Multi-Kernel CCI [BackQuant]Multi-Kernel CCI
Conceptual Foundation and Innovation
It offers a fresh take on the Commodity Channel Index (CCI) by integrating three distinct kernel functions—Exponential Decay, Gaussian Decay, and Cosine Decay—to create a more robust and adaptive momentum indicator. The use of these kernel functions allows the CCI calculation to be more responsive to price changes while smoothing out noise, providing traders with clearer trend signals and reducing false alerts in varying market conditions.
Technical Composition and Calculation
The core of this indicator is a multi-kernel approach to calculating the CCI, where three different decay kernels are applied to the price source. Each kernel provides a unique weighting mechanism for price data over a user-defined lookback period. The result is an average of these three kernel calculations, which serves as the foundation for the CCI calculation. This innovative approach makes the Multi-Kernel CCI more adaptive to different market conditions compared to traditional CCI calculations.
Exponential Decay Kernel: Applies an exponential weighting to recent price data, giving more importance to recent values while smoothing out older data.
Gaussian Decay Kernel: Weights data using a Gaussian function, ensuring smooth transitions between price points and reducing outliers' impact.
Cosine Decay Kernel: Utilizes a cosine function to apply a unique oscillating weight to the data, capturing cyclical market movements more effectively.
Adaptive Thresholding: Like the Adaptive Momentum Oscillator, this indicator adjusts its long and short thresholds dynamically using percentile-based calculations over historical CCI values.
Features and User Inputs The Multi-Kernel CCI offers a wide range of customization options for traders:
Kernel Calculation Length & Alpha: Traders can fine-tune the sensitivity of the CCI by adjusting the length of the kernel calculation and the alpha parameter for the Exponential Decay Kernel.
Adaptive Thresholds: The indicator provides percentile-based thresholds for both long and short signals, allowing traders to dynamically adjust their signals based on historical data.
Extreme Value Detection: This feature highlights extreme overbought and oversold conditions with customizable thresholds and background hues, visually aiding in identifying high-probability reversal zones.
Divergence Detection: The script includes a divergence detection feature, identifying regular and hidden bullish or bearish divergences to help traders spot potential trend reversals.
Practical Applications The Multi-Kernel CCI excels in markets where adaptive trend detection and momentum confirmation are critical. Traders can leverage this tool in several ways:
Adaptive Trend Following: The dynamically adjusting thresholds allow traders to capture trends more effectively while avoiding false signals during consolidations or choppy markets.
Reversal Detection: The multi-kernel approach ensures that reversals are detected with greater precision, particularly in volatile markets where traditional indicators might fail.
Divergence Identification: With built-in divergence detection, the indicator provides traders with an early warning of potential trend reversals, helping to time their entries and exits more effectively.
Advantages and Strategic Value The Multi-Kernel CCI offers several strategic advantages over traditional CCI indicators:
Multi-Kernel Smoothing:
By using multiple decay kernels, this CCI calculation is better suited to detect subtle changes in market momentum, reducing the impact of noise and providing clearer trend signals.
Dynamic Thresholds:
The adaptive percentile-based thresholds ensure that the indicator remains relevant across different market conditions, enhancing signal accuracy.
Visual and Analytical Aids:
With features like extreme value detection and divergence spotting, this indicator equips traders with powerful tools to confirm trend strength and identify potential reversals.
Summary and Usage Tips
The Multi-Kernel CCI is a highly versatile tool for traders seeking a more adaptive and robust momentum indicator. Its multi-kernel foundation provides smoother, more reliable signals, while the adaptive thresholds and divergence detection features help traders refine their entries and exits. The dynamic nature of this indicator makes it ideal for both trend-following and reversal strategies in volatile markets.
Traders should experiment with the kernel calculation length and alpha parameter to align the indicator's sensitivity with their specific trading style and market conditions. Additionally, the adaptive thresholds can be fine-tuned to ensure the CCI captures the most significant trend changes without being overly reactive to short-term fluctuations.
Thus following all of the key points here are some sample backtests on the 1D Chart
Disclaimer: Backtests are based off past results, and are not indicative of the future.
INDEX:BTCUSD
INDEX:ETHUSD
BINANCE:SOLUSD
Kernel
Gaussian Kernel Smoothing MomentumOverview:
The Gaussian Kernel Smoothing Momentum indicator analyzes and quantifies market momentum by applying statistical techniques to price and returns data. This indicator uses Gaussian kernel smoothing to filter noise and provide a more accurate representation of momentum. Additionally, it includes a option to evaluate the absolute score of the momentum to determine if the beginning of a "trend" is likely or if you can expect a "trend" to come to an end.
Kernels and Their Role In Time Series Analysis:
In statistical analysis, a kernel is a weighting function used to estimate the properties of a dataset. Kernels are particularly useful in non-parametric methods, where they serve to smooth data or estimate probability density functions without assuming a specific underlying distribution. The Gaussian kernel, one of the most commonly used, is characterized by its smooth, bell-shaped curve which provides a natural way to give more weight to data points closer to the target value and less weight to those further away.
Uses of Kernels in Time Series Analysis
Kernels play a significant role in time series analysis, especially in the context of smoothing and filtering. With kernel functions, you can reduce noise and extract the underlying systematic component or signal from the data. This process is essential for identifying long-term patterns in the data, which is often obscured by short-term fluctuations and random noise.
Kernel Smoothing
Kernel smoothing is a technique that applies a kernel function to a set of data points to create a smooth curve, effectively reducing the impact of random variations. In time series analysis, kernel smoothing helps to filter out short-term noise while retaining significant trends and "patterns". The Gaussian kernel, with its emphasis on nearby points, is particularly effective for this purpose, as it smooths the data in a way that highlights the underlying structure without overfitting to random fluctuations.
Additionally, kernels are used in non-parametric volatility estimation, option pricing models, and for detecting anomalies in financial data. Their flexibility and ability to handle complex, non-linear relationships make them well-suited for the often noisy data encountered in financial markets.
Momentum Component
The momentum component of the indicator is designed to quantify the directional movement of asset prices by applying the Gaussian kernel smoothing to the expected return of the price data. The data then has the variance stabilized and normalizes the distribution of price changes to be able to more efficiently analyze the momentum.
The Gaussian kernel smoothing function serves to filter out high-frequency noise, isolating the underlying systematic component of the momentum. This is achieved by weighting the data points based on their proximity to the current observation, with closer data points exerting a stronger influence. The resulting smoothed momentum provides a clearer of the directional bias in the market, devoid of short-term volatility.
Absolute Move Component
The absolute move component is a extension of the momentum analysis, focusing on the magnitude rather than the direction of the price movements. This component captures the absolute score of the smoothed momentum series, providing a measure of strength or intensity of the price movement, independent from its direction. The absolute move component also incorporates a Kalman filter to further smooth and refine the signal. The Kalman filter dynamically adjusts based on the observed variance in the data, to reduce the impact of outliers.
