Machine Learning SupertrendThe Machine Learning Supertrend is an advanced trend-following indicator that enhances the traditional Supertrend with Gaussian Process Regression (GPR) and kernel-based learning. Unlike conventional methods that rely purely on historical ATR values, this indicator integrates machine learning techniques to dynamically estimate volatility and forecast future price movements, resulting in a more adaptive and robust trend detection system.
At the core of this indicator lies Gaussian Process Regression (GPR), which utilizes a Radial Basis Function (RBF) kernel to model price distributions and anticipate future trends. Instead of simply looking at past price action, it constructs a kernel matrix, enabling a probabilistic approach to price forecasting. This allows the indicator to not only detect current trends but also project potential trend reversals with greater accuracy.
By applying machine learning to ATR estimation, the ML Supertrend dynamically adjusts its thresholds based on predicted values rather than a fixed multiplier. This makes the trend signals more responsive to market conditions, reducing false signals and minimizing whipsaws often seen with traditional Supertrend indicators. The upper and lower bands are no longer static but evolve based on the underlying price structure, improving the reliability of trend shifts.
When the price crosses these adaptive levels, the indicator detects a trend change and plots it accordingly. Green signifies a bullish trend, while red indicates a bearish one. Alerts can also be triggered when the trend shifts, allowing traders to react quickly to potential reversals.
What makes this approach powerful is its ability to adapt to different market conditions. Traditional ATR-based methods use fixed parameters that might not always be optimal, whereas this ML-driven Supertrend continuously refines its estimations based on real-time data. The result is a more intelligent, less lagging, and highly adaptive trend-following tool.
This indicator is particularly useful for traders looking to enhance trend-following strategies with AI-driven insights. It reduces noise, improves signal reliability, and even offers a degree of trend forecasting, making it ideal for those who want a more advanced and dynamic alternative to standard Supertrend indicators.
This indicator is provided for educational and informational purposes only. It does not constitute financial advice, and past performance is not indicative of future results. Trading involves risk, and users should conduct their own research and use proper risk management before making investment decisions.
Kernelregression
Machine Learning Price Target Prediction Signals [AlgoAlpha]Introducing the Machine Learning Price Target Predictions, a cutting-edge trading tool that leverages kernel regression to provide accurate price targets and enhance your trading strategy. This indicator combines trend-based signals with advanced machine learning techniques, offering predictive insights into potential price movements. Perfect for traders looking to make data-driven decisions with confidence.
What is Kernel Regression and How It Works
Kernel regression is a non-parametric machine learning technique that estimates the relationship between variables by weighting data points based on their similarity to a given input. The similarity is determined using a kernel function, such as the Gaussian (RBF) kernel, which assigns higher weights to closer data points and progressively lower weights to farther ones. This allows the model to make smooth and adaptive predictions, balancing recent data and historical trends.
Key Features
🎯 Predictive Price Targets : Uses kernel regression to estimate the magnitude of price movements.
📈 Dynamic Trend Analysis : Multiple trend detection methods, including EMA crossovers, Hull Moving Average, and SuperTrend.
🔧 Customizable Settings : Adjust bandwidth for kernel regression and tweak trend indicator parameters to suit your strategy.
📊 Visual Trade Levels : Displays take-profit and stop-loss levels directly on the chart with customizable colors.
📋 Performance Metrics : Real-time win rate, recommended risk-reward ratio, and training data size displayed in an on-chart table.
🔔 Alerts : Get notified for new trends, take-profit hits, and stop-loss triggers.
How to Use
🛠 Add the Indicator : Add it to your favorites and apply it to your chart. Configure the trend detection method (SuperTrend, HMA, or EMA crossover) and other parameters based on your preferences.
📊 Analyze Predictions : Observe the predicted move size, recommended risk-reward ratio, and trend direction. Use the displayed levels for trade planning.
🔔 Set Alerts : Enable alerts for trend signals, take-profit hits, or stop-loss triggers to stay informed without constant monitoring.
How It Works
The indicator calculates features such as price volatility, relative strength, and trend signals, which are stored during training periods. When a trend change is detected, the kernel regression model predicts the likely price move based on these features. Predictions are smoothed using the specified bandwidth to avoid overfitting while ensuring timely responses to feature changes. Visualized take-profit and stop-loss levels help traders optimize risk management. Real-time metrics like win rate and recommended risk-reward ratios provide actionable insights for decision-making.
