to ask questions - we will do our best to answer! And as always, constructive feedback is always welcome!
Nadaraya-Watson: Rational Quadratic Kernel (Non-Repainting)What is Nadaraya–Watson Regression?
Nadaraya–Watson Regression is a type of Kernel Regression, which is a non-parametric method for estimating the curve of best fit for a dataset. Unlike Linear Regression or Polynomial Regression, Kernel Regression does not assume any underlying distribution of the data. For estimation, it uses a kernel function, which is a weighting function that assigns a weight to each data point based on how close it is to the current point. The computed weights are then used to calculate the weighted average of the data points.
How is this different from using a Moving Average?
A Simple Moving Average is actually a special type of Kernel Regression that uses a Uniform (Retangular) Kernel function. This means that all data points in the specified lookback window are weighted equally. In contrast, the Rational Quadratic Kernel function used in this indicator assigns a higher weight to data points that are closer to the current point. This means that the indicator will react more quickly to changes in the data.
Why use the Rational Quadratic Kernel over the Gaussian Kernel?
The Gaussian Kernel is one of the most commonly used Kernel functions and is used extensively in many Machine Learning algorithms due to its general applicability across a wide variety of datasets. The Rational Quadratic Kernel can be thought of as a Gaussian Kernel on steroids; it is equivalent to adding together many Gaussian Kernels of differing length scales. This allows the user even more freedom to tune the indicator to their specific needs.
The formula for the Rational Quadratic function is:
K(x, x') = (1 + ||x - x'||^2 / (2 * alpha * h^2))^(-alpha)
where x and x' data are points, alpha is a hyperparameter that controls the smoothness (i.e. overall "wiggle") of the curve, and h is the band length of the kernel.
Does this Indicator Repaint?
No, this indicator has been intentionally designed to NOT repaint. This means that once a bar has closed, the indicator will never change the values in its plot. This is useful for backtesting and for trading strategies that require a non-repainting indicator.
Settings:
Bandwidth. This is the number of bars that the indicator will use as a lookback window.
Relative Weighting Parameter. The alpha parameter for the Rational Quadratic Kernel function. This is a hyperparameter that controls the smoothness of the curve. A lower value of alpha will result in a smoother, more stretched-out curve, while a lower value will result in a more wiggly curve with a tighter fit to the data. As this parameter approaches 0, the longer time frames will exert more influence on the estimation, and as it approaches infinity, the curve will become identical to the one produced by the Gaussian Kernel.
Color Smoothing. Toggles the mechanism for coloring the estimation plot between rate of change and cross over modes.
[LeonidasCrypto]EMA with Volatility GlowEMA Volatility Glow - Advanced Moving Average with Dynamic Volatility Visualization
Overview
The EMA Volatility Glow indicator combines dual exponential moving averages with a sophisticated volatility measurement system, enhanced by dynamic visual effects that respond to real-time market conditions.
Technical Components
Volatility Calculation Engine
BB Volatility Curve: Utilizes Bollinger Band width normalized through RSI smoothing
Multi-stage Noise Filtering: 3-layer exponential smoothing algorithm reduces market noise
Rate of Change Analysis: Dual-timeframe RoC calculation (14/11 periods) processed through weighted moving average
Dynamic Normalization: 100-period lookback for relative volatility assessment
Moving Average System
Primary EMA: Default 55-period exponential moving average with volatility-responsive coloring
Secondary EMA: Default 100-period exponential moving average for trend confirmation
Trend Analysis: Real-time bullish/bearish determination based on EMA crossover dynamics
Visual Enhancement Framework
Gradient Band System: Multi-layer volatility bands using Fibonacci ratios (0.236, 0.382, 0.618)
Dynamic Color Mapping: Five-tier color system reflecting volatility intensity levels
Configurable Glow Effects: Customizable transparency and intensity settings
Trend Fill Visualization: Directional bias indication between moving averages
Key Features
Volatility States:
Ultra-Low: Minimal market movement periods
Low: Reduced volatility environments
Medium: Normal market conditions
High: Increased volatility phases
Extreme: Exceptional market stress periods
Customization Options:
Adjustable EMA periods
Configurable glow intensity (1-10 levels)
Variable transparency controls
Toggleable visual components
Customizable gradient band width
Technical Calculations:
ATR-based gradient bands with noise filtering
ChartPrime-inspired multi-layer fill system
Real-time volatility curve computation
Smooth color gradient transitions
Applications
Trend Identification: Dual EMA system for directional bias assessment
Volatility Analysis: Real-time market stress evaluation
Risk Management: Visual volatility cues for position sizing decisions
Market Timing: Enhanced visual feedback for entry/exit consideration
Linear Regression Forecast Tool [Daveatt]Hello traders,
Navigating through the financial markets requires a blend of analysis, insight, and a touch of foresight.