What to make of this indicator
The smoothed momentum line helps determine whether the market is experiencing upward and downward momentum. If the momentum line is above zero and rising, this suggest a positive expected returns. Conversely, if the momentum line is below zero and falling, it indicates negative expected returns.
You should also pay attention to changes in the slope of the momentum line and the moving average of the smoothed momentum(weighted with an optimal sampling size algorithm). A flattening or reversal of the slope may signal a potential shift in market direction. For example, if the momentum line and moving average transitions from rising to falling, it means that the expected return is going from positive to negative so you can see the "trend" as weakening or forming a trend of negative expected returns.
The absolute move component is designed to measure the intensity or strength of the current market movement. A low absolute move value, especially when they are negative or at the lower end of their band, indicates that the momentum and expected return is close to zero, which suggest that the market is experiencing minimal directional movement, which can be a sign of consolidation. High absolute values signal that the market is undergoing a significant price movement. When the absolute move is high and/or rising, it indicates that the movement of the momentum is strong, regardless of whether it is bullish or bearish.
If the absolute move reaches unusually high levels, it could indicate that the market is experiencing an exceptional price move, which might be unsustainable. Traders can anticipate potential reversals or profit taking targets. However, you should avoid trying to trade reversals as exceptionally high values in a time series do not guarantee an immediate reversal. This high values often occur during periods of strong trends or significant events, which can continue longer than expected, and you cant time when it will return to its mean. The mean-reverting nature of some statistical models can suggest a return to the mean, but this assumption can be misleading in financial markets, where trends can persist despite overextending conditions.
Trend Regression Kernel [IkkeOmar]Kernel by @jdehorty huge shoutout to him! This is only an idea for how I use it when trading
All credit for the kernel goes to him, I did not make the kernel! I don't know how to make it more clear.
I use this to assist with top-down analysis.
timeframe I want to trade : timeframe to analyse with white noise and kernel:
1m : 1H
5m : 2H
15m : 4H
1H : 1D
In the chart you see that I have the 1H open, I use the white noise at a "lower setting length" (55 in this case), I change the source of to be the kernel on the higher timeframe. When a new trend is detected by the White noise I wait for price to retest the kernel before building a position. Another case described below:
Here i use the adaptive MCVF (I have made this free for everyone on TradingView) to buy when price is below the kernel while the trend for the white noise is bullish .
Notice that the Kernel is set on the 4H timeframe! The source of the white noise is the kernel!
Here is an example in a bearish trend:
Notice, I am on the 5m chart, kernel uses the 2H chart and the source of the white noise is the kernel.
I use the adaptive MCVF to help me get entries AFTER the first touch of the kernel.
Mandatory code explanation, with respect to the house rules:
Input settings:
Input Settings:
The script provides various input parameters to customize the indicator:
src: The source of price data, defaulted to closing prices.
h, r, x_0: Parameters for Kernel 1.
h2, r2, x_2: Parameters for Kernel 2.
Kernel Regression Functions:
Two functions kernel_regression1 and kernel_regression2 are defined to perform kernel regression calculations.
These functions estimate the trend using the Nadaraya-Watson kernel non-parametric regression method.
They take the source data (_src), the size of the data series (_size), and the lookback window (_h) as inputs.
They iterate over the data series and calculate the weighted sum of the values based on the specified kernel parameters.
The result is divided by the cumulative weight to obtain the estimated value.
Estimations:
The kernel_regression1 and kernel_regression2 functions are called with the respective parameters to estimate trends (yhat1 and yhat2).
Buy and Sell Signals:
Buy and sell signals are generated based on crossover and crossunder conditions between the two trend estimates (yhat1 and yhat2).
buySignal is true when yhat1 crosses above yhat2.
SellSignal is true when yhat1 crosses below yhat2.
Plotting:
The average of the two trend estimates (yhat1 and yhat2) is calculated and plotted.
The color of the plot is determined based on whether yhat1 is greater than yhat2, less than yhat2, or equal to yhat2.
Buy and sell signals are plotted using triangle shapes below and above bars, respectively.
Alerts:
Alert conditions are set based on buy and sell signals. Alerts are triggered when a crossover (long signal) or crossunder (short signal) occurs.
The alerts include information about the signal type, symbol, and price.
It's important to mention that the buy and sell signals from the indicator is very discretionary, I rarely use them, and if I do it's if they are in confluence with a correction i am biased towards or if it has confluence with some of my other systems.
The adaptive MCVF and White noise is free for everyone on TradingView, linked below:)
Huge shoutout to @jdehorty, original kernel below:
Kernels©2024, GoemonYae; copied from @jdehorty's "KernelFunctions" on 2024-03-09 to ensure future dependency compatibility. Will also add more functions to this script.
Library "KernelFunctions"
This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substition/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels.
rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar)
Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_relativeWeight (simple float) : Relative weighting of time frames. Smaller values resut in a more stretched out curve and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.
startAtBar (simple int)
Returns: yhat The estimated values according to the Rational Quadratic Kernel.
gaussian(_src, _lookback, startAtBar)
Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
startAtBar (simple int)
Returns: yhat The estimated values according to the Gaussian Kernel.
periodic(_src, _lookback, _period, startAtBar)
Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions which repeat themselves exactly.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period (simple int) : The distance between repititions of the function.
startAtBar (simple int)
Returns: yhat The estimated values according to the Periodic Kernel.
locallyPeriodic(_src, _lookback, _period, startAtBar)
Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.
Parameters:
_src (float) : The source series.
_lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period (simple int) : The distance between repititions of the function.
startAtBar (simple int)
Returns: yhat The estimated values according to the Locally Periodic Kernel.
Bandwidth Volatility - Silverman Rule of thumb EstimatorOverview
This indicator calculates volatility using the Rule of Thumb bandwidth estimator and incorporating the standard deviations of returns to get historical volatility. There are two options: one for the original rule of thumb bandwidth estimator, and another for the modified rule of thumb estimator. This indicator comes with the bandwidth , which is shown with the color gradient columns, which are colored by a percentile of the bandwidth, and the moving average of the bandwidth, which is the dark shaded area.
The rule of thumb bandwidth estimator is a simple and quick method for estimating the bandwidth parameter in kernel density estimation (KSE) or kernel regression. It provides a rough approximation of the bandwidth without requiring extensive computation resources or fine-tuning. One common rule of thumb estimator is Silverman rule, which is given by
h = 1.06*σ*n^(-1/5)
where
h is the bandwidth
σ is the standard deviation of the data
n is the number of data points
This rule of thumb is based on assuming a Gaussian kernel and aims to strike a balance between over-smoothing and under-smoothing the data. It is simple to implement and usually provides reasonable bandwidth estimates for a wide range of datasets. However , it is important to note that this rule of thumb may not always have optimal results, especially for non-Gaussian or multimodal distributions. In such cases, a modified bandwidth selection, such as cross-validation or even applying a log transformation (if the data is right-skewed), may be preferable.
How it works:
This indicator computes the bandwidth volatility using returns, which are used in the standard deviation calculation. It then estimates the bandwidth based on either the Silverman rule of thumb or a modified version considering the interquartile range. The percentile ranks of the bandwidth estimate are then used to visualize the volatility levels, identify high and low volatility periods, and show them with colors.
