Volatility Gaussian Bands [BigBeluga]The Volatility Gaussian Bands indicator is a cutting-edge tool designed to analyze market trends and volatility with high precision. By applying a Gaussian filter to smooth price data and implementing dynamic bands based on market volatility, this indicator provides clear signals for trend direction, strength, and potential reversals. With updated volatility calculations, it enhances the accuracy of trend detection, making it a powerful addition to any trader's toolkit.
⮁ KEY FEATURES & USAGE
● Gaussian Filter Trend Bands:
The Gaussian Filter forms the foundation of this indicator by smoothing price data to reveal the underlying trend. The trend is visualized through upper and lower bands that adjust dynamically based on market volatility. These bands provide clear visual cues for traders: a crossover above the upper band indicates a potential uptrend, while a cross below the lower band signals a potential downtrend. This feature allows traders to identify trends with greater accuracy and act accordingly.
● Dynamic Trend Strength Gauges:
The indicator includes trend strength gauges positioned at the top and bottom of the chart. These gauges dynamically measure the strength of the uptrend and downtrend, based on the middle Gaussian line. Even if the trend is downward, a rising midline will cause the upward trend strength gauge to show an increase, offering a nuanced view of the market’s momentum.
Weakening of the trend:
● Fast Trend Change Indicators:
Triangles with a "+" symbol appear on the chart to signal rapid changes in trend direction. These indicators are particularly useful when the trend changes swiftly while the midline continues to grow in its previous direction. For instance, during a downtrend, if the trend suddenly shifts upward while the midline is still declining, a triangle with a "+" will indicate this quick reversal. This feature is crucial for traders looking to capitalize on rapid market movements.
● Retest Signals:
Retest signals, displayed as triangles, highlight potential areas where the price may retest the Gaussian line during a trend. These signals provide an additional layer of analysis, helping traders confirm trend continuations or identify possible reversals. The retest signals can be customized based on the trader’s preferences.
⮁ CUSTOMIZATION
● Length Adjustment:
The length of the Gaussian filter can be customized to control the sensitivity of trend detection. Shorter lengths make the indicator more responsive, while longer lengths offer a smoother, more stable trend line.
● Volatility Calculation Mode:
Traders can select from different modes (AVG, MEDIAN, MODE) to calculate the Gaussian filter, allowing for flexibility in how trends are detected and analyzed.
● Retest Signals Toggle:
Enable or disable the retest signals based on your trading strategy. This toggle allows traders to choose whether they want these additional signals to appear on the chart, providing more control over the information displayed during their analysis.
⮁ CONCLUSION
The Volatility Gaussian Bands indicator is a versatile and powerful tool for traders focused on trend and volatility analysis. By combining Gaussian-filtered trend lines with dynamic volatility bands, trend strength gauges, and rapid trend change indicators, this tool provides a comprehensive view of market conditions. Whether you are following established trends or looking to catch early reversals, the Volatility Gaussian Bands offers the precision and adaptability needed to enhance your trading strategy.

# Gaussian

Gaussian Filter [BigBeluga]The Gaussian Filter - BigBeluga indicator is a trend-following tool that uses a Gaussian filter to smooth price data and identify directional shifts in the market. It provides dynamic signals for entering and exiting trades based on trend changes, helping traders stay aligned with the market's momentum. What sets this indicator apart is its ability to display precise entry and exit points with real-time tracking of percentage price changes, making it ideal for trend-based strategies.
SP500:
NIFTY50:
🔵 KEY FEATURES & USAGE
◉ Gaussian Filter Trend Line:
//@function GaussianFilter is used for smoothing, reducing noise, and computing derivatives of data.
//@param src (float) The source data (e.g., close price) to be smoothed.
//@param params (GaussianFilterParams) Gaussian filter parameters that include length and sigma.
//@returns (float) The smoothed value from the Gaussian filter.
gaussian_filter(float src, params) =>
var float weights = array.new_float(params.length) // Array to store Gaussian weights
total = 0.0
pi = math.pi
for i = 0 to params.length - 1
weight = math.exp(-0.5 * math.pow((i - params.length / 2) / params.sigma, 2.0))
/ math.sqrt(params.sigma * 2.0 * pi)
weights.set(i, weight)
total := total + weight
for i = 0 to params.length - 1
weights.set(i, weights.get(i) / total)
sum = 0.0
for i = 0 to params.length - 1
sum := sum + src * weights.get(i)
sum
The core functionality of the Gaussian Filter line is to show trend direction. When the trend line increases four times consecutively, it indicates an uptrend signal. Similarly, if it decreases four times in a row, it signals a downtrend. The smoothness of the filter helps traders stay on the right side of the market by filtering out noise and emphasizing the dominant trend direction.
◉ Entry and Exit Levels with Real-Time Price and Performance Data:
Each time the indicator detects a trend change, it plots an entry or exit level on the chart. For an uptrend, an entry level is marked, and for a downtrend, an exit level is plotted. These levels display the price at the time of the signal.
While the trend is ongoing, the indicator tracks the percentage change in price from the initial entry or exit signal to the current bar, updating in real-time. When a trend concludes, it displays the total percentage change from the entry or exit point to the trend's end. This feature provides valuable insights into how much the price has moved during each trend phase and allows traders to monitor the performance of each trade.
◉ Color-Coded Candlestick Representation with Trend Shift Alerts:
In addition to coloring the candlesticks based on the trend direction, the indicator also uses gray candles to highlight potential early trend shifts. For example, if the Gaussian Filter detects a downtrend but the price moves above the filter line, the candles turn gray, signaling a possible reversal or shift in momentum. Similarly, in an uptrend, if the price moves below the Gaussian Filter line, the candles turn gray as an early indication of potential bearish momentum. This visual cue helps traders stay alert to possible faster shifts in market direction, allowing for quicker decision-making.
🔵 CUSTOMIZATION
Length and Sigma for Gaussian Filter:
Adjust the length and sigma parameters to control how the Gaussian Filter smooths the price data. A longer length provides smoother trend lines, while adjusting sigma can fine-tune the level of smoothing applied.
Levels Display and Candle Coloring:
You can toggle the visibility of entry and exit levels as well as enable or disable the dynamic coloring of candlesticks based on the trend direction. The additional gray color setting provides an extra layer of information, allowing you to spot potential trend reversals early.
🔵 CONCLUSION
The Gaussian Filter indicator is a powerful tool for identifying and following market trends. By providing clear entry and exit signals, along with real-time tracking of price changes, it gives traders a structured way to manage trades and monitor performance. The color-coded candles, including gray to highlight possible trend shifts, add another dimension to visualizing market dynamics. The added flexibility of customizing colors and trend levels makes it a versatile indicator suitable for both trend-following and reversal strategies.