Kernel Regression Envelope with SMI OscillatorThis script combines the predictive capabilities of the **Nadaraya-Watson estimator**, implemented by the esteemed jdehorty (credit to him for his excellent work on the `KernelFunctions` library and the original Nadaraya-Watson Envelope indicator), with the confirmation strength of the **Stochastic Momentum Index (SMI)** to create a dynamic trend reversal strategy. The core idea is to identify potential overbought and oversold conditions using the Nadaraya-Watson Envelope and then confirm these signals with the SMI before entering a trade.
**Understanding the Nadaraya-Watson Envelope:**
The Nadaraya-Watson estimator is a non-parametric regression technique that essentially calculates a weighted average of past price data to estimate the current underlying trend. Unlike simple moving averages that give equal weight to all past data within a defined period, the Nadaraya-Watson estimator uses a **kernel function** (in this case, the Rational Quadratic Kernel) to assign weights. The key parameters influencing this estimation are:
* **Lookback Window (h):** This determines how many historical bars are considered for the estimation. A larger window results in a smoother estimation, while a smaller window makes it more reactive to recent price changes.
* **Relative Weighting (alpha):** This parameter controls the influence of different time frames in the estimation. Lower values emphasize longer-term price action, while higher values make the estimator more sensitive to shorter-term movements.
* **Start Regression at Bar (x\_0):** This allows you to exclude the potentially volatile initial bars of a chart from the calculation, leading to a more stable estimation.
The script calculates the Nadaraya-Watson estimation for the closing price (`yhat_close`), as well as the highs (`yhat_high`) and lows (`yhat_low`). The `yhat_close` is then used as the central trend line.
**Dynamic Envelope Bands with ATR:**
To identify potential entry and exit points around the Nadaraya-Watson estimation, the script uses **Average True Range (ATR)** to create dynamic envelope bands. ATR measures the volatility of the price. By multiplying the ATR by different factors (`nearFactor` and `farFactor`), we create multiple bands:
* **Near Bands:** These are closer to the Nadaraya-Watson estimation and are intended to identify potential immediate overbought or oversold zones.
* **Far Bands:** These are further away and can act as potential take-profit or stop-loss levels, representing more extreme price extensions.
The script calculates both near and far upper and lower bands, as well as an average between the near and far bands. This provides a nuanced view of potential support and resistance levels around the estimated trend.
**Confirming Reversals with the Stochastic Momentum Index (SMI):**
While the Nadaraya-Watson Envelope identifies potential overextended conditions, the **Stochastic Momentum Index (SMI)** is used to confirm a potential trend reversal. The SMI, unlike a traditional stochastic oscillator, oscillates around a zero line. It measures the location of the current closing price relative to the median of the high/low range over a specified period.
The script calculates the SMI on a **higher timeframe** (defined by the "Timeframe" input) to gain a broader perspective on the market momentum. This helps to filter out potential whipsaws and false signals that might occur on the current chart's timeframe. The SMI calculation involves:
* **%K Length:** The lookback period for calculating the highest high and lowest low.
* **%D Length:** The period for smoothing the relative range.
* **EMA Length:** The period for smoothing the SMI itself.
The script uses a double EMA for smoothing within the SMI calculation for added smoothness.
**How the Indicators Work Together in the Strategy:**
The strategy enters a long position when:
1. The closing price crosses below the **near lower band** of the Nadaraya-Watson Envelope, suggesting a potential oversold condition.
2. The SMI crosses above its EMA, indicating positive momentum.
3. The SMI value is below -50, further supporting the oversold idea on the higher timeframe.
Conversely, the strategy enters a short position when:
1. The closing price crosses above the **near upper band** of the Nadaraya-Watson Envelope, suggesting a potential overbought condition.
2. The SMI crosses below its EMA, indicating negative momentum.
3. The SMI value is above 50, further supporting the overbought idea on the higher timeframe.
Trades are closed when the price crosses the **far band** in the opposite direction of the trade. A stop-loss is also implemented based on a fixed value.
**In essence:** The Nadaraya-Watson Envelope identifies areas where the price might be deviating significantly from its estimated trend. The SMI, calculated on a higher timeframe, then acts as a confirmation signal, suggesting that the momentum is shifting in the direction of a potential reversal. The ATR-based bands provide dynamic entry and exit points based on the current volatility.
**How to Use the Script:**
1. **Apply the script to your chart.**
2. **Adjust the "Kernel Settings":**
* **Lookback Window (h):** Experiment with different values to find the smoothness that best suits the asset and timeframe you are trading. Lower values make the envelope more reactive, while higher values make it smoother.
* **Relative Weighting (alpha):** Adjust to control the influence of different timeframes on the Nadaraya-Watson estimation.
* **Start Regression at Bar (x\_0):** Increase this value if you want to exclude the initial, potentially volatile, bars from the calculation.
* **Stoploss:** Set your desired stop-loss value.
3. **Adjust the "SMI" settings:**
* **%K Length, %D Length, EMA Length:** These parameters control the sensitivity and smoothness of the SMI. Experiment to find settings that work well for your trading style.
* **Timeframe:** Select the higher timeframe you want to use for SMI confirmation.
4. **Adjust the "ATR Length" and "Near/Far ATR Factor":** These settings control the width and sensitivity of the envelope bands. Smaller ATR lengths make the bands more reactive to recent volatility.
5. **Customize the "Color Settings"** to your preference.
6. **Observe the plots:**
* The **Nadaraya-Watson Estimation (yhat)** line represents the estimated underlying trend.
* The **near and far upper and lower bands** visualize potential overbought and oversold zones based on the ATR.
* The **fill areas** highlight the regions between the near and far bands.
7. **Look for entry signals:** A long entry is considered when the price touches or crosses below the lower near band and the SMI confirms upward momentum. A short entry is considered when the price touches or crosses above the upper near band and the SMI confirms downward momentum.
8. **Manage your trades:** The script provides exit signals when the price crosses the far band. The fixed stop-loss will also close trades if the price moves against your position.
**Justification for Combining Nadaraya-Watson Envelope and SMI:**
The combination of the Nadaraya-Watson Envelope and the SMI provides a more robust approach to identifying potential trend reversals compared to using either indicator in isolation. The Nadaraya-Watson Envelope excels at identifying potential areas where the price is overextended relative to its recent history. However, relying solely on the envelope can lead to false signals, especially in choppy or volatile markets. By incorporating the SMI as a confirmation tool, we add a momentum filter that helps to validate the potential reversals signaled by the envelope. The higher timeframe SMI further helps to filter out noise and focus on more significant shifts in momentum. The ATR-based bands add a dynamic element to the entry and exit points, adapting to the current market volatility. This mashup aims to leverage the strengths of each indicator to create a more reliable trading strategy.
Cosine Kernel Regressions [QuantraSystems]Cosine Kernel Regressions
Introduction
The Cosine Kernel Regressions indicator (CKR) uses mathematical concepts to offer a unique approach to market analysis. This indicator employs Kernel Regressions using bespoke tunable Cosine functions in order to smoothly interpret a variety of market data, providing traders with incredibly clean insights into market trends.
The CKR is particularly useful for traders looking to understand underlying trends without the 'noise' typical in raw price movements. It can serve as a standalone trend analysis tool or be combined with other indicators for more robust trading strategies.
Legend
Fast Trend Signal Line - This is the foreground oscillator, it is colored upon the earliest confirmation of a change in trend direction.
Slow Trend Signal Line - This oscillator is calculated in a similar manner. However, it utilizes a lower frequency within the cosine tuning function, allowing it to capture longer and broader trends in one signal. This allows for tactical trading; the user can trade smaller moves without losing sight of the broader trend.
Case Study
In this case study, the CKR was used alongside the Triple Confirmation Kernel Regression Oscillator (KRO)
Initially, the KRO indicated an oversold condition, which could be interpreted as a signal to enter a long position in anticipation of a price rebound. However, the CKR’s fast trend signal line had not yet confirmed a positive trend direction - suggesting that entering a trade too early and without confirmation could be a mistake.
Waiting for a confirmed positive trend from the CKR proved beneficial for this trade. A few candles after the oversold signal, the CKR's fast trend signal line shifted upwards, indicating a strong upward momentum. This was the optimal entry point suggested by the CKR, occurring after the confirmation of the trend change, which significantly reduced the likelihood of entering during a false recovery or continuation of the downtrend.
This is one of the many uses of the CKR - by timing entries using the fast signal line , traders could avoid unnecessary losses by preventing premature entries.
Methodology
The methodology behind CKR is a multi-layered approach and utilizes many ‘base’ indicators.
Relative Strength Index
Stochastic Oscillator
Bollinger Band Percent
Chande Momentum Oscillator
Commodity Channel Index
Fisher Transform
Volume Zone Oscillator
The calculated output from each indicator is standardized and scaled before being averaged. This prevents any single indicator from overpowering the resulting signal.
// ╔════════════════════════════════╗ //
// ║ Scaling/Range Adjustment ║ //
// ╚════════════════════════════════╝ //
RSI_ReScale (_res ) => ( _res - 50 ) * 2.8
STOCH_ReScale (_stoch ) => ( _stoch - 50 ) * 2
BBPCT_ReScale (_bbpct ) => ( _bbpct - 0.5 ) * 120
CMO_ReScale (_chandeMO ) => ( _chandeMO * 1.15 )
CCI_ReScale (_cci ) => ( _cci / 2 )
FISH_ReScale (_fish1 ) => ( _fish1 * 30 )
VZO_ReScale (_VP, _TV ) => (_VP / _TV) * 110
These outputs are then fed into a customized cosine kernel regression function, which smooths the data, and combines all inputs into a single coherent output.
// ╔════════════════════════════════╗ //
// ║ COSINE KERNEL REGRESSIONS ║ //
// ╚════════════════════════════════╝ //
// Define a function to compute the cosine of an input scaled by a frequency tuner
cosine(x, z) =>
// Where x = source input
// y = function output
// z = frequency tuner
var y = 0.
y := math.cos(z * x)
Y
// Define a kernel that utilizes the cosine function
kernel(x, z) =>
var y = 0.
y := cosine(x, z)
math.abs(x) <= math.pi/(2 * z) ? math.abs(y) : 0. // cos(zx) = 0
// The above restricts the wave to positive values // when x = π / 2z
The tuning of the regression is adjustable, allowing users to fine-tune the sensitivity and responsiveness of the indicator to match specific trading strategies or market conditions. This robust methodology ensures that CKR provides a reliable and adaptable tool for market analysis.
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.
Triple Confirmation Kernel Regression Overlay [QuantraSystems]Kernel Regression Oscillator - Overlay
Introduction
The Kernel Regression Oscillator (ᏦᏒᎧ) represents an advanced tool for traders looking to capitalize on market trends.
This Indicator is valuable in identifying and confirming trend directions, as well as probabilistic and dynamic oversold and overbought zones.
It achieves this through a unique composite approach using three distinct Kernel Regressions combined in an Oscillator.
The additional Chart Overlay Indicator adds confidence to the signal.
Which is this Indicator.
This methodology helps the trader to significantly reduce false signals and offers a more reliable indication of market movements than more widely used indicators can.
Legend
The upper section is the Overlay. It features the Signal Wave to display the current trend.
Its Overbought and Oversold zones start at 50% and end at 100% of the selected Standard Deviation (default σ = 3), which can indicate extremely rare situations which can lead to either a softening momentum in the trend or even a mean reversion situation.
The lower one is the Base Chart.
The Indicator is linked here
It features the Kernel Regression Oscillator to display a composite of three distinct regressions, also displaying current trend.
Its Overbought and Oversold zones start at 50% and end at 100% of the selected Standard Deviation (default σ = 2), which can indicate extremely rare situations.
Case Study
To effectively utilize the ᏦᏒᎧ, traders should use both the additional Overlay and the Base
Chart at the same time. Then focus on capturing the confluence in signals, for example:
If the 𝓢𝓲𝓰𝓷𝓪𝓵 𝓦𝓪𝓿𝓮 on the Overlay and the ᏦᏒᎧ on the Base Chart both reside near the extreme of an Oversold zone the probability is higher than normal that momentum in trend may soften or the token may even experience a reversion soon.
If a bar is characterized by an Oversold Shading in both the Overlay and the Base Chart, then the probability is very high to experience a reversion soon.
In this case the trader may want to look for appropriate entries into a long position, as displayed here.
If a bar is characterized by an Overbought Shading in either Overlay or Base Chart, then the probability is high for momentum weakening or a mean reversion.
In this case the trade may have taken profit and closed his long position, as displayed here.
Please note that we always advise to find more confluence by additional indicators.
Recommended Settings
Swing Trading (1D chart)
Overlay
Bandwith: 45
Width: 2
SD Lookback: 150
SD Multiplier: 2
Base Chart
Bandwith: 45
SD Lookback: 150
SD Multiplier: 2
Fast-paced, Scalping (4min chart)
Overlay
Bandwith: 75
Width: 2
SD Lookback: 150
SD Multiplier: 3
Base Chart
Bandwith: 45
SD Lookback: 150
SD Multiplier: 2
Notes
The Kernel Regression Oscillator on the Base Chart is also sensitive to divergences if that is something you are keen on using.
For maximum confluence, it is recommended to use the indicator both as a chart overlay and in its Base Chart.
Please pay attention to shaded areas with Standard Deviation settings of 2 or 3 at their outer borders, and consider action only with high confidence when both parts of the indicator align on the same signal.
This tool shows its best performance on timeframes lower than 4 hours.
Traders are encouraged to test and determine the most suitable settings for their specific trading strategies and timeframes.
The trend following functionality is indicated through the "𝓢𝓲𝓰𝓷𝓪𝓵 𝓦𝓪𝓿𝓮" Line, with optional "Up" and "Down" arrows to denote trend directions only (toggle “Show Trend Signals”).
Methodology
The Kernel Regression Oscillator takes three distinct kernel regression functions,
used at similar weight, in order to calculate a balanced and smooth composite of the regressions. Part of it are:
The Epanechnikov Kernel Regression: Known for its efficiency in smoothing data by assigning less weight to data points further away from the target point than closer data points, effectively reducing variance.
The Wave Kernel Regression: Similarly assigning weight to the data points based on distance, it captures repetitive and thus wave-like patterns within the data to smoothen out and reduce the effect of underlying cyclical trends.
The Logistic Kernel Regression: This uses the logistic function in order to assign weights by probability distribution on the distance between data points and target points. It thus avoids both bias and variance to a certain level.
kernel(source, bandwidth, kernel_type) =>
switch kernel_type
"Epanechnikov" => math.abs(source) <= 1 ? 0.75 * (1 - math.pow(source, 2)) : 0.0
"Logistic" => 1/math.exp(source + 2 + math.exp(-source))
"Wave" => math.abs(source) <= 1 ? (1 - math.abs(source)) * math.cos(math.pi * source) : 0.
kernelRegression(src, bandwidth, kernel_type) =>
sumWeightedY = 0.
sumKernels = 0.
for i = 0 to bandwidth - 1
base = i*i/math.pow(bandwidth, 2)
kernel = kernel(base, 1, kernel_type)
sumWeightedY += kernel * src
sumKernels += kernel
(src - sumWeightedY/sumKernels)/src
// Triple Confirmations
Ep = kernelRegression(source, bandwidth, 'Epanechnikov' )
Lo = kernelRegression(source, bandwidth, 'Logistic' )
Wa = kernelRegression(source, bandwidth, 'Wave' )
By combining these regressions in an unbiased average, we follow our principle of achieving confluence for a signal or a decision, by stacking several edges to increase the probability that we are correct.
// Average
AV = math.avg(Ep, Lo, Wa)
The Standard Deviation bands take defined parameters from the user, in this case sigma of ideally between 2 to 3,
to help the indicator detect extremely improbable conditions and thus take an inversely probable signal from it to forward to the user.
The parameter settings and also the visualizations allow for ample customizations by the trader. The indicator comes with default and recommended settings.
For questions or recommendations, please feel free to seek contact in the comments.
Triple Confirmation Kernel Regression Base [QuantraSystems]Kernel Regression Oscillator - BASE
Introduction
The Kernel Regression Oscillator (ᏦᏒᎧ) represents an advanced tool for traders looking to capitalize on market trends.
This Indicator is valuable in identifying and confirming trend directions, as well as probabilistic and dynamic oversold and overbought zones.
It achieves this through a unique composite approach using three distinct Kernel Regressions combined in an Oscillator. The additional Chart Overlay Indicator adds confidence to the signal.
This methodology helps the trader to significantly reduce false signals and offers a more reliable indication of market movements than more widely used indicators can.
Legend
The upper section is the Overlay. It features the Signal Wave to display the current trend.
Its Overbought and Oversold zones start at 50% and end at 100% of the selected Standard Deviation (default σ = 3), which can indicate extremely rare situations which can lead to either a softening momentum in the trend or even a mean reversion situation.
The lower one is the Base Chart - This Indicator.
It features the Kernel Regression Oscillator to display a composite of three distinct regressions, also displaying current trend.
Its Overbought and Oversold zones start at 50% and end at 100% of the selected Standard Deviation (default σ = 2), which can indicate extremely rare situations.
Case Study
To effectively utilize the ᏦᏒᎧ, traders should use both the additional Overlay and the Base
Chart at the same time. Then focus on capturing the confluence in signals, for example:
If the 𝓢𝓲𝓰𝓷𝓪𝓵 𝓦𝓪𝓿𝓮 on the Overlay and the ᏦᏒᎧ on the Base Chart both reside near the extreme of an Oversold zone the probability is higher than normal that momentum in trend may soften or the token may even experience a reversion soon.
If a bar is characterized by an Oversold Shading in both the Overlay and the Base Chart, then the probability is very high to experience a reversion soon.
In this case the trader may want to look for appropriate entries into a long position, as displayed here.
If a bar is characterized by an Overbought Shading in either Overlay or Base Chart, then the probability is high for momentum weakening or a mean reversion.
In this case the trade may have taken profit and closed his long position, as displayed here.
Please note that we always advise to find more confluence by additional indicators.
Recommended Settings
Swing Trading (1D chart)
Overlay
Bandwith: 45
Width: 2
SD Lookback: 150
SD Multiplier: 2
Base Chart
Bandwith: 45
SD Lookback: 150
SD Multiplier: 2
Fast-paced, Scalping (4min chart)
Overlay
Bandwith: 75
Width: 2
SD Lookback: 150
SD Multiplier: 3
Base Chart
Bandwith: 45
SD Lookback: 150
SD Multiplier: 2
Notes
The Kernel Regression Oscillator on the Base Chart is also sensitive to divergences if that is something you are keen on using.
For maximum confluence, it is recommended to use the indicator both as a chart overlay and in its Base Chart.
Please pay attention to shaded areas with Standard Deviation settings of 2 or 3 at their outer borders, and consider action only with high confidence when both parts of the indicator align on the same signal.
This tool shows its best performance on timeframes lower than 4 hours.
Traders are encouraged to test and determine the most suitable settings for their specific trading strategies and timeframes.
The trend following functionality is indicated through the "𝓢𝓲𝓰𝓷𝓪𝓵 𝓦𝓪𝓿𝓮" Line, with optional "Up" and "Down" arrows to denote trend directions only (toggle “Show Trend Signals”).
Methodology
The Kernel Regression Oscillator takes three distinct kernel regression functions,
used at similar weight, in order to calculate a balanced and smooth composite of the regressions. Part of it are:
The Epanechnikov Kernel Regression: Known for its efficiency in smoothing data by assigning less weight to data points further away from the target point than closer data points, effectively reducing variance.
The Wave Kernel Regression: Similarly assigning weight to the data points based on distance, it captures repetitive and thus wave-like patterns within the data to smoothen out and reduce the effect of underlying cyclical trends.
The Logistic Kernel Regression: This uses the logistic function in order to assign weights by probability distribution on the distance between data points and target points. It thus avoids both bias and variance to a certain level.
kernel(source, bandwidth, kernel_type) =>
switch kernel_type
"Epanechnikov" => math.abs(source) <= 1 ? 0.75 * (1 - math.pow(source, 2)) : 0.0
"Logistic" => 1/math.exp(source + 2 + math.exp(-source))
"Wave" => math.abs(source) <= 1 ? (1 - math.abs(source)) * math.cos(math.pi * source) : 0.
kernelRegression(src, bandwidth, kernel_type) =>
sumWeightedY = 0.
sumKernels = 0.
for i = 0 to bandwidth - 1
base = i*i/math.pow(bandwidth, 2)
kernel = kernel(base, 1, kernel_type)
sumWeightedY += kernel * src
sumKernels += kernel
(src - sumWeightedY/sumKernels)/src
// Triple Confirmations
Ep = kernelRegression(source, bandwidth, 'Epanechnikov' )
Lo = kernelRegression(source, bandwidth, 'Logistic' )
Wa = kernelRegression(source, bandwidth, 'Wave' )
By combining these regressions in an unbiased average, we follow our principle of achieving confluence for a signal or a decision, by stacking several edges to increase the probability that we are correct.
// Average
AV = math.avg(Ep, Lo, Wa)
The Standard Deviation bands take defined parameters from the user, in this case sigma of ideally between 2 to 3,
to help the indicator detect extremely improbable conditions and thus take an inversely probable signal from it to forward to the user.
The parameter settings and also the visualizations allow for ample customizations by the trader. The indicator comes with default and recommended settings.
For questions or recommendations, please feel free to seek contact in the comments.