Modified Rule of thumb Bandwidth:
The modified rule of thumb bandwidth formula combines elements of standard deviations and interquartile ranges, scaled by a multiplier of 0.9 and inversely with a number of periods. This modification aims to provide a more robust and adaptable bandwidth estimation method, particularly suitable for financial time series data with potentially skewed or heavy-tailed data.
Formula for Modified Rule of Thumb Bandwidth:
h = 0.9 * min(σ, (IQR/1.34))*n^(-1/5)
This modification introduces the use of the IQR divided by 1.34 as an alternative to the standard deviation. It aims to improve the estimation, mainly when the underlying distribution deviates from a perfect Gaussian distribution.
Analysis
Rule of thumb Bandwidth: Provides a broader perspective on volatility trends, smoothing out short-term fluctuations and focusing more on the overall shape of the density function.
Historical Volatility: Offers a more granular view of volatility, capturing day-to-day or intra-period fluctuations in asset prices and returns.
Modelling Requirements
Rule of thumb Bandwidth: Provides a broader perspective on volatility trends, smoothing out short-term fluctuations and focusing more on the overall shape of the density function.
Historical Volatility: Offers a more granular view of volatility, capturing day-to-day or intra-period fluctuations in asset prices and returns.
Pros of Bandwidth as a volatility measure
Robust to Data Distribution: Bandwidth volatility, especially when estimated using robust methods like Silverman's rule of thumb or its modifications, can be less sensitive to outliers and non-normal distributions compared to some other measures of volatility
Flexibility: It can be applied to a wide range of data types and can adapt to different underlying data distributions, making it versatile for various analytical tasks.
How can traders use this indicator?
In finance, volatility is thought to be a mean-reverting process. So when volatility is at an extreme low, it is expected that a volatility expansion happens, which comes with bigger movements in price, and when volatility is at an extreme high, it is expected for volatility to eventually decrease, leading to smaller price moves, and many traders view this as an area to take profit in.
In the context of this indicator, low volatility is thought of as having the green color, which indicates a low percentile value, and also being below the moving average. High volatility is thought of as having the yellow color and possibly being above the moving average, showing that you can eventually expect volatility to decrease.
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.
Bollinger Bands (Nadaraya Smoothed) | Flux ChartsTicker: AMEX:SPY , Timeframe: 1m, Indicator settings: default
General Purpose
This script is an upgrade to the classic Bollinger Bands. The idea behind Bollinger bands is the detection of price movements outside of a stock's typical fluctuations. Bollinger Bands use a moving average over period n plus/minus the standard deviation over period n times a multiplier. When price closes above or below either band this can be considered an abnormal movement. This script allows for the classic Bollinger Band interpretation while de-noising or "smoothing" the bands.
Efficacy
Ticker: AMEX:SPY , Timeframe: 1m, Indicator settings: Standard Dev: 2; Level 1 : off; Level 2: off; labels: off
Upper Band Key:
Blue: Bollinger No smoothing
Orange: Bollinger SMA smoothing period of 10
Purple: Bollinger EMA smoothing period of 10
Red: Nadaraya Smoothed Bollinger bandwidth of 6
Here we chose periods so that each would have a similar offset from the original Bollinger's. Notice that the Red Band has a much smoother result while on average having a similar fit to the other smoothing techniques. Increasing the EMA's or SMA's period would result in them being smoother however the offset would increase making them less accurate to the original data.
Ticker: AMEX:SPY , Timeframe: 1m, Indicator settings: Standard Dev: 2; Level 1: off; Level 2: off; labels: off
Upper Band Key:
Blue: Bollinger No smoothing
Orange: Bollinger SMA smoothing period of 20
Purple: Bollinger EMA smoothing period of 20
Red: Nadaraya Smoothed Bollinger bandwidth of 6
This makes the Nadaraya estimator a particularly efficacious technique in this use case as it achieves a superior smoothness to fit ratio.
How to Use
This indicator is not intended to be used on its own. Its use case is to identify outlier movements and periods of consolidation. The Smoothing Factor when lowered results in a more reactive but noisy graph. This setting is also known as the "bandwidth" ; it essentially raises the amplitude of the kernel function causing a greater weighting to recent data similar to lowering the period of a SMA or EMA. The repaint smoothing simply draws on the Bollinger's each chart update. Typically repaint would be used for processing and displaying discrete data however currently it's simply another way to display the Bollinger Bands.
What makes this script unique.
Since Bollinger bands use standard deviation they have excess noise. By noise we mean minute fluctuations which most traders will not find useful in their strategies. The Nadaraya-Watson estimator, as used, is essentially a weighted average akin to an ema. A gaussian kernel is placed at the candlestick of interest. That candlestick's value will have the highest weight. From that point the other candlesticks' values effect on the average will decrease with the slope of the kernel function. This creates a localized mean of the Bollinger Bands allowing for reduced noise with minimal distortion of the original Bollinger data.
AI Momentum [YinYang]Overview:
AI Momentum is a kernel function based momentum Indicator. It uses Rational Quadratics to help smooth out the Moving Averages, this may give them a more accurate result. This Indicator has 2 main uses, first it displays ‘Zones’ that help you visualize the potential movement areas and when the price is out of bounds (Overvalued or Undervalued). Secondly it creates signals that display the momentum of the current trend.
The Zones are composed of the Highest Highs and Lowest lows turned into a Rational Quadratic over varying lengths. These create our Rational High and Low zones. There is however a second zone. The second zone is composed of the avg of the Inner High and Inner Low zones (yellow line) and the Rational Quadratic of the current Close. This helps to create a second zone that is within the High and Low bounds that may represent momentum changes within these zones. When the Rationalized Close crosses above the High and Low Zone Average it may signify a bullish momentum change and vice versa when it crosses below.
There are 3 different signals created to display momentum:
Bullish and Bearish Momentum. These signals display when there is current bullish or bearish momentum happening within the trend. When the momentum changes there will likely be a lull where there are neither Bullish or Bearish momentum signals. These signals may be useful to help visualize when the momentum has started and stopped for both the bulls and the bears. Bullish Momentum is calculated by checking if the Rational Quadratic Close > Rational Quadratic of the Highest OHLC4 smoothed over a VWMA. The Bearish Momentum is calculated by checking the opposite.
Overly Bullish and Bearish Momentum. These signals occur when the bar has Bullish or Bearish Momentum and also has an Rationalized RSI greater or less than a certain level. Bullish is >= 57 and Bearish is <= 43. There is also the option to ‘Factor Volume’ into these signals. This means, the Overly Bullish and Bearish Signals will only occur when the Rationalized Volume > VWMA Rationalized Volume as well as the previously mentioned factors above. This can be useful for removing ‘clutter’ as volume may dictate when these momentum changes will occur, but it can also remove some of the useful signals and you may miss the swing too if the volume just was low. Overly Bullish and Bearish Momentum may dictate when a momentum change will occur. Remember, they are OVERLY Bullish and Bearish, meaning there is a chance a correction may occur around these signals.