Gaussian Kernel Smoothing EMAGaussian Kernel Smoothing EMA
The Gaussian Kernel Smoothing EMA integrates the exponential moving average with kernel smoothing techniques to refine the trend tool. Kernel smoothing is a non-parametric technique used to estimate a smooth curve from a set of data points. It is particularly useful in reducing noise and capturing the underlying structure of data. The smoothed value at each point is calculated as a weighted average of neighboring points, with the weights determined by a kernel function.
The Gaussian kernel is a popular choice in kernel smoothing due to its properties of being smooth, symmetric, and having infinite support. This function gives higher weights to data points closer to the target point and lower weights to those further away, resulting in a smooth and continuous estimate. Since price isn't normally distributed a logarithmic transformation is performed to remove most of its skewness to be able to fit the Gaussian kernel.
This indicator also has a bandwidth, which in kernel smoothing controls the width of the window over which the smoothing is performed. It determines how much influence nearby data points have on the smoothed value. In this indicator, the bandwidth is dynamically adjusted based on the standard deviation of the log-transformed prices so that the smoothing adapts to the underlying variability and potential volatility.
Bandwidth Factor: The bandwidth factor in this indicator is used to adjust the degree of the smoothing applied to the MA. In kernel smoothing, Bandwidth controls the width of the window over which the smoothing is applied. It determines how many data points around a central point are considered when calculating a smooth value. A smaller bandwidth results in less smoothing, while a larger bandwidth smooths out more noise, leading to a broader, more general trend.

LOWESS (Locally Weighted Scatterplot Smoothing) [ChartPrime]LOWESS (Locally Weighted Scatterplot Smoothing)
⯁ OVERVIEW
The LOWESS (Locally Weighted Scatterplot Smoothing) [ ChartPrime ] indicator is an advanced technical analysis tool that combines LOWESS smoothing with a Modified Adaptive Gaussian Moving Average. This indicator provides traders with a sophisticated method for trend analysis, pivot point identification, and breakout detection.
◆ KEY FEATURES
LOWESS Smoothing: Implements Locally Weighted Scatterplot Smoothing for trend analysis.
Modified Adaptive Gaussian Moving Average: Incorporates a volatility-adapted Gaussian MA for enhanced trend detection.
Pivot Point Identification: Detects and visualizes significant pivot highs and lows.
Breakout Detection: Tracks and optionally displays the count of consecutive breakouts.
Gaussian Scatterplot: Offers a unique visualization of price movements using randomly colored points.
Customizable Parameters: Allows users to adjust calculation length, pivot detection, and visualization options.
◆ FUNCTIONALITY DETAILS
⬥ LOWESS Calculation:
Utilizes a weighted local regression to smooth price data.
Adapts to local trends, reducing noise while preserving important price movements.
⬥ Modified Adaptive Gaussian Moving Average:
Combines Gaussian weighting with volatility adaptation using ATR and standard deviation.
Smooths the Gaussian MA using LOWESS for enhanced trend visualization.
⬥ Pivot Point Detection and Visualization:
Identifies pivot highs and lows using customizable left and right bar counts.
Draws lines and labels to mark broke pivot points on the chart.
⬥ Breakout Tracking:
Monitors price crossovers of pivot lines to detect breakouts.
Optionally displays and updates the count of consecutive breakouts.
◆ USAGE
Trend Analysis: Use the color and direction of the smoothed Gaussian MA line to identify overall trend direction.
Breakout Trading: Monitor breakouts from pivot levels and their persistence using the breakout count feature.
Volatility Assessment: The spread of the Gaussian scatterplot can provide insights into market volatility.
⯁ USER INPUTS
Length: Sets the lookback period for LOWESS and Gaussian MA calculations (default: 30).
Pivot Length: Determines the number of bars to the left for pivot calculation (default: 5).
Count Breaks: Toggle to show the count of consecutive breakouts (default: false).
Gaussian Scatterplot: Toggle to display the Gaussian MA as a scatterplot (default: true).
⯁ TECHNICAL NOTES
Implements a custom LOWESS function for efficient local regression smoothing.
Uses a modified Gaussian MA calculation that adapts to market volatility.
Employs Pine Script's line and label drawing capabilities for clear pivot point visualization.
Utilizes random color generation for the Gaussian scatterplot to enhance visual distinction between different time periods.
The LOWESS (Locally Weighted Scatterplot Smoothing) indicator offers traders a sophisticated tool for trend analysis and breakout detection. By combining advanced smoothing techniques with pivot point analysis, it provides a comprehensive view of market dynamics. The indicator's adaptability to different market conditions and its customizable nature make it suitable for various trading styles and timeframes.