My Linear Regression Forecast Tool is here to add that touch of foresight to your analysis toolkit on TradingView!
Linear Regression is the heart of this tool, a statistical method that explores the relationship between a dependent variable and one (or more) independent variable(s).
In simpler terms, it finds a straight line that best fits a set of data points.
This "line of best fit" then becomes a visual representation of the relationship in the data, providing a basis for making predictions.
Here's what the Linear Regression Forecast Tool brings to your trading table:
Multiple Indicator Choices: Select from various market indicators like Simple Moving Averages, Bollinger Bands, or the Volume Weighted Average Price as the basis for your linear regression analysis.
Customizable Forecast Periods: Define how many periods ahead you want to forecast, adjusting to your analysis needs, whether that's looking 5, 7, or 10 periods into the future.
On-Chart Forecast Points: The tool plots the forecasted points on your chart, providing a straightforward visual representation of potential future values based on past data.
In this script:
1. We first calculate the indicator using the specified period.
2. We then use the ta.linreg function to calculate a linear regression curve fitted to the indicator over the last Period bars.
3. We calculate the slope of the linear regression curve using the last two points on the curve.
We use this slope to extrapolate the linear regression curve to forecast the next X points of the indicator.
4/ Finally, we use the plot function to plot the original indicator and the forecasted points on the chart, using the offset parameter to shift the forecasted points to the right (into the future).
This method assumes that the trend represented by the linear regression curve will continue, which may not always be the case, especially in volatile or changing market conditions.
Examples:
Works with a moving average
Works with a Bollinger band
The code can be adapted to work with any other indicator (imagine RSI, MACD, other Moving Average Type, PSAR, Supertrend, etc...)
Conclusion
The Linear Regression Forecast Tool doesn't promise to tell the future but provides a structured way to visualize possible future price trends based on historical data. I
Remember, no tool can predict market conditions with certainty.
It's always advisable to corroborate findings with other analysis methods and stay updated with market news and events.
Happy trading!
Risk-Adjusted Return OscillatorThe Risk-Adjusted Return Oscillator (RAR) is designed to aid traders in predicting future price action by analysing the risk-adjusted performance of an asset. This oscillator is displayed directly on the price chart, unlike other oscillators.
By considering the risk-return relationship, the indicator helps identify periods of overvaluation or undervaluation, allowing traders to anticipate potential price reversals or trend accelerations.
HOW TO USE
The Risk-Adjusted Return Oscillator analyses the risk-adjusted performance of an asset to detect price reversals and accelerations. Here's how to interpret its signals:
Ranging Market:
Overbought Signal: When the RAR curve reaches the overbought level (upper red line), it suggests a potential reversal signal. It indicates that the asset may be overvalued, and a price correction or trend reversal could occur.
Oversold Signal: When the RAR curve reaches the oversold level (lower red line), it indicates a potential reversal signal. It suggests that the asset may be undervalued, and a price correction or trend reversal could take place.
Trending Market:
Overbought Signal: In a trending market, an overbought signal (RAR curve reaching upper red line) suggests trend acceleration. It indicates that the existing trend is gaining strength, and buying pressure is increasing.
Oversold Signal: In a trending market, an oversold signal (RAR curve reaching lower red line) also signifies trend acceleration. It suggests that the prevailing trend is intensifying, and selling pressure is increasing.
Thus, it's important to consider the market context when interpreting overbought and oversold signals. In ranging markets, these signals act as potential reversal points. However, in trending markets, they indicate trend acceleration, reinforcing the current price direction.
SETTINGS
Period Length: Adjust the number of bars used to calculate returns and standard deviation.
Smoothing: Define the smoothing period for the RAR curve.
Show Overbought/Oversold Signals: Choose whether to display triangular shapes for overbought and oversold conditions.
Complete MA DivisionThis indicator simply divides two moving averages and calculates the slope of the resulting curve to show when an asset's momentum is slowing down. The original idea was in a recent youtube video by Ben Cowen . His indicator didn't show the complete history of the moving average, so I wanted to try a little trick to get the moving averages at the beginning of time even when using a large moving average period. I accomplished this by counting the number off current bars using the cum() function. After the count is hit, the period will be constant.