Bull and Bear Crosses. These signals occur when the Rationalized Close crosses the Gaussian Close that is 2 bars back. These signals may show when there is a strong change in momentum, but be careful as more often than not they’re predicting that the momentum may change in the opposite direction.
Tutorial:
As we can see in the example above, generally what happens is we get the regular Bullish or Bearish momentum, followed by the Rationalized Close crossing the Zone average and finally the Overly Bullish or Bearish signals. This is normally the order of operations but isn’t always how it happens as sometimes momentum changes don’t make it that far; also the Rationalized Close and Zone Average don’t follow any of the same math as the Signals which can result in differing appearances. The Bull and Bear Crosses are also quite sporadic in appearance and don’t generally follow any sort of order of operations. However, they may occur as a Predictor between Bullish and Bearish momentum, signifying the beginning of the momentum change.
The Bull and Bear crosses may be a Predictor of momentum change. They generally happen when there is no Bullish or Bearish momentum happening; and this helps to add strength to their prediction. When they occur during momentum (orange circle) there is a less likely chance that it will happen, and may instead signify the exact opposite; it may help predict a large spike in momentum in the direction of the Bullish or Bearish momentum. In the case of the orange circle, there is currently Bearish Momentum and therefore the Bull Cross may help predict a large momentum movement is about to occur in favor of the Bears.
We have disabled signals here to properly display and talk about the zones. As you can see, Rationalizing the Highest Highs and Lowest Lows over 2 different lengths creates inner and outer bounds that help to predict where parabolic movement and momentum may move to. Our Inner and Outer zones are great for seeing potential Support and Resistance locations.
The secondary zone, which can cross over and change from Green to Red is also a very important zone. Let's zoom in and talk about it specifically.
The Middle Zone Crosses may help deduce where parabolic movement and strong momentum changes may occur. Generally what may happen is when the cross occurs, you will see parabolic movement to the High / Low zones. This may be the Inner zone but can sometimes be the outer zone too. The hard part is sometimes it can be a Fakeout, like displayed with the Blue Circle. The Cross doesn’t mean it may move to the opposing side, sometimes it may just be predicting Parabolic movement in a general sense.
When we turn the Momentum Signals back on, we can see where the Fakeout occurred that it not only almost hit the Inner Low Zone but it also exhibited 2 Overly Bearish Signals. Remember, Overly bearish signals mean a momentum change in favor of the Bulls may occur soon and overly Bullish signals mean a momentum change in favor of the Bears may occur soon.
You may be wondering, well what does “may occur soon” mean and how do we tell?
The purpose of the momentum signals is not only to let you know when Momentum has occurred and when it is still prevalent. It also matters A LOT when it has STOPPED!
In this example above, we look at when the Overly Bullish and Bearish Momentum has STOPPED. As you can see, when the Overly Bullish or Bearish Momentum stopped may be a strong predictor of potential momentum change in the opposing direction.
We will conclude our Tutorial here, hopefully this Indicator has been helpful for showing you where momentum is occurring and help predict how far it may move. We have been dabbling with and are planning on releasing a Strategy based on this Indicator shortly.
Settings:
1. Momentum:
Show Signals: Sometimes it can be difficult to visualize the zones with signals enabled.
Factor Volume: Factor Volume only applies to Overly Bullish and Bearish Signals. It's when the Volume is > VWMA Volume over the Smoothing Length.
Zone Inside Length: The Zone Inside is the Inner zone of the High and Low. This is the length used to create it.
Zone Outside Length: The Zone Outside is the Outer zone of the High and Low. This is the length used to create it.
Smoothing length: Smoothing length is the length used to smooth out our Bullish and Bearish signals, along with our Overly Bullish and Overly Bearish Signals.
2. Kernel Settings:
Lookback Window: The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars. Recommended range: 3-50.
Relative Weighting: Relative weighting of time frames. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel. Recommended range: 0.25-25.
Start Regression at Bar: Bar index on which to start regression. The first bars of a chart are often highly volatile, and omission of these initial bars often leads to a better overall fit. Recommended range: 5-25.
If you have any questions, comments, ideas or concerns please don't hesitate to contact us.
HAPPY TRADING!
Relational Quadratic Kernel Channel [Vin]The Relational Quadratic Kernel Channel (RQK-Channel-V) is designed to provide more valuable potential price extremes or continuation points in the price trend.
Example:
Usage:
Lookback Window: Adjust the "Lookback Window" parameter to control the number of previous bars considered when calculating the Rational Quadratic Estimate. Longer windows capture longer-term trends, while shorter windows respond more quickly to price changes.
Relative Weight: The "Relative Weight" parameter allows you to control the importance of each data point in the calculation. Higher values emphasize recent data, while lower values give more weight to historical data.
Source: Choose the data source (e.g., close price) that you want to use for the kernel estimate.
ATR Length: Set the length of the Average True Range (ATR) used for channel width calculation. A longer ATR length results in wider channels, while a shorter length leads to narrower channels.
Channel Multipliers: Adjust the "Channel Multiplier" parameters to control the width of the channels. Higher multipliers result in wider channels, while lower multipliers produce narrower channels. The indicator provides three sets of channels, each with its own multiplier for flexibility.
Details:
Rational Quadratic Kernel Function:
The Rational Quadratic Kernel Function is a type of smoothing function used to estimate a continuous curve or line from discrete data points. It is often used in time series analysis to reduce noise and emphasize trends or patterns in the data.
The formula for the Rational Quadratic Kernel Function is generally defined as:
K(x) = (1 + (x^2) / (2 * α * β))^(-α)
Where:
x represents the distance or difference between data points.
α and β are parameters that control the shape of the kernel. These parameters can be adjusted to control the smoothness or flexibility of the kernel function.
In the context of this indicator, the Rational Quadratic Kernel Function is applied to a specified source (e.g., close prices) over a defined lookback window. It calculates a smoothed estimate of the source data, which is then used to determine the central value of the channels. The kernel function allows the indicator to adapt to different market conditions and reduce noise in the data.
The specific parameters (length and relativeWeight) in your indicator allows to fine-tune how the Rational Quadratic Kernel Function is applied, providing flexibility in capturing both short-term and long-term trends in the data.
To know more about unsupervised ML implementations, I highly recommend to follow the users, @jdehorty and @LuxAlgo
Optimizing the parameters:
Lookback Window (length): The lookback window determines how many previous bars are considered when calculating the kernel estimate.
For shorter-term trading strategies, you may want to use a shorter lookback window (e.g., 5-10).
For longer-term trading or investing, consider a longer lookback window (e.g., 20-50).
Relative Weight (relativeWeight): This parameter controls the importance of each data point in the calculation.
A higher relative weight (e.g., 2 or 3) emphasizes recent data, which can be suitable for trend-following strategies.
A lower relative weight (e.g., 1) gives more equal importance to historical and recent data, which may be useful for strategies that aim to capture both short-term and long-term trends.
ATR Length (atrLength): The length of the Average True Range (ATR) affects the width of the channels.