Normalised Gaussian MACD Heikin Ashi [AlgoAlpha]🌟🚀Introducing the Normalised Gaussian MACD Heikin Ashi by AlgoAlpha !
Elevate your trading game with this multipurpose indicator, crafted to pinpoint trend continuation opportunities while highlighting volatility and oversold/overbought conditions. Whether you're embarking on your trading journey or you're a seasoned market navigator, this tool is equipped with intuitive visual cues to amplify your decision-making prowess and enrich your market analysis toolkit. Let's dive into the key features, utilization strategies, and the innovative logic underpinning this indispensable trading asset.
Key Features:
🔧 Enhanced Customization : Tailor your experience with adjustable parameters including Fast Length, Slow Length, Source, Macd Smoothing Length, Signal Smoothing, and more.
🖌️ Visual Enhancements : Opt for Heikin Ashi Candles display and choose to show or hide MACD and Signal lines for a clutter-free chart.
🌈 Color Customization : Personalize your chart with selectable primary and secondary up and down colors to suit your visual preferences.
🔔 Advanced Alert System : Stay ahead with comprehensive alert conditions for market movements, including trend reversals, bullish and bearish swings.
How to Use:
Configure the Inputs : Start by customizing the indicator’s settings to match your trading style. Adjust the length parameters, source selection, and smoothing lengths to fine-tune the indicator’s sensitivity.
Interpret the Candles and Colors : Keep an eye on the Heikin Ashi Candles (if enabled) and the color shifts within the MACD Line Candles and Histogram. These visual cues are pivotal for identifying market trends.
Analyze with Flexibility : Make use of the option to display or hide the MACD and Signal lines based on your analysis requirements. This can help in focusing on the essential information without overcrowding your chart.
Utilize Alerts for Timely Decisions : Leverage the extensive alert system to get notified about potential market movements. These alerts can help you capture the right moment to enter or exit trades.
Basic Logic:
The Normalised Gaussian MACD Heikin Ashi by AlgoAlpha integrates Gaussian filters to elevate the traditional MACD indicator's efficiency, providing a more detailed analysis of market trends and momentum. This sophisticated approach reduces noise and enhances signal speed, which is crucial for identifying momentum trading opportunities.
Gaussian Filter Implementation : The core innovation lies in applying a Gaussian filter to the input price series. This mathematical technique smooths the price data, significantly reducing market noise and making trend signals clearer and more reliable. The Gaussian filter calculates a smoothed value for each data point by weighting nearby data points, with the weights decreasing as the distance from the current data point increases.
Refined MACD Calculation : The Gaussian MACD is derived from the difference between two Gaussian smoothed moving averages (fast and slow), which are then normalized to account for market volatility. This normalization process involves dividing the difference by a measure of market range (such as the high minus the low), and multiplying by a factor (usually 100) to scale the indicator appropriately.
🔑 This script is a versatile tool designed to aid in the identification of momentum and reversals, helping traders to make informed decisions based on technical analysis. Its customization options allow for a tailored analysis experience, fitting the unique needs and strategies of each trader.

RSI in Candlestick MODEDescription:
The "RSI Bar" indicator is a versatile tool designed to enhance your technical analysis on trading charts. This Pine Script™ code calculates the Relative Strength Index (RSI) for open, close, high, and low prices, and represents the results as bars on the chart. The bars are color-coded based on whether the closing RSI is higher or lower than the opening RSI.
Additionally, the indicator incorporates advanced features such as Pareto analysis and Gaussian smoothing. The Pareto analysis helps identify significant lows and highs in the RSI, providing insights into potential trend reversals. The Gaussian smoothing further refines the analysis, contributing to a more accurate representation of the average RSI trend.
Key Features:
RSI calculation for open, close, high, and low prices.
Color-coded bars for easy visualization of RSI trends.
Pareto analysis to highlight key RSI levels indicating potential reversals.
Gaussian smoothing for improved trend analysis and visualization.
Heiken-Ashi