Changing the curve smoothing will smooth the actual curve. Both moving average periods should be divisible by the curve smoothing.
Changing the slope smoothness will dictate when the slope is starting to slow down. Keep this high to break through the noise.
Start of Red = Good time to sell
Start of Green = Good time to buy
There is a weird issue with the smoothness of the line so just keep your moving averages divisible by the curve smoothing. I couldn't figure that issue out yet.
Yope BTC virus channelThis is a new version of the BTC tops channel, combined with a fitted curve of the function described in Cane Island Crypto's paper "Bitcoin Spreads Like a Virus" by Timothy Peterson (pink curve).
The big question is: Where will BTC price go from here? will it follow either of both curves? Which one?
The blue channel is nothing more than a curve function that seems to "fit well" the historical prive of bitcoin, while the pink curve actually has some pretty solid theory behind it ;)
NOTE: This script only works with the BLX ticker and on the 1W, 3D and 1D time-frames!
Feedback and comments welcome.
Time-Decaying Percentile Oscillator [BackQuant]Time-Decaying Percentile Oscillator
1. Big-picture idea
Traditional percentile or stochastic oscillators treat every bar in the look-back window as equally important. That is fine when markets are slow, but if volatility regime changes quickly yesterday’s print should matter more than last month’s. The Time-Decaying Percentile Oscillator attempts to fix that blind spot by assigning an adjustable weight to every past price before it is ranked. The result is a percentile score that “breathes” with market tempo much faster to flag new extremes yet still smooth enough to ignore random noise.
2. What the script actually does
Build a weight curve
• You pick a look-back length (default 28 bars).
• You decide whether weights fall Linearly , Exponentially , by Power-law or Logarithmically .
• A decay factor (lower = faster fade) shapes how quickly the oldest price loses influence.
• The array is normalised so all weights still sum to 1.
Rank prices by weighted mass
• Every close in the window is paired with its weight.
• The pairs are sorted from low to high.
• The cumulative weight is walked until it equals your chosen percentile level (default 50 = median).
• That price becomes the Time-Decayed Percentile .
Find dispersion with robust statistics
• Instead of a fragile standard deviation the script measures weighted Median-Absolute-Deviation about the new percentile.
• You multiply that deviation by the Deviation Multiplier slider (default 1.0) to get a non-parametric volatility band.
Build an adaptive channel
• Upper band = percentile + (multiplier × deviation)
• Lower band = percentile – (multiplier × deviation)
Normalise into a 0-100 oscillator
• The current close is mapped inside that band:
0 = lower band, 50 = centre, 100 = upper band.
• If the channel squeezes, tiny moves still travel the full scale; if volatility explodes, it automatically widens.
Optional smoothing
• A second-stage moving average (EMA, SMA, DEMA, TEMA, etc.) tames the jitter.
• Length 22 EMA by default—change it to tune reaction speed.
Threshold logic
• Upper Threshold 70 and Lower Threshold 30 separate standard overbought/oversold states.
• Extreme bands 85 and 15 paint background heat when aggressive fade or breakout trades might trigger.
Divergence engine
• Looks back twenty bars.
• Flags Bullish divergence when price makes a lower low but oscillator refuses to confirm (value < 40).
• Flags Bearish divergence when price prints a higher high but oscillator stalls (value > 60).
3. Component walk-through
• Source – Any price series. Close by default, switch to typical price or custom OHLC4 for futures spreads.
• Look-back Period – How many bars to rank. Short = faster, long = slower.
• Base Percentile Level – 50 shows relative position around the median; set to 25 / 75 for quartile tracking or 90 / 10 for extreme tails.
• Deviation Multiplier – Higher values widen the dynamic channel, lowering whipsaw but delaying signals.
• Decay Settings
– Type decides the curve shape. Exponential (default 1.16) mimics EMA logic.
– Factor < 1 shrinks influence faster; > 1 spreads influence flatter.
– Toggle Enable Time Decay off to compare with classic equal-weight stochastic.
• Smoothing Block – Choose one of seven MA flavours plus length.
• Thresholds – Overbought / Oversold / Extreme levels. Push them out when working on very mean-reverting assets like FX; pull them in for trend monsters like crypto.
• Display toggles – Show or hide threshold lines, extreme filler zones, bar colouring, divergence labels.
• Colours – Bullish green, bearish red, neutral grey. Every gradient step is automatically blended to generate a heat map across the 0-100 range.
4. How to read the chart
• Oscillator creeping above 70 = market auctioning near the top of its adaptive range.
• Fast poke above 85 with no follow-through = exhaustion fade candidate.
• Slow grind that lives above 70 for many bars = valid bullish trend, not a fade.
• Cross back through 50 shows balance has shifted; treat it like a micro trend change.
• Divergence arrows add extra confidence when you already see two-bar reversal candles at range extremes.
• Background shading (semi-transparent red / green) warns of extreme states and throttles your position size.
5. Practical trading playbook
Mean-reversion scalps
1. Wait for oscillator to reach your desired OB/ OS levels
2. Check the slope of the smoothing MA—if it is flattening the squeeze is mature.
3. Look for a one- or two-bar reversal pattern.
4. Enter against the move; first target = midline 50, second target = opposite threshold.
5. Stop loss just beyond the extreme band.
Trend continuation pullbacks
1. Identify a clean directional trend on the price chart.
2. During the trend, TDP will oscillate between midline and extreme of that side.
3. Buy dips when oscillator hits OS levels, and the same for OB levels & shorting
4. Exit when oscillator re-tags the same-side extreme or prints divergence.
Volatility regime filter
• Use the Enable Time Decay switch as a regime test.
• If equal-weight oscillator and decayed oscillator diverge widely, market is entering a new volatility regime—tighten stops and trade smaller.
Divergence confirmation for other indicators
• Pair TDP divergence arrows with MACD histogram or RSI to filter false positives.
• The weighted nature means TDP often spots divergence a bar or two earlier than standard RSI.
Swing breakout strategy
1. During consolidation, band width compresses and oscillator oscillates around 50.
2. Watch for sudden expansion where oscillator blasts through extreme bands and stays pinned.
3. Enter with momentum in breakout direction; trail stop behind upper or lower band as it re-expands.
6. Customising decay mathematics
Linear – Each older bar loses the same fixed amount of influence. Intuitive and stable; good for slow swing charts.
Exponential – Influence halves every “decay factor” steps. Mirrors EMA thinking and is fastest to react.
Power-law – Mid-history bars keep more authority than exponential but oldest data still fades. Handy for commodities where seasonality matters.
Logarithmic – The gentlest curve; weight drops sharply at first then levels off. Mimics how traders remember dramatic moves for weeks but forget ordinary noise quickly.
Turn decay off to verify the tool’s added value; most users never switch back.
7. Alert catalogue
• TD Overbought / TD Oversold – Cross of regular thresholds.
• TD Extreme OB / OS – Breach of danger zones.
• TD Bullish / Bearish Divergence – High-probability reversal watch.
• TD Midline Cross – Momentum shift that often precedes a window where trend-following systems perform.
8. Visual hygiene tips
• If you already plot price on a dark background pick Bullish Color and Bearish Color default; change to pastel tones for light themes.
• Hide threshold lines after you memorise the zones to declutter scalping layouts.
• Overlay mode set to false so the oscillator lives in its own panel; keep height about 30 % of screen for best resolution.
9. Final notes
Time-Decaying Percentile Oscillator marries robust statistical ranking, adaptive dispersion and decay-aware weighting into a simple oscillator. It respects both recent order-flow shocks and historical context, offers granular control over responsiveness and ships with divergence and alert plumbing out of the box. Bolt it onto your price action framework, trend-following system or volatility mean-reversion playbook and see how much sooner it recognises genuine extremes compared to legacy oscillators.
Backtest thoroughly, experiment with decay curves on each asset class and remember: in trading, timing beats timidity but patience beats impulse. May this tool help you find that edge.
Fibonacci Sequence Moving Average [BackQuant]Fibonacci Sequence Moving Average with Adaptive Oscillator
1. Overview
The Fibonacci Sequence Moving Average indicator is a two‑part trading framework that combines a custom moving average built from the famous Fibonacci number set with a fully featured oscillator, normalisation engine and divergence suite. The moving average half delivers an adaptive trend line that respects natural market rhythms, while the oscillator half translates that trend information into a bounded momentum stream that is easy to read, easy to compare across assets and rich in confluence signals. Everything from weighting logic to colour palettes can be customised, so the tool comfortably fits scalpers zooming into one‑minute candles as well as position traders running multi‑month trend following campaigns.
2. Core Calculation
Fibonacci periods – The default length array is 5, 8, 13, 21, 34. A single multiplier input lets you scale the whole family up or down without breaking the golden‑ratio spacing. For example a multiplier of 3 yields 15, 24, 39, 63, 102.
Component averages – Each period is passed through Simple Moving Average logic to produce five baseline curves (ma1 through ma5).
Weighting methods – You decide how those five values are blended:
• Equal weighting treats every curve the same.
• Linear weighting applies factors 1‑to‑5 so the slowest curve counts five times as much as the fastest.
• Exponential weighting doubles each step for a fast‑reacting yet still smooth line.
• Fibonacci weighting multiplies each curve by its own period value, honouring the spirit of ratio mathematics.
Smoothing engine – The blended average is then smoothed a second time with your choice of SMA, EMA, DEMA, TEMA, RMA, WMA or HMA. A short smoothing length keeps the result lively, while longer lengths create institution‑grade glide paths that act like dynamic support and resistance.
3. Oscillator Construction
Once the smoothed Fib MA is in place, the script generates a raw oscillator value in one of three flavours:
• Distance – Percentage distance between price and the average. Great for mean‑reversion.
• Momentum – Percentage change of the average itself. Ideal for trend acceleration studies.
• Relative – Distance divided by Average True Range for volatility‑aware scaling.
That raw series is pushed through a look‑back normaliser that rescales every reading into a fixed −100 to +100 window. The normalisation window defaults to 100 bars but can be tightened for fast markets or expanded to capture long regimes.
4. Visual Layer
The oscillator line is gradient‑coloured from deep red through sky blue into bright green, so you can spot subtle momentum shifts with peripheral vision alone. There are four horizontal guide lines: Extreme Bear at −50, Bear Threshold at −20, Bull Threshold at +20 and Extreme Bull at +50. Soft fills above and below the thresholds reinforce the zones without cluttering the chart.
The smoothed Fib MA can be plotted directly on price for immediate trend context, and each of the five component averages can be revealed for educational or research purposes. Optional bar‑painting mirrors oscillator polarity, tinting candles green when momentum is bullish and red when momentum is bearish.
5. Divergence Detection
The script automatically looks for four classes of divergences between price pivots and oscillator pivots:
Regular Bullish, signalling a possible bottom when price prints a lower low but the oscillator prints a higher low.
Hidden Bullish, often a trend‑continuation cue when price makes a higher low while the oscillator slips to a lower low.
Regular Bearish, marking potential tops when price carves a higher high yet the oscillator steps down.
Hidden Bearish, hinting at ongoing downside when price posts a lower high while the oscillator pushes to a higher high.
Each event is tagged with an ℝ or ℍ label at the oscillator pivot, colour‑coded for clarity. Look‑back distances for left and right pivots are fully adjustable so you can fine‑tune sensitivity.
6. Alerts
Five ready‑to‑use alert conditions are included:
• Bullish when the oscillator crosses above +20.
• Bearish when it crosses below −20.
• Extreme Bullish when it pops above +50.
• Extreme Bearish when it dives below −50.
• Zero Cross for momentum inflection.
Attach any of these to TradingView notifications and stay updated without staring at charts.
7. Practical Applications
Swing trading trend filter – Plot the smoothed Fib MA on daily candles and only trade in its direction. Enter on oscillator retracements to the 0 line.
Intraday reversal scouting – On short‑term charts let Distance mode highlight overshoots beyond ±40, then fade those moves back to mean.
Volatility breakout timing – Use Relative mode during earnings season or crypto news cycles to spot momentum surges that adjust for changing ATR.
Divergence confirmation – Layer the oscillator beneath price structure to validate double bottoms, double tops and head‑and‑shoulders patterns.
8. Input Summary
• Source, Fibonacci multiplier, weighting method, smoothing length and type
• Oscillator calculation mode and normalisation look‑back
• Divergence look‑back settings and signal length
• Show or hide options for every visual element
• Full colour and line width customisation
9. Best Practices
Avoid using tiny multipliers on illiquid assets where the shortest Fibonacci window may drop under three bars. In strong trends reduce divergence sensitivity or you may see false counter‑trend flags. For portfolio scanning set oscillator to Momentum mode, hide thresholds and colour bars only, which turns the indicator into a heat‑map that quickly highlights leaders and laggards.
10. Final Notes
The Fibonacci Sequence Moving Average indicator seeks to fuse the mathematical elegance of the golden ratio with modern signal‑processing techniques. It is not a standalone trading system, rather a multi‑purpose information layer that shines when combined with market structure, volume analysis and disciplined risk management. Always test parameters on historical data, be mindful of slippage and remember that past performance is never a guarantee of future results. Trade wisely and enjoy the harmony of Fibonacci mathematics in your technical toolkit.
Gaussian Price Filter [BackQuant]Gaussian Price Filter
Overview and History of the Gaussian Transformation
The Gaussian transformation, often associated with the Gaussian (normal) distribution, is a mathematical function characteristically prominent in statistics and probability theory. The bell-shaped curve of the Gaussian function, expressing the normal distribution, is ubiquitously employed in various scientific and engineering disciplines, including financial market analysis. This transformation's core utility in trading and economic forecasting is derived from its efficacy in smoothing data series and highlighting underlying trends, which are pivotal for making strategic trading decisions.
The Gaussian filter, specifically, is a type of data-smoothing algorithm that mitigates the random "noise" of market price data, thus enhancing the visibility of crucial trend changes and patterns. Historically, this concept was adapted from fields such as signal processing and image editing, where precise extraction of useful information from noisy environments is critical.
1. What is a Gaussian Transformation?
A Gaussian transformation involves the application of a Gaussian function to a set of data points. The function is applied as a filter in the context of trading algorithms to smooth time series data, which helps in identifying the intrinsic trends obscured by market volatility. The transformation is characterized by its parameter, sigma (σ), representing the standard deviation, which determines the width of the Gaussian bell curve. The breadth of this curve impacts the degree of smoothing: a wider curve (higher sigma value) results in more smoothing, beneficial for longer-term trend analysis.
2. Filtering Price with Gaussian Transformation and its Benefits
In the provided Script, the Gaussian transformation is utilized to filter price data. The filtering process involves convolving the price data with Gaussian weights, which are calculated based on the chosen length (the number of data points considered) and sigma. This convolution process smooths out short-term fluctuations and highlights longer-term movements, facilitating a clearer analysis of market trends.
Benefits:
Reduces noise: It filters out minor price movements and random fluctuations, which are often misleading.
Enhances trend recognition: By smoothing the data, it becomes easier to identify significant trends and reversals.
Improves decision-making: Traders can make more informed decisions by focusing on substantive, smoothed data rather than reacting to random noise.
3. Potential Limitations and Issues
While Gaussian filters are highly effective in smoothing data, they are not without limitations:
Lag introduction: Like all moving averages, the Gaussian filter introduces a lag between the actual price movements and the output signal, which can delay decision-making.
Feature blurring: Over-smoothing might obscure significant price movements, especially if a large sigma is used.
Parameter sensitivity: The choice of length and sigma significantly affects the output, requiring optimization and backtesting to determine the best settings for specific market conditions.
4. Extending Gaussian Filters to Other Indicators
The methodology used to filter price data with a Gaussian filter can similarly be applied to other technical indicators, such as RSI (Relative Strength Index) or MACD (Moving Average Convergence Divergence). By smoothing these indicators, traders can reduce false signals and enhance the reliability of the indicators' outputs, leading to potentially more accurate signals and better timing for entering or exiting trades.
5. Application in Trading
In trading, the Gaussian Price Filter can be strategically used to:
Spot trend reversals: Smoothed price data can more clearly indicate when a trend is starting to change, which is crucial for catching reversals early.
Define entry and exit points: The filtered data points can help in setting more precise entry and exit thresholds, minimizing the risk and maximizing the potential return.
Filter other data streams: Apply the Gaussian filter on volume or open interest data to identify significant changes in market dynamics.
6. Functionality of the Script
The script is designed to:
Calculate Gaussian weights (f_gaussianWeights function): Generates the weights used for the Gaussian kernel based on the provided length and sigma.
Apply the Gaussian filter (f_applyGaussianFilter function): Uses the weights to compute the smoothed price data.
Conditional Trend Detection and Coloring: Determines the trend direction based on the filtered price and colors the price bars on the chart to visually represent the trend.
7. Specific Actions of This Code
The Pine Script provided by BackQuant executes several specific actions:
Input Handling: It allows users to specify the source data (src), kernel length, and sigma directly in the chart settings.
Weight Calculation and Normalization: Computes the Gaussian weights and normalizes them to ensure their sum equals one, which maintains the original data scale.
Filter Application: Applies the normalized Gaussian kernel to the price data to produce a smoothed output.
Trend Identification and Visualization: Identifies whether the market is trending upwards or downwards based on the smoothed data and colors the bars green (up) or red (down) to indicate the trend direction.