Longer ATR lengths result in wider channels, which may be suitable for capturing broader price movements.
Shorter ATR lengths result in narrower channels, which can be helpful for identifying smaller price swings.
Channel Multipliers (channelMultiplier1, channelMultiplier2, channelMultiplier3): These parameters determine the width of the channels relative to the ATR.
Adjust these multipliers based on your risk tolerance and desired channel width.
Higher multipliers result in wider channels, which may lead to fewer signals but potentially larger price movements.
Lower multipliers create narrower channels, which can result in more frequent signals but potentially smaller price movements.
Kernel Regression ToolkitThis toolkit provides filters and extra functionality for non-repainting Nadaraya-Watson estimator implementations made by @jdehorty. For the sake of ease I have nicknamed it "kreg". Filters include a smoothing formula and zero lag formula. The purpose of this script is to help traders test, experiment and develop different regression lines. Regression lines are best used as trend lines and can be an invaluable asset for quickly locating first pullbacks and breaks of trends.
Other features include two J lines and a blend line. J lines are featured in tools like Stochastic KDJ. The formula uses the distance between K and D lines to make the J line. The blend line adds the ability to blend two lines together. This can be useful for several tasks including finding a center/median line between two lines or for blending in the characteristics of a different line. Default is set to 50 which is a 50% blend of the two lines. This can be increased and decreased to taste. This tool can be overlaid on the chart or on top of another indicator if you set the source. It can even be moved into its own window to create a unique oscillator based on whatever sources you feed it.
Below are the standard settings for the kernel estimation as documented by @jdehorty:
Lookback Window: The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars. Recommended range: 3-50
Weighting: Relative weighting of time frames. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel. Recommended range: 0.25-25
Level: Bar index on which to start regression. Controls how tightly fit the kernel estimate is to the data. Smaller values are a tighter fit. Larger values are a looser fit. Recommended range: 2-25
Lag: Lag for crossover detection. Lower values result in earlier crossovers. Recommended range: 1-2
For more information on this technique refer to to the original open source indicator by @jdehorty located here:
KernelFunctionsFiltersLibrary "KernelFunctionsFilters"
This library provides filters for non-repainting kernel functions for Nadaraya-Watson estimator implementations made by @jdehorty. Filters include a smoothing formula and zero lag formula. You can find examples in the code. For more information check out the original library KernelFunctions.
rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_relativeWeight (simple float)
startAtBar (simple int)
_filter (simple string)
gaussian(_src, _lookback, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
startAtBar (simple int)
_filter (simple string)
periodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
locallyPeriodic(_src, _lookback, _period, startAtBar, _filter)
Parameters:
_src (float)
_lookback (simple int)
_period (simple int)
startAtBar (simple int)
_filter (simple string)
j(line1, line2)
Parameters:
line1 (float)
line2 (float)
Nadaraya-Watson OscillatorThis indicator is based on the work of @jdehorty and his amazing Nadaraya-Watson Kernel Envelope, which you can see here:
General Description
The Nadaraya-Watson Oscillator (NWO) will give the same information as the Nadaraya-Watson Envelope, but as an oscillator off the main chart, by plotting the relationship between price and the Kernel and its bands. This also means that we can now detect divergences between price and the NWO.
You can see the relationship between the two here:
You can think of this indicator as the kernel envelope version of a Bollinger Band %B. In ranging markets the bands are perfect for mean reversion trades, but in certain situations the break of one of the bands can signal the beggining of a strong trend and price will remain close to the bands for a long period and will only give small pullbacks. As with any indicator, confluence with price and other tools must be taken into account.
Main Features
As with @jdehorty 's Envelope, you can change the following settings:
Lookback Window.
Relative Weighting.
The initial bar for the regression.
ATR period for the bands.
Inner and Outer Multiples for the bands.
I also added the following:
A middle band around the Kernel to filter out false crossovers.
A Hull Moving Average to smoothen out the movements of the oscillator and give extra confirmation of turnover points.
Colors
Some special things to note regarding the coloring:
The zero line features a gradient that changes color every time the Kernel slope changes direction.
The Oscillator plot has a gradient coloring that gets stronger the closer it gets to each of the bands.
Every time the oscillator crosses over/under the outer bands the background will be highlighted.
Happy trading!
Capital Line PackThe Capital Line Pack ( CLP ) indicator is a technical analysis tool that is designed to help traders and investors identify potential buying and selling opportunities in financial markets by using, inter alia, kernel regression methodoliges. It is a standalone indicator that can be placed on top of price chart displaying the Base MA, Capital Line and standard deviation bands.
The Capital Line is calculated based on volatility, measured by a z-scores* of a selected price source and a moving average (Base MA). The Base MA serves as the foundation for the Capital Line calculation and plays a critical role in determining its behavior and responsiveness to price movements. By selecting different types of moving averages as the Base MA, traders can adjust the sensitivity of the Capital Line to changes in market conditions, which can impact the signals generated by the indicator. The Base MA can be set at the user's choice including: SMA, EMA, Volume Weighted Moving Average (VWMA), Kernel Regression MA, HEMA, DEMA, T3.
For example, if a trader selects a EMA as the Base MA, the Capital Line will respond more quickly to changes in price compared to a more smoothed moving average, like a Volume Weighted Moving Average (VWMA) or Kernel Regression MA. This means that the Capital Line will be more sensitive to short-term price fluctuations with a EMA as the Base MA, while a VWMA or Kernel Regression MA will be less reactive to short-term price movements and more focused on longer-term trends.
Therefore, the choice of Base MA can have a significant impact on the behavior of the Capital Line, and traders need to select the most appropriate Base MA that suits their trading strategy and risk management preferences.
*The z-scores are calculated by comparing the current price to the average price over a certain period of time, and then dividing the difference by the standard deviation of the prices over that same period of time.
The Bands are calculated by adding and subtracting a standard deviation from the Base MA.
Bands help identify the volatility of the market, and when the bands are narrow, it suggests that the market is in a range-bound or flat period.
Indicator incorporates trade signals (labels and alerts). The method by which signals are generated can be selected by the user from several options:
Cap line color switch: Turning blue when it rises and red when it starts to fall.
Cap Line crosses the Base MA: This can be useful when the Base MA is weighted, for example, by volume, and the Cap Line Bandwidth and Relative weighting are set to small values.
Price crosses the Base MA: This is a popular and widely-used method that can provide reliable signals during trending market conditions. However, it may generate false signals during range-bound or flat market conditions.
Crossing of secondary MAs which can be selected in the indicator settings: This method provides traders with more flexibility and control over the signals generated by the indicator, but it may also be more complex and require more advanced technical analysis skills.
One of the standout features of our indicator is the ability to choose from several different style themes:
Pro
Modern
and Stealth
The "Pro" and "Modern" themes offer a clean and visually appealing display, while the "Stealth" theme is perfect for traders who want to focus on the price action or other indicators. The "Stealth" theme shades all the elements of the indicator while still keeping them in the field of visibility, allowing traders to concentrate on the most important aspects of their charts.