Kernel Regression RibbonKernel Regression Ribbon is a flexible, visually pleasing trend identification tool. Plotting 8 different kernel regressions of different types and parameters allows the user to see where levels of support and resistance are being tested, retested and broken.
What’s Kernel Regression?
A statistical method for estimating the best fitting curve for a dataset, in this case, a time/price chart.
How’s Kernel Regression different from a Moving Average?
A Moving Average is basically a simple form of Kernel Regression, in that it uses a fixed (Retangular) Kernel function. In an MA, all data points are weighted equally over its length. However, a Kernel function reacts more to data points that are closer to the current point. This means it will adapt more quickly to changes in data than an MA. Due to this adaptability, Kernel functions often form part of Machine Learning.
Using this indicator:
Explore the default Regular mode first to get a feel for the inputs, which are more numerous than for MAs. Try out different settings, filters and intervals to get the best out of each kernel. Not all parameters are available for each KR. There are info tips to explain this in the menu, but I’ve also included handy, optional labels on the chart for each KR as a more accessible guide.
Once you know your way round the Regular mode, check out the Presets and start changing the parameters of each kernel to your liking in the “User KR1, KR2, … “ mode. Each kernel type has its strong and weak points. Blending different kernels is where this indicator comes into its own. Give your charts a funky shine!
This indicator does NOT repaint.
This script acknowledges, and hopefully showcases, the great work of @veryfid Kernel Regression Toolkit.

Strategy Gaussian Anomaly DerivativeConcept behind this Strategy :
Considering a normal "buy/sell" situation, an asset would be bought in average at the median price following a Gaussian like concept. A higher or lower average trend would significate that the current perceived value is respectively higher or lower than the current median price, which mean that the buyers are evaluating the price underpriced or overpriced.
This behaviour would be even more relevent depending on its derivative evolution.
Therefore, this Strategy setup is based on this Gaussian like concept anomaly of average close positionning compare to high-low average derivative, such as the derivative of the following ploted basic signal : 1-(high+low)/(2*close).
This Strategy can actually be used like a trend change and continuation strength indicator aswell.
In the Setup Signal part :
You can define the filtering of the basis signal "1-(high+low)/(2*close)" on EMA or SMA as you wish.
You can define the corresponding period and the threathold as a mutiply of the average 1/3 of all time value of the basis signal.
You can define the SMA filtering period of the Derivative signal and the corresponding threathold on the same mutiply of the average 1/3 of all time value of the derivative.
In the Setup Strategy part :
You can set up your strategy assesment based on Long and/or Short. You can also define the considered period.
The most successful tuned strategies I did were based on the derivative indicator with periods on the basis signal and the derivative under 30, can be 1 to 3 of te derivative and 7 to 21 for the basis signal. The threathold depends on the asset volatility aswell, 1 is usually the most efficient but 0 to 10 can be relevent depending on the situation I met. You can find an example of tuning for this strategy based on Kering's case hereafter.
I hoping that you will enjoy using this Strategy, don't hesitate to comment, to question, to correct or complete it ! I would be very curious about similar famous approaches that would have already been made.
Thank to you !

ALMA Smoothed Gaussian Moving AverageThis indicator is an altered version of the Gaussian Moving Average (GMA) (Credit to author: © LeafAlgo ). The GMA applies weights to the prices, giving more importance to the values closer to the current period and gradually diminishing the significance of older prices. The ALMA Smoothed Gaussian Moving Average (ASGMA) applies an ALMA smoothing to its price data to minimize lag and provide a more accurate representation of the underlying trend by dynamically adapting to changing market conditions. The Arnaud Legoux Moving Average (ALMA) is a specialized smoothing technique that adjusts the weights of the moving average based on market volatility. Its calculation uses Wavelet Transform techniques which enables this type of smoothing to capture both high-frequency and low-frequency components of a signal or data. The rationale for this mashup between ALMA and Gaussian filtering is to smooth the moving average line over the smoothed price data and produce stronger trend signals.
ASGMA serves as a trend-following indicator, identifying both bullish and bearish trends. It provides buy and sell signals indicated by "B" and "S" labels plotted alongside the price data. Additionally, the ASGMA's Exponential Moving Average (EMA) line alternates between green and red, indicating bullish and bearish momentum, respectively.
The ASGMA also incorporates two popular momentum indicators, the Relative Strength Index (RSI) and the Chande Momentum Oscillator (CMO). The inclusion of these indicators aims to enhance trend identification and reversal signals. For a strong buy signal, all three indicators (RSI, CMO, and ASGMA) must indicate bullish conditions, resulting in a vertical green line. Conversely, a vertical red line is plotted when all indicators indicate bearish conditions, representing a strong sell signal.
The ASGMA, with its unique combination of smoothing techniques and indicator amalgamation, provides traders and investors with powerful analytical tools. It can be applied in trend-following strategies using the regular buy and sell signals generated by labels and the EMA line. Alternatively, the vertical lines offer stronger buy and sell signals. These features aid in identifying potential entry and exit points, thereby enhancing trading decisions and market analysis. However, it is important to remember that the future performance of any trading strategy is fundamentally unknowable, and past results do not guarantee future performance.