In addition to its trade signals, alerts, labels, and customizable themes, the indicator also offers several trend highlighting options to help traders visually backtest their trades. These options include candle coloring, background coloring, and highlighting with a histogram.
The candle coloring feature allows traders to customize the color of the candlesticks on their chart based on the direction of the trend. For example, bullish candles could be colored in teal, while bearish candles could be colored purple etc. This can make it easier for traders to identify trend movements and backtest their strategy.
The background coloring feature works similarly to the candle coloring feature, but it applies a color to the background of the chart rather than the candlesticks. This can be a useful way to highlight trends on the chart without obscuring the price action.
The histogram highlighting feature displays a histogram on the chart to show the difference between the upper and lower bands. This can be a useful way to visualize the strength of the trend and backtest trades based on the histogram readings.
NB! Remember, it is important to have a solid trading plan in place and to properly manage risk when trading.
Some traders may, depending upon customized settings, use the Capital Line as a capital risk management feature in trading. Our Capital Line indicator can be a useful tool, but it should not be the only factor considered when making trade decisions.
WaveTrend 3D█ OVERVIEW
WaveTrend 3D (WT3D) is a novel implementation of the famous WaveTrend (WT) indicator and has been completely redesigned from the ground up to address some of the inherent shortcomings associated with the traditional WT algorithm.
█ BACKGROUND
The WaveTrend (WT) indicator has become a widely popular tool for traders in recent years. WT was first ported to PineScript in 2014 by the user @LazyBear, and since then, it has ascended to become one of the Top 5 most popular scripts on TradingView.
The WT algorithm appears to have origins in a lesser-known proprietary algorithm called Trading Channel Index (TCI), created by AIQ Systems in 1986 as an integral part of their commercial software suite, TradingExpert Pro. The software’s reference manual states that “TCI identifies changes in price direction” and is “an adaptation of Donald R. Lambert’s Commodity Channel Index (CCI)”, which was introduced to the world six years earlier in 1980. Interestingly, a vestige of this early beginning can still be seen in the source code of LazyBear’s script, where the final EMA calculation is stored in an intermediate variable called “tci” in the code.
█ IMPLEMENTATION DETAILS
WaveTrend 3D is an alternative implementation of WaveTrend that directly addresses some of the known shortcomings of the indicator, including its unbounded extremes, susceptibility to whipsaw, and lack of insight into other timeframes.
In the canonical WT approach, an exponential moving average (EMA) for a given lookback window is used to assess the variability between price and two other EMAs relative to a second lookback window. Since the difference between the average price and its associated EMA is essentially unbounded, an arbitrary scaling factor of 0.015 is typically applied as a crude form of rescaling but still fails to capture 20-30% of values between the range of -100 to 100. Additionally, the trigger signal for the final EMA (i.e., TCI) crossover-based oscillator is a four-bar simple moving average (SMA), which further contributes to the net lag accumulated by the consecutive EMA calculations in the previous steps.
The core idea behind WT3D is to replace the EMA-based crossover system with modern Digital Signal Processing techniques. By assuming that price action adheres approximately to a Gaussian distribution, it is possible to sidestep the scaling nightmare associated with unbounded price differentials of the original WaveTrend method by focusing instead on the alteration of the underlying Probability Distribution Function (PDF) of the input series. Furthermore, using a signal processing filter such as a Butterworth Filter, we can eliminate the need for consecutive exponential moving averages along with the associated lag they bring.
Ideally, it is convenient to have the resulting probability distribution oscillate between the values of -1 and 1, with the zero line serving as a median. With this objective in mind, it is possible to borrow a common technique from the field of Machine Learning that uses a sigmoid-like activation function to transform our data set of interest. One such function is the hyperbolic tangent function (tanh), which is often used as an activation function in the hidden layers of neural networks due to its unique property of ensuring the values stay between -1 and 1. By taking the first-order derivative of our input series and normalizing it using the quadratic mean, the tanh function performs a high-quality redistribution of the input signal into the desired range of -1 to 1. Finally, using a dual-pole filter such as the Butterworth Filter popularized by John Ehlers, excessive market noise can be filtered out, leaving behind a crisp moving average with minimal lag.
Furthermore, WT3D expands upon the original functionality of WT by providing:
First-class support for multi-timeframe (MTF) analysis
Kernel-based regression for trend reversal confirmation
Various options for signal smoothing and transformation
A unique mode for visualizing an input series as a symmetrical, three-dimensional waveform useful for pattern identification and cycle-related analysis
█ SETTINGS
This is a summary of the settings used in the script listed in roughly the order in which they appear. By default, all default colors are from Google's TensorFlow framework and are considered to be colorblind safe.
Source: The input series. Usually, it is the close or average price, but it can be any series.
Use Mirror: Whether to display a mirror image of the source series; for visualizing the series as a 3D waveform similar to a soundwave.
Use EMA: Whether to use an exponential moving average of the input series.
EMA Length: The length of the exponential moving average.
Use COG: Whether to use the center of gravity of the input series.
COG Length: The length of the center of gravity.
Speed to Emphasize: The target speed to emphasize.
Width: The width of the emphasized line.
Display Kernel Moving Average: Whether to display the kernel moving average of the signal. Like PCA, an unsupervised Machine Learning technique whereby neighboring vectors are projected onto the Principal Component.
Display Kernel Signal: Whether to display the kernel estimator for the emphasized line. Like the Kernel MA, it can show underlying shifts in bias within a more significant trend by the colors reflected on the ribbon itself.
Show Oscillator Lines: Whether to show the oscillator lines.
Offset: The offset of the emphasized oscillator plots.
Fast Length: The length scale factor for the fast oscillator.
Fast Smoothing: The smoothing scale factor for the fast oscillator.
Normal Length: The length scale factor for the normal oscillator.
Normal Smoothing: The smoothing scale factor for the normal frequency.
Slow Length: The length scale factor for the slow oscillator.
Slow Smoothing: The smoothing scale factor for the slow frequency.
Divergence Threshold: The number of bars for the divergence to be considered significant.
Trigger Wave Percent Size: How big the current wave should be relative to the previous wave.
Background Area Transparency Factor: Transparency factor for the background area.
Foreground Area Transparency Factor: Transparency factor for the foreground area.
Background Line Transparency Factor: Transparency factor for the background line.
Foreground Line Transparency Factor: Transparency factor for the foreground line.
Custom Transparency: Transparency of the custom colors.
Total Gradient Steps: The maximum amount of steps supported for a gradient calculation is 256.
Fast Bullish Color: The color of the fast bullish line.
Normal Bullish Color: The color of the normal bullish line.
Slow Bullish Color: The color of the slow bullish line.
Fast Bearish Color: The color of the fast bearish line.
Normal Bearish Color: The color of the normal bearish line.
Slow Bearish Color: The color of the slow bearish line.
Bullish Divergence Signals: The color of the bullish divergence signals.
Bearish Divergence Signals: The color of the bearish divergence signals.
█ ACKNOWLEDGEMENTS
@LazyBear - For authoring the original WaveTrend port on TradingView
@PineCoders - For the beautiful color gradient framework used in this indicator
@veryfid - For the inspiration of using mirrored signals for cycle analysis and using multiple lookback windows as proxies for other timeframes
Nadaraya-Watson: Envelope (Non-Repainting)Due to popular request, this is an envelope implementation of my non-repainting Nadaraya-Watson indicator using the Rational Quadratic Kernel. For more information on this implementation, please refer to the original indicator located here:
What is an Envelope?
In technical analysis, an "envelope" typically refers to a pair of upper and lower bounds that surrounds price action to help characterize extreme overbought and oversold conditions. Envelopes are often derived from a simple moving average (SMA) and are placed at a predefined distance above and below the SMA from which they were generated. However, envelopes do not necessarily need to be derived from a moving average; they can be derived from any estimator, including a kernel estimator such as Nadaraya-Watson.
How to use this indicator?
Overall, this indicator offers a high degree of flexibility, and the location of the envelope's bands can be adjusted by (1) tweaking the parameters for the Rational Quadratic Kernel and (2) adjusting the lookback window for the custom ATR calculation. In a trending market, it is often helpful to use the Nadaraya-Watson estimate line as a floating SR and/or reversal zone. In a ranging market, it is often more convenient to use the two Upper Bands and two Lower Bands as reversal zones.
How are the Upper and Lower bounds calculated?
In this indicator, the Rational Quadratic (RQ) Kernel estimates the price value at each bar in a user-defined lookback window. From this estimation, the upper and lower bounds of the envelope are calculated based on a custom ATR calculated from the kernel estimations for the high, low, and close series, respectively. These calculations are then scaled against a user-defined multiplier, which can be used to further customize the Upper and Lower bounds for a given chart.
How to use Kernel Estimations like this for other indicators?
Kernel Functions are highly underrated, and when calibrated correctly, they have the potential to provide more value than any mundane moving average. For those interested in using non-repainting Kernel Estimations for technical analysis, I have written a Kernel Functions library that makes it easy to access various well-known kernel functions quickly. The Rational Quadratic Kernel is used in this implementation, but one can conveniently swap out other kernels from the library by modifying only a single line of code. For more details and usage examples, please refer to the Kernel Functions library located here:
Nadaraya-Watson non repainting [LPWN]// ENGLISH
The problem of the wonderfuls Nadaraya-Watson indicators is that they repainting, @jdehorty made an aproximation of the Nadaraya-Watson Estimator using raational Quadratic Kernel so i used this indicator as inspiration i just added the Upper and lower band using ATR with this we get an aproximation of Nadaraya-Watson Envelope without repainting
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.
ATR Period. Period to calculate the ATR (upper and lower bands)
Multiplier. Separation of the bands
// SPANISH
El problema de los maravillosos indicadores de Nadaraya-Watson es que repintan, @jdehorty hizo una aproximación delNadaraya-Watson Estimator usando un Kernel cuadrático racional, así que usé este indicador como inspiración y solo agregamos la banda superior e inferior usando ATR con esto obtenemos una aproximación de Nadaraya-Watson Envelope sin volver a pintar
Configuración:
Banda ancha. Este es el número de barras que el indicador utilizará como ventana retrospectiva.
Parámetro de ponderación relativa. El parámetro alfa para la función Rational Quadratic Kernel. Este es un hiperparámetro que controla la suavidad de la curva. Un valor más bajo de alfa dará como resultado una curva más suave y estirada, mientras que un valor más bajo dará como resultado una curva más ondulada con un ajuste más ajustado a los datos. A medida que este parámetro se acerque a 0, los marcos de tiempo más largos ejercerán más influencia en la estimación y, a medida que se acerque al infinito, la curva será idéntica a la que produce el Gaussian Kernel.
Suavizado de color. Alterna el mecanismo para colorear el gráfico de estimación entre la tasa de cambio y los modos cruzados.
Período ATR. Periodo para calcular el ATR (bandas superior e inferior)
Multiplicador. Separación de las bandas
KernelFunctionsLibrary "KernelFunctions"
This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substitution/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels. Compared to Moving Averages (which are really just simple kernels themselves), these kernel functions are more adaptive and afford the user an unprecedented degree of customization and flexibility.
rationalQuadratic(_src, _lookback, _relativeWeight, _startAtBar)
Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_relativeWeight : Relative weighting of time frames. Smaller values result in a more stretched-out curve, and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Rational Quadratic Kernel.
gaussian(_src, _lookback, _startAtBar)
Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Gaussian Kernel.
periodic(_src, _lookback, _period, _startAtBar)
Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions that repeat themselves exactly.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period : The distance between repititions of the function.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Periodic Kernel.
locallyPeriodic(_src, _lookback, _period, _startAtBar)
Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.
Parameters:
_src : The source series.
_lookback : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.
_period : The distance between repititions of the function.
_startAtBar : Bar index on which to start regression. The first bars of a chart are often highly volatile, and omitting these initial bars often leads to a better overall fit.
Returns: yhat The estimated values according to the Locally Periodic Kernel.
Quantitative Kernel DelimiterQuantitative Kernel Delimiter QKD - aka "Fire and ICE" - is a six-level multiple Kernel regression estimator with cross-timeframe semi-coordinated delimiters (bands) enabled by mathematical validation to our own Kernel regression code with historical Kernel formulas having custom variable bandwidths , mults , and window width – all achieving an advanced alerting system and directional price-action pointers for Novice, Intermediate and Advanced Traders within the TradingView Graphical User Interface.
In the course of our work, we have found that such six delimiters are ideal for generating signals of varying strengths.
99.9% of observations should be in our delimiters' range:
Kernel regression is a nonparametric smoothing method for data modeling.
Kernel regression of statistics was derived independently by Nadaraya and Watson in 1964 with a mathematical foundation given by Parzen’s earlier work on kernel density estimation.
If you are interested in reading more about the mathematical basis of this method from which our code is derived, you can follow these scholarly links:
Expert Trading Systems: Modeling Financial Markets with Kernel Regression
Estimation of the bandwidth parameter in Nadaraya-Watson
Adaptive optimal kernel density estimation for directional data
How kernel regression differs from the other Moving Averages?
In most MA's data points in the specified lookback window are weighted equally. In contrast, the Gaussian 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 market.
Regression method from which our code is derived is a widely known formula that is laid out in many sources, we used this source:
Kernel regression estimation
Kernel
During the regression counting process, a `kernel function` is used, which is traditionally chosen from a wide variety of symmetric functions.
In this indicator, we use the Gaussian density of statistics as the kernel function.
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 kernel regression averages all the data contained within the range of the kernel function.
The effective range of the kernel function is defined by its window width .
Kernel Delimiters (Bands / Levels)
This indicator has 6 tailored price range* delimiters:
Cold / Fire - the furthest delimiters. In a range market when the price enters the cold/fire zones it is assumed that it has deviated strongly from the average and there is a high probability that it will immediately return to the average, or at least into the underlying zone, also in a trending market it signals a change in trend.