Adaptive Gaussian Moving AverageThe Adaptive Gaussian Moving Average (AGMA) is a versatile technical indicator that combines the concept of a Gaussian Moving Average (GMA) with adaptive parameters based on market volatility. The indicator aims to provide a smoothed trend line that dynamically adjusts to different market conditions, offering a more responsive analysis of price movements.
Calculation:
The AGMA is calculated by applying a weighted moving average based on a Gaussian distribution. The length parameter determines the number of bars considered for the calculation. The adaptive parameter enables or disables the adaptive feature. When adaptive is true, the sigma value, which represents the standard deviation, is dynamically calculated using the standard deviation of the closing prices over the volatilityPeriod. When adaptive is false, a user-defined fixed value for sigma can be input.
Interpretation:
The AGMA generates a smoothed line that follows the trend of the price action. When the AGMA line is rising, it suggests an uptrend, while a declining line indicates a downtrend. The adaptive feature allows the indicator to adjust its sensitivity based on market volatility, making it more responsive during periods of high volatility and less sensitive during low volatility conditions.
Potential Uses in Strategies:
-- Trend Identification : Traders can use the AGMA to identify the direction of the prevailing trend. Buying opportunities may arise when the price is above the AGMA line during an uptrend, while selling opportunities may be considered when the price is below the AGMA line during a downtrend.
-- Trend Confirmation : The AGMA can be used in conjunction with other technical indicators or trend-following strategies to confirm the strength and sustainability of a trend. A strong and steady AGMA line can provide additional confidence in the prevailing trend.
-- Volatility-Based Strategies : Traders can utilize the adaptive feature of the AGMA to build volatility-based strategies. By adjusting the sigma value based on market volatility, the indicator can dynamically adapt to changing market conditions, potentially improving the accuracy of entry and exit signals.
Limitations:
-- Lagging Indicator : Like other moving averages, the AGMA is a lagging indicator that relies on historical price data. It may not provide timely signals during rapidly changing market conditions or sharp price reversals.
-- Whipsaw in Sideways Markets : During periods of low volatility or when the market is moving sideways, the AGMA may generate false signals or exhibit frequent crossovers around the price, leading to whipsaw trades.
-- Subjectivity of Parameters : The choice of length, adaptive parameters, and volatility period requires careful consideration and customization based on individual preferences and trading strategies. Traders need to adjust these parameters to suit the specific market and timeframe they are trading.
Overall, the Adaptive Gaussian Moving Average can be a valuable tool in trend identification and confirmation, especially when combined with other technical analysis techniques. However, traders should exercise caution, conduct thorough analysis, and consider the indicator's limitations when incorporating it into their trading strategies.

Adaptive Weighted Moving Average (AWMA)The script is a technical analysis indicator that calculates a weighted moving average of a given data series. The weighted moving average is calculated using a custom weighting scheme that adjusts the weights based on the volatility of the market, as measured by the average true range (ATR) indicator. The resulting weighted moving average is smoothed using a Gaussian moving average, and the resulting smoothed moving average is plotted on the chart.
To use this script, the user can customize several input parameters, including the length of the moving average, the primary and secondary weights to use in the custom weighting scheme, the ATR length, and the smoothing parameter for the Gaussian moving average. With these inputs, the script calculates and plots the weighted moving average on the chart, allowing the user to analyze the trend and behavior of the data series using a custom weighted moving average.

MTF MA Ribbon and Bands + BB, Gaussian F. and R. VWAP with StDev█ Multi Timeframe Moving Average Ribbon and Bands + Bollinger Bands, Gaussian Filter and Rolling Volume Weighted Average Price with Standard Deviation Bands
Up to 9 moving averages can be independently applied.
The length , type and timeframe of each moving average are configurable .
The lines, colors and background fill are customizable too.
This script can also display:
Moving Average Bands
Bollinger Bands
Gaussian Filter
Rolling VWAP and Standard Deviation Bands
Types of Moving Averages:
Simple Moving Average (SMA)
Exponential Moving Average (EMA)
Smoothed Moving Average (SMMA)
Weighted Moving Average (WMA)
Volume Weighted Moving Average (VWMA)
Least Squares Moving Average (LSMA)
Hull Moving Average (HMA)
Arnaud Legoux Moving Average (ALMA)
█ Moving Average
Moving Averages are price based, lagging (or reactive) indicators that display the average price of a security over a set period of time.
A Moving Average is a good way to gauge momentum as well as to confirm trends, and define areas of support and resistance.
█ Bollinger Bands
Bollinger Bands consist of a band of three lines which are plotted in relation to security prices.
The line in the middle is usually a Simple Moving Average (SMA) set to a period of 20 days (the type of trend line and period can be changed by the trader, a 20 day moving average is by far the most popular).
The SMA then serves as a base for the Upper and Lower Bands which are used as a way to measure volatility by observing the relationship between the Bands and price.
█ Gaussian Filter
Gaussian filter can be used for smoothing.
It rejects high frequencies (fast movements) better than an EMA and has lower lag.
A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve.
In the case of low-pass filters, only the upper half of the curve describes the filter.
The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components.
█ Rolling VWAP
The typical VWAP is designed to be used on intraday charts, as it resets at the beginning of the day.
Such VWAPs cannot be used on daily, weekly or monthly charts. Instead, this rolling VWAP uses a time period that automatically adjusts to the chart's timeframe.
You can thus use the rolling VWAP on any chart that includes volume information in its data feed.
Because the rolling VWAP uses a moving window, it does not exhibit the jumpiness of VWAP plots that reset.
Made with the help from scripts of: adam24x, VishvaP, loxx and pmk07.

Nadaraya-Watson CombineThis is a combination of the Lux Algo Nadaraya-Watson Estimator and Envelope. Please note the repainting issue.
In addition, I've added a plot of the actual values of the current barstate of
the Nadaraya-Watson windows as they are computed (lines 92-95). It only plots values for the current data at
each time update. It is interesting to compare the trajectory of the end points of the Estimator and
Envelope to the smoothing function at each time update. Due to the kernel smoothing at each update the
history is lost at each update (repaint).
I've added a feature to allow adjustment to the kernel smoothing algorithm as suggested by thomsonraja (line 59).
The settings and usage are repeated from Lux Algo below.
Settings
Window Size: Determines the number of recent price observations to be used to fit the Nadaraya-Watson Estimator.
Bandwidth: Controls the degree of smoothness of the envelopes , with higher values returning smoother results.
Mult: Controls the envelope width.
Src: Input source of the indicator.
Kernel power: See line 59, adjusts the exponential power (powh) as suggested by thomsonraja
Kernel denominator: See line 59, adjusts the denominator (den) as suggested by thomsonraja
Usage
This tool outlines extremes made by the prices within the selected window size.
This is achieved by estimating the underlying trend in the price using kernel smoothing,
calculating the mean absolute deviations from it, and adding/subtracting it
from the estimated underlying trend.
I repeat Lux Algo's caution: 'we do not recommend this tool to be used alone
or solely for real time applications.'

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.

Possible RSI [Loxx]Possible RSI is a normalized, variety second-pass normalized, Variety RSI with Dynamic Zones and optionl High-Pass IIR digital filtering of source price input. This indicator includes 7 types of RSI.
High-Pass Fitler (optional)
The Ehlers Highpass Filter is a technical analysis tool developed by John F. Ehlers. Based on aerospace analog filters, this filter aims at reducing noise from price data. Ehlers Highpass Filter eliminates wave components with periods longer than a certain value. This reduces lag and makes the oscialltor zero mean. This turns the RSI output into something more similar to Stochasitc RSI where it repsonds to price very quickly.
First Normalization Pass
RSI (Relative Strength Index) is already normalized. Hence, making a normalized RSI seems like a nonsense... if it was not for the "flattening" property of RSI. RSI tends to be flatter and flatter as we increase the calculating period--to the extent that it becomes unusable for levels trading if we increase calculating periods anywhere over the broadly recommended period 8 for RSI. In order to make that (calculating period) have less impact to significant levels usage of RSI trading style in this version a sort of a "raw stochastic" (min/max) normalization is applied.
Second-Pass Variety Normalization Pass
There are three options to choose from:
1. Gaussian (Fisher Transform), this is the default: The Fisher Transform is a function created by John F. Ehlers that converts prices into a Gaussian normal distribution. The normaliztion helps highlights when prices have moved to an extreme, based on recent prices. This may help in spotting turning points in the price of an asset. It also helps show the trend and isolate the price waves within a trend.
2. Softmax: The softmax function, also known as softargmax: or normalized exponential function, converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and used in multinomial logistic regression. The softmax function is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes, based on Luce's choice axiom.
3. Regular Normalization (devaitions about the mean): Converts a vector of K real numbers into a probability distribution of K possible outcomes without using log sigmoidal transformation as is done with Softmax. This is basically Softmax without the last step.
Dynamic Zones
As explained in "Stocks & Commodities V15:7 (306-310): Dynamic Zones by Leo Zamansky, Ph .D., and David Stendahl"
Most indicators use a fixed zone for buy and sell signals. Here’ s a concept based on zones that are responsive to past levels of the indicator.
One approach to active investing employs the use of oscillators to exploit tradable market trends. This investing style follows a very simple form of logic: Enter the market only when an oscillator has moved far above or below traditional trading lev- els. However, these oscillator- driven systems lack the ability to evolve with the market because they use fixed buy and sell zones. Traders typically use one set of buy and sell zones for a bull market and substantially different zones for a bear market. And therein lies the problem.
Once traders begin introducing their market opinions into trading equations, by changing the zones, they negate the system’s mechanical nature. The objective is to have a system automatically define its own buy and sell zones and thereby profitably trade in any market — bull or bear. Dynamic zones offer a solution to the problem of fixed buy and sell zones for any oscillator-driven system.
An indicator’s extreme levels can be quantified using statistical methods. These extreme levels are calculated for a certain period and serve as the buy and sell zones for a trading system. The repetition of this statistical process for every value of the indicator creates values that become the dynamic zones. The zones are calculated in such a way that the probability of the indicator value rising above, or falling below, the dynamic zones is equal to a given probability input set by the trader.
To better understand dynamic zones, let's first describe them mathematically and then explain their use. The dynamic zones definition:
Find V such that:
For dynamic zone buy: P{X <= V}=P1
For dynamic zone sell: P{X >= V}=P2
where P1 and P2 are the probabilities set by the trader, X is the value of the indicator for the selected period and V represents the value of the dynamic zone.
The probability input P1 and P2 can be adjusted by the trader to encompass as much or as little data as the trader would like. The smaller the probability, the fewer data values above and below the dynamic zones. This translates into a wider range between the buy and sell zones. If a 10% probability is used for P1 and P2, only those data values that make up the top 10% and bottom 10% for an indicator are used in the construction of the zones. Of the values, 80% will fall between the two extreme levels. Because dynamic zone levels are penetrated so infrequently, when this happens, traders know that the market has truly moved into overbought or oversold territory.
Calculating the Dynamic Zones
The algorithm for the dynamic zones is a series of steps. First, decide the value of the lookback period t. Next, decide the value of the probability Pbuy for buy zone and value of the probability Psell for the sell zone.
For i=1, to the last lookback period, build the distribution f(x) of the price during the lookback period i. Then find the value Vi1 such that the probability of the price less than or equal to Vi1 during the lookback period i is equal to Pbuy. Find the value Vi2 such that the probability of the price greater or equal to Vi2 during the lookback period i is equal to Psell. The sequence of Vi1 for all periods gives the buy zone. The sequence of Vi2 for all periods gives the sell zone.
In the algorithm description, we have: Build the distribution f(x) of the price during the lookback period i. The distribution here is empirical namely, how many times a given value of x appeared during the lookback period. The problem is to find such x that the probability of a price being greater or equal to x will be equal to a probability selected by the user. Probability is the area under the distribution curve. The task is to find such value of x that the area under the distribution curve to the right of x will be equal to the probability selected by the user. That x is the dynamic zone.
7 Types of RSI
See here to understand which RSI types are included:
Included:
Bar coloring
4 signal types
Alerts
Loxx's Expanded Source Types
Loxx's Variety RSI
Loxx's Dynamic Zones

Gaussian Filter MACD [Loxx]Gaussian Filter MACD is a MACD that uses an 1-4 Pole Ehlers Gaussian Filter for its calculations. Compare this with Ehlers Fisher Transform.
What is Ehlers Gaussian filter?
This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag. published by John F. Ehlers in "Rocket Science For Traders". First implemented in Wealth-Lab by Dr René Koch.
A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components.
A gaussian filter with...
one pole is equivalent to an EMA filter.
two poles is equivalent to EMA ( EMA ())
three poles is equivalent to EMA ( EMA ( EMA ()))
and so on...
For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters: Lag = N * P / (2 * ¶2), where,
N is the number of poles, and
P is the critical period
Special initialization of filter stages ensures proper working in scans with as few bars as possible.
From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass filtters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life."
References John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters"
Included
Loxx's Expanded Source Types
Signals, zero or signal crossing, signal crossing is very noisy
Alerts
Bar coloring

STD-Filtered, Gaussian Moving Average (GMA) [Loxx]STD-Filtered, Gaussian Moving Average (GMA) is a 1-4 pole Ehlers Gaussian Filter with standard deviation filtering. This indicator should perform similar to Ehlers Fisher Transform.
The purpose of the standard deviation filter is to filter out noise by and by default it will filter 1 standard deviation. Adjust this number and the filter selections (price, both, GMA, none) to reduce the signal noise.
What is Ehlers Gaussian filter?
This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag. published by John F. Ehlers in "Rocket Science For Traders". First implemented in Wealth-Lab by Dr René Koch.
A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components.
A gaussian filter with...
one pole is equivalent to an EMA filter.
two poles is equivalent to EMA(EMA())
three poles is equivalent to EMA(EMA(EMA()))
and so on...
For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters: Lag = N * P / (2 * ¶2), where,
N is the number of poles, and
P is the critical period
Special initialization of filter stages ensures proper working in scans with as few bars as possible.
From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass filtters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life."
References John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters"
Included
Loxx's Expanded Source Types
Signals
Alerts
Bar coloring
Related indicators
STD-Filtered, Gaussian-Kernel-Weighted Moving Average
One-Sided Gaussian Filter w/ Channels
Fisher Transform w/ Dynamic Zones
R-sqrd Adapt. Fisher Transform w/ D. Zones & Divs.

STD-Filtered, Gaussian-Kernel-Weighted Moving Average [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average is a moving average that weights price by using a Gaussian kernel function to calculate data points. This indicator also allows for filtering both source input price and output signal using a standard deviation filter.
Purpose
This purpose of this indicator is to take the concept of Kernel estimation and apply it in a way where instead of predicting past values, the weighted function predicts the current bar value at each bar to create a moving average that is suitable for trading. Normally this method is used to create an array of past estimators to model past data but this method is not useful for trading as the past values will repaint. This moving average does NOT repaint, however you much allow signals to close on the current bar before taking the signal. You can compare this to Nadaraya-Watson Estimator wherein they use Nadaraya-Watson estimator method with normalized kernel weighted function to model price.
What are Kernel Functions?
A kernel function is used as a weighing function to develop non-parametric regression model is discussed. In the beginning of the article, a brief discussion about properties of kernel functions and steps to build kernels around data points are presented.
Kernel Function
In non-parametric statistics, a kernel is a weighting function which satisfies the following properties.
A kernel function must be symmetrical. Mathematically this property can be expressed as K (-u) = K (+u). The symmetric property of kernel function enables its maximum value (max(K(u)) to lie in the middle of the curve.
The area under the curve of the function must be equal to one. Mathematically, this property is expressed as: integral −∞ + ∞ ∫ K(u)d(u) = 1
Value of kernel function can not be negative i.e. K(u) ≥ 0 for all −∞ < u < ∞.
Kernel Estimation
In this article, Gaussian kernel function is used to calculate kernels for the data points. The equation for Gaussian kernel is:
K(u) = (1 / sqrt(2pi)) * e^(-0.5 *(j / bw)^2)
Where xi is the observed data point. j is the value where kernel function is computed and bw is called the bandwidth. Bandwidth in kernel regression is called the smoothing parameter because it controls variance and bias in the output. The effect of bandwidth value on model prediction is discussed later in this article.
Included
Loxx's Expanded Source types
Signals
Alerts
Bar coloring

T.O/REG/Gauss LineHi Dear Traders/Dealers!
I present you here 3 lines that I developed myself base on statistical issues.
+Reg. Line
+Gauss Line
+T.O Line
-Reg. Line based on linear regression of previous inputs to make an average value.
-Gauss Line based on Gaussian mean value, Standard Deviation and it uses previous inputs to make an average value.
-T.O Line based on Gaussian and RMA methods generate an average value.
Hopefully useful for you!
Best regards and happy trading
Shakib

SUPRESHi Dears!
I hope that you enjoyed my "FLEX KDJ IND" till today!
Here, I want to publish one of my other golden indicators for you!
Contents:
+ SUPRES
+ SUPERTREND
+ T.O Line
- SUPRES (SUPPORT/RESISTANCE) is sensitive to trading volumes and with "BACHWARD" you can adjust the length of previous indices in investigation and "MEMORY" is an argument for calling maximum lines that have to be kept for "SUPPORT" and "RESIST".
- SUPERTREND is the normal prepared indicator which is defined in "TRADING VIEW"
-T.O is my suggestion instead of "EMA" to check the phase of session.
I hope that you enjoy this Indicator, please do not forgot to "Warm-It-UP"!
Happy trading,
Shakib

One-Sided Gaussian Support & Resistance Rate [Loxx]One-Sided Gaussian Support & Resistance Rate is a mean reversion oscillator much like Fisher Transform. This indicator is built using a one-sided Gaussian filter. If you pair this with Fisher Transform and line up the settings, you'll notice similar outcomes. You'll notice that as the oscillator levels out at around zero or one that this signifies a zone of resistance or support. See here for more details on calculating the OS Gaussian Filter:
Included:
Bar coloring
Signals
Alerts
Ehlers 2-Pole Super Smoothing for smoothing source inputs

One-Sided Gaussian Filter w/ Channels [Loxx]One-Sided Gaussian Filter w/ Channels is a Gaussian Moving Average that is calculated using a Fibonacci weighting function. Keltner channels have been added to show zones of exhaustion. A better name would be "Half Gaussian bell weighted" or "Half normal distribution weighted" indicator, since the weights for calculation of the average (similar to linear weighted average) are taken from a normal distribution curve like function--but only the half of the curve is used for calculation.
Information of the Gaussian distribution can be found here : en.wikipedia.org and once you take a look at the standard normal distribution curve, it will be much clearer what is exactly done in this indicator.
After the Gaussian Filter is applied to the source input, an Ehlers' 2-Pole Super Smoother is applied to reduce noise without significant lag.
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types

Goertzel Cycle Period Adaptive Fisher Transform [Loxx]Goertzel Cycle Period Adaptive Fisher Transform is an adaptive Fisher Transform using the Goertzel Cycle Algorithm to derive length inputs.
What is Goertzel Cycle Algorithm?
Read here:
What is Fisher Transform?
The Fisher Transform is a technical indicator created by John F. Ehlers that converts prices into a Gaussian normal distribution.
The indicator highlights when prices have moved to an extreme, based on recent prices. This may help in spotting turning points in the price of an asset. It also helps show the trend and isolate the price waves within a trend.
Included:
Zero-line and signal cross options for bar coloring
Customizable overbought/oversold thresh-holds
Alerts
Signals
***Please note, the Goertzel Cycle Algorithm is processor heavy, so this indicator will take some time to load.