ALERT: the indicator performs best during relatively sideways price action within an established range. The trader must check higher timeframes during hits on the extreme Cold or Fire delimiter bands as a break in the lower, or even higher timeframe price range may result in a need to reset the regression calculation once price velocity calms down after a major move allowing the indicator to best function again. The reset will be done automatically by the indicator’s code. The indicator is not intended for use with unusually aggressive pricing behavior. Always beware of extreme market conditions. The indicator is intended as an ordinary range trading tool.
Gold / Green - we call it the middle ground / golden mean / happy medium zone. When the price comes out here but the momentum is not enough to get to the higher zone we consider it a good signal.
Pro - most often we receive signals in this area. We call it the professional zone because it is literally the zone for professional traders who know what they are dealing with.
*NOTE: the indicator is intended to be used as a range trading tool, and does not protect against total BREAKS from one Range to a new Range, wherein the bands reset for the trader.
Alerts / Labels
We have spent a lot of time implementing and testing signal labels* and alerts**.
Now you have access to an advanced alert system.
*NOTE: DUE TO the ongoing regression calculations performed by our code, the trader will note that a label may change color at a later point in time, or even soon after the hit on the quantitative delimiter band in question. This is a process that was reviewed and is favored to achieve visual clarity over historical accuracy for the trader. Real-time trading hits of price line to band, along with alerts generated, remain accurate. We look forward to receiving feedback on this issue from the end users. Additional revisions by our team on this matter are anticipated if a harmony between visual clarity and historical accuracy is not satisfied.
**NOTE: Smaller and especially micro timeframes will result in more repeated alerts given the tight proximity with price vis-à-vis the quantitative delimiter. Larger timeframes tend to eliminate any issue with repeated alerts aside from obvious re-contacting of the quantitative delimiter by the active price line.
You can turn off alerts you don't need in the indicator settings.
All alerts are set with one click.
Themes
Different people like different things, which is why we decided to make several visual design themes so you can choose what suits you.
Themes will continue to evolve over time.
Pro Theme:
Modern Theme:
How to remove colored text labels next to price scale to maximize screen space on mobile:
Go to General Chart Settings :
Click on “SCALES”
Un select “Indicators and financial name.”
Dynamic Mode
Projection of Indicator bands on history is subject to repainting due to its regressive calculation nature. Be cautious: old signals are drawn once at the first loading of the chart and by default (to speed up the start-up time of the indicator) correspond to the current regression levels. All labels remain in their places as the chart progresses. Also new, real-time labels appear on the chart, and do not disappear. In order to display the old signals on the chart as they were at the time of their appearance, uncheck the "History labels transition" in the indicator settings (it may increase the initial loading time of the chart but will give you an opportunity to check the alerts you received before and may also be useful for visual backtesting).
Because of the very nature of modeling financial markets (i.e., thousands of data records and perhaps hundreds of candidate predictors), the need for computational speed is paramount.
The use of kernel regression in data modeling for the types of problems associated with financial markets requires careful consideration of computational time.
Once we acknowledge that the order of the data is important, then the choice of the learning-data-set becomes crucial. The time dimension introduces another level of complexity to the analysis: how much importance do we attach to recent data records as opposed to earlier records? Is there a simple way to take this effect into consideration? Common sense leads us to the basic conclusion that if we are to predict a value of Y at a given time, we should only use learning data from an earlier time. But this procedure tends to be overly restrictive. This problem has a simple solution: All that one must do is to make the learning data set dynamic . In other words, once a record has been tested, it is then available for updating the learning data set prior to testing the next record. The analyst can allow the learning data set to grow, or, alternatively, for each record added, the earliest remaining record in the learning set can be discarded. These two alternatives have led us to the necessity of using moving window option and adding a disclaimer that dynamic mode is enabled.
This indicator will be updated frequently based on community feedback see the Author’s instructions below to get instant access
―――――――――――――――――――――
Liability Disclaimer
Never fully rely on one indicator as you trade. Successful trading may require an orchestral mindset and harmonіc blend of trading tools, know-how, and devices. VIP Trader . com is not responsible for any damages or losses incurred by use or misused of this indicator. Neither this description above, nor the indicator, is intended to be used as financial advisory tool, nor to be used without proper education or training in the field of trading.
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.
STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT is the backtest for the following indicator
Included:
This backtest uses a special implementation of ATR and ATR smoothing called "True Range Double" which is a range calculation that accounts for volatility skew.
You can set the backtest to 1-2 take profits with stop-loss
Signals can't exit on the same candle as the entry, this is coded in a way for 1-candle delay post entry
This should be coupled with the INDICATOR version linked above for the alerts and signals. Strategies won't paint the signal "L" or "S" until the entry actually happens, but indicators allow this, which is repainting on current candle, but this is an FYI if you want to get serious with Pinescript algorithmic botting
You can restrict the backtest by dates
It is advised that you understand what Heikin-Ashi candles do to strategies, the default settings for this backtest is NON Heikin-Ashi candles but you have the ability to change that in the source selection
This is a mathematically heavy, heavy-lifting strategy. Make sure you do your own research so you understand what is happening here.
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.
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
Nadaraya-Watson Envelope [LuxAlgo]This indicator builds upon the previously posted Nadaraya-Watson smoothers. Here we have created an envelope indicator based on Kernel Smoothing with integrated alerts from crosses between the price and envelope extremities. Unlike the Nadaraya-Watson estimator, this indicator follows a contrarian methodology.
Please note that by default this indicator can be subject to repainting. Users can use a non-repainting smoothing method available from the settings. The triangle labels are designed so that the indicator remains useful in real-time applications.
🔶 USAGE
🔹 Non Repainting
This tool can outline extremes made by the prices. This is achieved by estimating the underlying trend in the price, then calculating the mean absolute deviations from it, the obtained result is added/subtracted to the estimated underlying trend.
The non-repainting method estimates the underlying trend in price using an "endpoint Nadaraya-Watson estimator", and would return similar results to more classical band indicators.
🔹 Repainting
The repainting method makes use of the Nadaraya-Watson estimator to estimate the underlying trend in the price. The construction of the band extremities is the same as in the non-repainting method.
We can expect the price to reverse when crossing one of the envelope extremities. Crosses between the price and the envelopes extremities are indicated with triangles on the chart.
For real-time applications, triangles are always displayed when a cross occurs and remain displayed at the location it first appeared even if the cross is no longer visible after a recalculation of the envelope.
By popular demand, we have integrated alerts for this indicator from the crosses between the price and the envelope extremities. However, we do not recommend this precise method to be used alone or for solely real-time applications. We do not have data supporting the performance of this tool over more classical bands/envelope/channels indicators.
🔶 SETTINGS
Bandwidth: Controls the degree of smoothness of the envelopes, with higher values returning smoother results.
Mult: Controls the envelope width.
Source: Input source of the indicator.
Repainting Smoothing: Determine if a repainting or non-repainting method should be used for the calculation of the indicator.
🔶 RELATED SCRIPTS
For more information on the Nadaraya-Watson estimator see:
