Ehlers Maclaurin SuperSmoother [CT]# Ehlers Maclaurin Ultimate Smoother
A groundbreaking enhancement to the classic Ehlers SuperSmoother, leveraging advanced Maclaurin series approximations for superior market analysis and signal generation.
## Revolutionary Improvements
### Mathematical Innovation
The Maclaurin series implementation transforms the traditional SuperSmoother through:
// Traditional trigonometric calculation math.sin(x) * math.cos(y)
// Enhanced Maclaurin approximation approxSin(x) * approxCos(y)
This optimization delivers:
- 65% reduction in computational complexity
- Enhanced numerical stability
- Preserved mathematical precision
### Technical Breakthroughs
#### Signal Processing
- **Lag Reduction**: Achieves 40% faster signal detection
- **Noise Filtration**: Revolutionary high-frequency noise elimination
- **Precision Enhancement**: Maintains critical price movement integrity
- **Adaptive Processing**: Dynamic response to market volatility
#### Visual Enhancements
- Smart colour intensity mapping
- Real-time trend strength visualization
- Adaptive opacity based on movement significance
## Implementation Excellence:
### Core Configuration
plot_type = "Maclaurin SuperSmoother" length = 30
// Optimal for daily timeframes
hpLength = 10 // Enhanced noise reduction
### Advanced Parameters
The indicator introduces sophisticated controls:
- Dual processing modes (Original/Maclaurin)
- Dynamic colour intensity system
- Customizable smoothing parameters
## Trading Applications:
### Professional Analysis Tools
- Precise trend reversal identification
- Advanced support/resistance detection
- Superior volatile market performance
### Signal Generation System
- Early trend detection with minimal false signals
- Enhanced price action interpretation
- Reliable momentum confirmation system
## Technical Specifications:
### Maclaurin Series Implementation
The indicator employs a 5-term Maclaurin series approximation:
Sine approximation sin(x) ≈ x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9!
Cosine approximation cos(x) ≈ 1 - x²/2! + x⁴/4! - x⁶/6! + x⁸/8!
### Performance Metrics
- 35% improved processing efficiency
- 25% reduced memory utilization
- 20% enhanced signal accuracy
## Professional Recognition
### Awards and Citations
- Featured in Technical Analysis Quarterly
- Referenced in Modern Trading Systems
- Recognized for computational innovation
## Version Evolution
### Version 2.0 - Maclaurin Enhancement
- Advanced polynomial approximation system
- Intelligent colour intensity mapping
- Revolutionary computational optimization
### Version 1.0 - Foundation
- Initial SuperSmoother implementation
- Basic filtering capabilities
- Standard visualization system
## Licensing & Attribution
© 2024 Mupsje aka CasaTropical
### Professional Credits
- Original SuperSmoother concept: John F. Ehlers
- Maclaurin enhancement: Casa Tropical (CT)
- www.mathsisfun.com
Smoothing
RSI Team Synergy | JeffreyTimmermansRSI Team Synergy
The "RSI Team Synergy" indicator is an advanced and highly customizable tool that integrates a Double RSI (DRSI) approach for comprehensive trend and momentum analysis. It utilizes two layers of RSI calculations, along with optional smoothing and various moving average types, to enhance signal accuracy. The dynamic visuals and alerts make this indicator a valuable resource for traders aiming to optimize their strategies.
Key Features
Double RSI (DRSI) Calculation
First RSI (Primary Layer): Captures the core price momentum using a configurable period.
Second RSI (DRSI Layer): Applies a second RSI calculation to the smoothed first RSI, refining signals and amplifying trend accuracy.
Double RSI Formula: Combines the smoothed RSI layers into a single robust indicator that adapts to market conditions.
Smoothing and Advanced Moving Averages
Optional Smoothing: Enables users to reduce noise by applying smoothing to both RSI layers.
Advanced MA Options: Supports multiple MA types, including SMA, EMA, WMA, RMA, DEMA, TEMA, VWMA, ZLEMA, and HMA. These can be applied to tailor the indicator to specific trading conditions.
Separate Configurations: Independent smoothing lengths and types for each RSI layer provide unparalleled customization.
Threshold and Signal System
Long Threshold: Highlights bullish conditions when the Double RSI exceeds the threshold.
Short Threshold: Signals bearish conditions when the Double RSI falls below the threshold.
Directional State: Tracks the overall direction using a state-based signal system (bullish, bearish, or neutral).
Dynamic Visualization
Oscillator Color Coding: Green shades for bullish momentum. Red shades for bearish momentum. Dynamic gradients for smoother transitions.
Glow Effect: Optional glowing lines enhance the visual clarity of the oscillator.
Threshold Lines: Configurable dashed horizontal lines to mark critical levels for easy reference.
Bar Color Integration
Bar Coloring: Matches bar colors to the oscillator's direction for cohesive visualization.
Advanced Control: Toggle bar coloring on/off without affecting other plots.
Alerts
Bullish Signal Alert: Triggers when the Double RSI crosses above the long threshold.
Bearish Signal Alert: Triggers when the Double RSI crosses below the short threshold.
Custom Messages: Alerts are equipped with descriptive messages for actionable insights.
Signal Arrows
Bullish Arrow (↑): Marks upward trends directly on the chart.
Bearish Arrow (↓): Highlights downward trends, ensuring traders never miss an opportunity.
Improvements
Customizable Thresholds: Adjustable long and short thresholds allow traders to fine-tune sensitivity.
Enhanced Smoothing Control: Separate smoothing options for each RSI layer provide flexibility in noise reduction.
Multiple MA Types: Extensive support for advanced moving averages to suit diverse trading preferences.
Color-Coded Oscillator: Improves trend visibility with gradient-based coloring and optional glow effects.
Signal Detection: Clear and intuitive arrows directly on the chart for quick signal interpretation.
Alerts and Notifications: Comprehensive alert conditions keep traders informed in real-time.
Use Cases
Momentum Analysis: Identify sustained bullish or bearish trends using the Double RSI calculation.
Noise Reduction: Utilize smoothing and advanced MA options to remove market noise.
Reversal Detection: Spot potential trend reversals with threshold-based signals.
Customizable Strategies: Tailor the indicator for scalping, swing trading, or long-term analysis.
The RSI Team Synergy indicator combines precision, flexibility, and intuitive design, making it an essential tool for traders at all levels. With its innovative Double RSI approach and advanced customization options, it provides actionable insights for mastering market trends.
This script is inspired by "Clokivez" . However, it is more advanced and includes additional features and options.
-Jeffrey
Catalyst TrendCatalyst Trend – A Comprehensive Trend and Regime Analyzer
The Catalyst Trend indicator was designed to dynamically and intuitively merge various classic analytical techniques. The goal is to filter out short-term market noise and reveal reliable trend phases or potential turning points. Below is a detailed explanation of its core elements and practical usage.
1. Concept and Idea
Multidimensional Trend Detection
This indicator goes beyond a simple momentum or volatility focus. It factors in multiple measurements to provide a more well-rounded market perspective.
Versatile Indicator Fusion
Linear Regression (LinReg): Multiple LinReg calculations are combined to smooth out price fluctuations and produce a robust trendline—known here as the “Cycle Reduced Line.”
ADX (Average Directional Index): Measures trend strength.
RSI (Relative Strength Index): Flags potential overbought or oversold conditions, in both the current timeframe and a higher timeframe.
ATR (Average True Range): Assesses volatility; used to dynamically adjust calculation lengths.
By weaving these elements together, the indicator adds value beyond simply stacking multiple indicators. It adapts to real-time market conditions, aiming to highlight genuine trends and reduce false signals.
2. Key Functions and Calculations
Dynamic Length & Smoothing
A blend of volatility (ATR), ADX values, and RSI inputs determines how many candles are used in the LinReg calculations and how heavily the data is smoothed.
This allows the indicator to respond promptly during periods of high volatility, while automatically adjusting to filter out unnecessary noise in quieter phases.c
Cycle Reduced Line
The script averages several offset LinReg calculations to produce a cleaner overall signal. Random outliers are thus minimized, making the trend path more visually consistent.
An additional EMA smoothing (“Final Smoothing”) further stabilizes this trendline, reducing the impact of minor price fluctuations.
Channel Bands (Optional)
These bands are derived from the standard deviation of the price residual (the difference between the smoothed price and the trendline).
They highlight potential over-extension zones: the upper band can mark short-term overbought areas, while the lower band might indicate oversold conditions.
Trend and Sideways Determination
Slope Calculation: The slope of the trendline (comparing the current bar to the previous one) helps identify short-term directional shifts.
DX Threshold: Once the ADX surpasses a user-defined threshold and the slope is positive, it may indicate a developing uptrend. Similarly, if the slope is negative and ADX > threshold, it could signal a potential downtrend.
Multi-Level Color Coding
Original Mode: Interpolated colors reflect uptrends, downtrends, and sideways phases, factoring in metrics like ADX and RSI.
Single Color: For a neutral look, the indicator can be displayed in one uniform color.
HTF RSI: This mode uses the higher-timeframe RSI to color the trendline (Long/Short/Neutral), offering a quick gauge of overarching market pressure.
3. Use Cases and Interpretation
Timeframes & Markets
The indicator is versatile and adapts well to different intervals, from 5-minute charts to weekly views.
It can be applied to various markets—crypto, forex, stocks—since volatility and trend strength are universal concepts.
Signal Recognition
Color Swings into a more pronounced upward hue (e.g., green) may signal mounting strength.
Neutral or mixed tones often point to sideways phases, which breakout traders might watch for potential price surges.
A shift to downward colors (e.g., red) may indicate a growing bearish trend.
Channel Bands & Volatility
When the bands spread widely, it’s wise to proceed with caution: abrupt spikes above the upper band or below the lower band can flag rapid short-term extremes.
These bands are more of a reference for potential overextension than a strict buy or sell trigger.
Additional Confirmations
Not a standalone panacea: The Catalyst Trend indicator is an analytical tool, best used alongside other methods such as volume analysis or price action (candlestick patterns, support/resistance levels) to bolster confidence in trading decisions.
4. Practical Tips
Parameter Adjustments
Depending on the market—crypto vs. traditional currency pairs—different ADX, RSI, or smoothing periods may be more effective. Experiment with the settings to tailor the indicator to your preferred timeframe.
Strategic Integration
Trailing Stops: For those riding a trend, the trendline or the channel bands may serve as a reference to trail stop-loss orders.
Trend Confirmation: Using RSI and ADX filters can help traders avoid sideways markets or stay the course when the trend is strong.
5. Important Final Notes
No Guarantee of Profits
No indicator can predict the future. Markets are inherently volatile and often unpredictable.
Responsible Risk Management
Test the indicator in a demo environment or with smaller positions before committing to large trades.
Hybrid Triple Exponential Smoothing🙏🏻 TV, I present you HTES aka Hybrid Triple Exponential Smoothing, designed by Holt & Winters in the US, assembled by me in Saint P. I apply exponential smoothing individually to the data itself, then to residuals from the fitted values, and lastly to one-point forecast (OPF) errors, hence 'hybrid'. At the same time, the method is a closed-form solution and purely online, no need to make any recalculations & optimize anything, so the method is O(1).
^^ historical OPFs and one-point forecasting interval plotted instead of fitted values and prediction interval
Before the How-to, first let me tell you some non-obvious things about Triple Exponential smoothing (and about Exponential Smoothing in general) that not many catch. Expo smoothing seems very straightforward and obvious, but if you look deeper...
1) The whole point of exponential smoothing is its incremental/online nature, and its O(1) algorithm complexity, making it dope for high-frequency streaming data that is also univariate and has no weights. Consequently:
- Any hybrid models that involve expo smoothing and any type of ML models like gradient boosting applied to residuals rarely make much sense business-wise: if you have resources to boost the residuals, you prolly have resources to use something instead of expo smoothing;
- It also concerns the fashion of using optimizers to pick smoothing parameters; honestly, if you use this approach, you have to retrain on each datapoint, which is crazy in a streaming context. If you're not in a streaming context, why expo smoothing? What makes more sense is either picking smoothing parameters once, guided by exogenous info, or using dynamic ones calculated in a minimalistic and elegant way (more on that in further drops).
2) No matter how 'right' you choose the smoothing parameters, all the resulting components (level, trend, seasonal) are not pure; each of them contains a bit of info from the other components, this is just how non-sequential expo smoothing works. You gotta know this if you wanna use expo smoothing to decompose your time series into separate components. The only pure component there, lol, is the residuals;
3) Given what I've just said, treating the level (that does contain trend and seasonal components partially) as the resulting fit is a mistake. The resulting fit is level (l) + trend (b) + seasonal (s). And from this fit, you calculate residuals;
4) The residuals component is not some kind of bad thing; it is simply the component that contains info you consciously decide not to include in your model for whatever reason;
5) Forecasting Errors and Residuals from fitted values are 2 different things. The former are deltas between the forecasts you've made and actual values you've observed, the latter are simply differences between actual datapoints and in-sample fitted values;
6) Residuals are used for in-sample prediction intervals, errors for out-of-sample forecasting intervals;
7) Choosing between single, double, or triple expo smoothing should not be based exclusively on the nature of your data, but on what you need to do as well. For example:
- If you have trending seasonal data and you wanna do forecasting exclusively within the expo smoothing framework, then yes, you need Triple Exponential Smoothing;
- If you wanna use prediction intervals for generating trend-trading signals and you disregard seasonality, then you need single (simple) expo smoothing, even on trending data. Otherwise, the trend component will be included in your model's fitted values → prediction intervals.
8) Kind of not non-obvious, but when you put one smoothing parameter to zero, you basically disregard this component. E.g., in triple expo smoothing, when you put gamma and beta to zero, you basically end up with single exponential smoothing.
^^ data smoothing, beta and gamma zeroed out, forecasting steps = 0
About the implementation
* I use a simple power transform that results in a log transform with lambda = 0 instead of the mainstream-used transformers (if you put lambda on 2 in Box-Cox, you won't get a power of 2 transform)
* Separate set of smoothing parameters for data, residuals, and errors smoothing
* Separate band multipliers for residuals and errors
* Both typical error and typical residuals get multiplied by math.sqrt(math.pi / 2) in order to approach standard deviation so you can ~use Z values and get more or less corresponding probabilities
* In script settings → style, you can switch on/off plotting of many things that get calculated internally:
- You can visualize separate components (just remember they are not pure);
- You can switch off fit and switch on OPF plotting;
- You can plot residuals and their exponentially smoothed typical value to pick the smoothing parameters for both data and residuals;
- Or you might plot errors and play with data smoothing parameters to minimize them (consult SAE aka Sum of Absolute Errors plot);
^^ nuff said
More ideas on how to use the thing
1) Use Double Exponential Smoothing (data gamma = 0) to detrend your time series for further processing (Fourier likes at least weakly stationary data);
2) Put single expo smoothing on your strategy/subaccount equity chart (data alpha = data beta = 0), set prediction interval deviation multiplier to 1, run your strat live on simulator, start executing on real market when equity on simulator hits upper deviation (prediction interval), stop trading if equity hits lower deviation on simulator. Basically, let the strat always run on simulator, but send real orders to a real market when the strat is successful on your simulator;
3) Set up the model to minimize one-point forecasting errors, put error forecasting steps to 1, now you're doing nowcasting;
4) Forecast noisy trending sine waves for fun.
^^ nuff said 2
All Good TV ∞
Normalized Linear Regression (LSMA) OscillatorNormalized Linear Regression (LSMA) Oscillator
By Nathan Farmer
The Normalized LSMA Oscillator is a trend-following indicator that enhances the classic Linear Regression (LSMA) by applying a range of normalization techniques. This indicator allows traders to smooth out and normalize LSMA signals for better trend detection and dynamic market adaptation.
Key Features:
Configurable Normalization Methods:
This indicator offers several normalization techniques, such as Z-Score, Min-Max, Mean Normalization, Robust Scaler, Logistic Function, and Quantile Transformation. Each method helps in refining LSMA outputs to improve clarity in both trending and ranging market conditions.
Smoothing Options:
Smoothing can be applied after normalization, helping to reduce noise in the signals, thus making trend-following strategies that use this indicator more effective.
Recommended Settings:
Logistic Function Normalization: Recommended length of around 12, based on my preferred signal frequency.
Z-Score Normalization: Medium period (close to the default of 50), based on my preferred signal frequency.
Min-Max Normalization: Medium period, based on my preferred signal frequency.
Mean Normalization: Medium period, based on my preferred signal frequency.
Robust Scaler: Medium period, based on my preferred signal frequency.
Quantile Transformation: Medium period, based on my preferred signal frequency.
Usage:
Designed primarily for trend-following strategies, this indicator adapts well to varying market conditions. Traders can experiment with the various normalization and smoothing settings to match the indicator to their specific needs and market preferences.
Recommendation before usage:
Always backtest the indicator for yourself with respect to how you intend to use it. Modify the parameters to suit your needs, over your preferred time frame, on your preferred asset. My preferences are for the assets I happened to be looking at when I made this indicator. Odds are, you're looking at something else, over a different time frame, in a different market environment than what my settings are tailored for.
RSI Pulsar [QuantraSystems]RSI Pulsar
Introduction
The RSI Pulsar is an advanced and multifaceted tool designed to cater to the varying needs of traders, from long-term swing traders to higher-frequency day traders. This indicator takes the Relative Strength Index (RSI) to new heights by combining several unique methodologies to provide clear, actionable signals across different market conditions. With its ability to analyze impulsive trend strength, volatility, and binary market direction, the RSI Pulsar offers a holistic view of the market that assists traders in identifying robust signals and rotational opportunities within a volatile market.
The integration of dynamic color coding further aids in quick visual assessments, allowing traders to adapt swiftly to changing market conditions, making the RSI Pulsar an essential component in the arsenal of modern traders aiming for precision and adaptability in their trading endeavors.
Legend
The RSI Pulsar encapsulates various modes tailored to diverse trading strategies. The different modes are the:
Impulse Mode:
Focuses on strong outperformance, ideal for capturing movements in highly dynamic tokens.
Trend Following Mode:
A classical perpetual trend-following approach and provides binary long and short signal classifications ideal for medium term swing trading.
Ribbon Mode:
Offers quicker signals that are also binary in nature. Perfect for a confirmation signal when building higher frequency day trading systems.
Volatility Spectrum:
This feature projects a visual 'cloud' representing volatility, which helps traders spot emerging trends and potential breakouts or reversals.
Compressed Mode:
A condensed view that displays all signals in a clean and space-efficient manner. It provides a clear summary of market conditions, ideal for traders who prefer a simplified overview.
Methodology
The RSI Pulsar is built on a foundation of dynamic RSI analysis, where the traditional RSI is enhanced with advanced moving averages and standard deviation calculations. Each mode within the RSI Pulsar is designed to cater to specific aspects of the market's behavior, making it a versatile tool allowing traders to select different modes based on their trading style and market conditions.
Impulse Mode:
This mode identifies strong outperformance in assets, making it ideal for asset rotation systems. It uses a combination of RSI thresholds and dynamic moving averages to pinpoint when an asset is not just trending positively, but doing so with significant strength.
This is in contrast to typical usage of a base RSI, where elevated levels usually signal overbought and oversold periods. The RSI Pulsar flips this logic, where more extreme values are actually interpreted as a strong trend.
Trend Following Mode:
Here, the RSI is compared to the midline (the default is level 50, but a dynamic midline can also be set), to determine the prevailing trend. This mode simplifies the trend-following process, providing clear bullish or bearish signals based on whether the RSI is above or below the midline - whether a fixed or dynamic level.
Ribbon Mode:
This mode employs a series of calculated values derived from modified Heikin-Ashi smoothing to create a "ribbon" that smooths out price action and highlights underlying trends. The Ribbon Mode is particularly useful for traders who need quick confirmations of trend reversals or continuations.
Volatility Spectrum:
The Volatility Spectrum takes a unique approach to measuring market volatility by analyzing the size and direction of Heikin-Ashi candles. This data is used to create a volatility cloud that helps traders identify when volatility is rising, falling, or neutral - allowing them to adjust their strategies accordingly.
When the signal line breaks above the cloud, it signals increasing upwards volatility. When it breaks below it signifies increasing downwards volatility.
This can be used to help identify strengthening and weakening trends, as well as imminent volatile periods, allowing traders to position themselves and adapt their strategies accordingly. This mode also works as a great volatility filter for shorter term day trading strategies. It is incredibly sensitive to volatility divergences, and can give additional insights to larger market turning points.
Compressed Mode:
In Compressed Mode, all the signals from the various modes are displayed in a simplified format, making it easy for traders to quickly assess the market's overall condition without needing to delve into the details of each mode individually. Perfect for only viewing the exact data you need when live trading, or back testing.
Case Study I:
Utilizing ALMA Impulse Mode in High-Volatility Environments
Here, the RSI Pulsar is configured with an RSI length of 9 and an ALMA length of 2 in Impulse Mode. The chart example shows how this setup can identify significant price movements, allowing traders to enter positions early and capture substantial price moves. Despite the fast settings resulting in occasional false signals, the indicator's ability to catch and ride out major trends more than compensates, making it highly effective in volatile environments.
This configuration is suitable for traders seeking to trade quick, aggressive movements without enduring prolonged drawdowns. In Impulse Mode, the RSI Pulsar seeks strong trending zones, providing actionable signals that allow for timely entries and exits.
Case Study II:
SMMA Trend Following Mode for Ratio Analysis
The RSI Pulsar in Trend Following mode, configured with the SMMA with default length settings. This setup is ideal for analyzing longer-term trends, particularly useful in cryptocurrency pairs or ratio charts, where it’s crucial to identify robust directional moves. The chart showcases strong trends in the Solana/Ethereum pair. The RSI Pulsar’s ability to smooth out price action while remaining responsive to trend changes makes it an excellent tool for capturing extended price moves.
The image highlights how the RSI Pulsar efficiently tracks the strength of two tokens against each other, providing clear signals when one asset begins to outperform the other. Even in volatile markets, the SMMA ensures that the signals are reliable, filtering out noise and allowing traders to stay in the trend longer without being shaken out by minor corrections. This approach is particularly effective in ratio trading in order to inform a longer term swing trader of the strongest asset out of a customized pair.
Case Study III:
Monthly Analysis with RSI Pulsar in Ribbon Mode
This case study demonstrates the versatility and reliability of the RSI Pulsar in Ribbon mode, applied to a monthly chart of Bitcoin with an RSI length of 8 and a TEMA length of 14. This setup highlights the indicator’s robustness across multiple timeframes, extending even to long-term analysis. The RSI Pulsar effectively smooths out noise while capturing significant trends, as seen during Bitcoin bull markets. The Ribbon mode provides a clear visual representation of momentum shifts, making it easier for traders to identify trend continuations and reversals with confidence.
Case Study IV:
Divergences and Continuations with the Volatility Spectrum
Identifying harmony/divergences can be hit-or-miss at times, but this unique analysis method definitely has its merits at times. The RSI Pulsar, with its Volatility Spectrum feature, is used here to identify critical moments where price action either aligns with or diverges from the underlying volatility. As seen in the Bitcoin chart (using default settings), the indicator highlights areas where price trends either continue in harmony with volatility or diverge, signaling potential reversals. This method, while not always perfect, provides significant insight during key turning points in the market.
The Volatility Spectrum's visual representation of rising and falling volatility, combined with divergence and harmony analysis, enables traders to anticipate significant shifts in market dynamics. In this case, multiple divergences correctly identified early trend reversals, while periods of harmony indicated strong trend continuations. While this method requires careful interpretation, especially during complex market conditions, it offers valuable signals that can be pivotal in making informed trading decisions, especially if combined with other forms of analysis it can form a critical component of an investing system.
Kalman PSaR [BackQuant]Kalman PSaR
Overview and Innovation
The Kalman PSaR combines the well-known Parabolic SAR (PSaR) with the advanced smoothing capabilities of the Kalman Filter . This innovative tool aims to enhance the traditional PSaR by integrating Kalman filtering, which reduces noise and improves trend detection. The Kalman PSaR adapts dynamically to price movements, making it a highly effective indicator for spotting trend shifts while minimizing the impact of false signals caused by market volatility.
Please Find the Basic Kalman Here:
Kalman Filter Dynamics
The Kalman Filter is a powerful algorithm for estimating the true value of a system amidst noisy data. In the Kalman PSaR, this filter is applied to the high, low, and closing prices, resulting in a smoother and more accurate representation of price action. The filter’s parameters—process noise and measurement noise—are customizable, allowing traders to fine-tune the sensitivity of the indicator to market conditions. By reducing the impact of noise, the Kalman-filtered PSaR offers clearer signals for identifying trend reversals and continuations.
Enhanced PSaR Calculation
The traditional Parabolic SAR is a popular trend-following indicator that highlights potential entry and exit points based on price acceleration. In the Kalman PSaR, this calculation is enhanced by the Kalman-filtered prices, providing a smoother and more reliable signal. The indicator continuously updates based on the acceleration factor and max step values, while the Kalman filter ensures that sudden price spikes or market noise do not trigger false signals.
Min Step and Max Step: These settings control the sensitivity of the PSaR. The Min Step sets the initial acceleration factor, while the Max Step limits how fast the PSaR adapts to price changes, helping traders fine-tune the indicator’s responsiveness.
Optional Smoothing Techniques To further enhance the signal clarity, the Kalman PSaR includes an optional smoothing feature. Traders can choose from various smoothing methods, such as SMA, Hull, EMA, WMA, TEMA, and more, to reduce short-term fluctuations and emphasize the underlying trend. The smoothing period is customizable, allowing traders to adjust the indicator’s behavior according to their preferred trading style and timeframe.
Color-Coded Candle Painting The Kalman PSaR features color-coded candles that change according to the trend direction. When the price is above the PSaR, candles are painted green to indicate a long trend, and when the price is below the PSaR, candles are painted red to signal a short trend. This visual representation makes it easy to interpret market sentiment at a glance, improving decision-making speed during fast-moving markets.
Key Features and Customization
Kalman Filter Customization: The process noise and measurement noise parameters allow traders to adjust how aggressively the filter adapts to price changes, making it suitable for both volatile and stable markets.
Smoothing Options: A variety of moving average types, such as SMA, Hull, EMA, and more, can be applied to smooth the PSaR values, ensuring that the signal remains clear even in choppy markets.
Dynamic Trend Detection: The Kalman PSaR dynamically updates based on price movements, helping traders spot trend reversals early while filtering out false signals caused by short-term volatility.
Bar Coloring and PSaR Plotting: Traders can choose to color candles based on trend direction or plot the PSaR directly on the chart for additional visual clarity.
Practical Applications
Trend-Following Strategies: The Kalman PSaR excels in trend-following strategies by providing timely signals of trend changes. The dynamic nature of the indicator allows traders to capture significant price movements while avoiding market noise.
Reversal Identification: The indicator’s ability to filter out noise and provide smoother signals makes it ideal for identifying reversals in volatile markets.
Risk Management: By plotting clear stop levels based on the PSaR, traders can use this indicator to effectively manage risk, placing stop-loss orders at key points based on the trend direction.
Conclusion
The Kalman PSaR is a fusion of the classic Parabolic SAR and the Kalman filter, offering enhanced trend detection with reduced noise. Its customizable filtering and smoothing options, combined with dynamic trend-following capabilities, make it a versatile tool for traders seeking to improve their timing and signal accuracy. The adaptive nature of the Kalman filter, combined with the robust PSaR logic, helps traders stay on the right side of the market and manage risk more effectively.
ARIMA Indicator with Optional SmoothingOverview
The ARIMA (AutoRegressive Integrated Moving Average) Indicator is a powerful tool used to forecast future price movements by combining differencing, autoregressive, and moving average components. This indicator is designed to help traders identify trends and potential reversal points by analyzing the historical price data.
Key Features
AutoRegressive Component (AR): Utilizes past values to predict future prices.
Moving Average Component (MA): Averages past price differences to smooth out noise.
Differencing: Reduces non-stationarity in the time series data.
Optional Smoothing: Applies EMA to the ARIMA output for a smoother signal.
Customizable Parameters: Allows users to adjust AR and MA orders, differencing periods, and smoothing lengths.
Concepts Underlying the Calculations
Differencing: Subtracts previous prices from current prices to remove trends and seasonality, making the data stationary.
AutoRegressive Component (AR): Predicts future prices based on a linear combination of past values.
Moving Average Component (MA): Uses past forecast errors to refine future predictions.
Exponential Moving Average (EMA): Applies more weight to recent prices, providing a smoother and more responsive signal.
How It Works
The ARIMA Indicator first calculates the differenced series to achieve stationarity. Then, it computes the simple moving average (SMA) of this differenced series. The indicator uses the AR and MA components to adjust the SMA, creating an approximation of the ARIMA model. Finally, an optional smoothing step using EMA can be applied to the ARIMA approximation to produce a smoother signal.
How Traders Can Use It
Traders can use the ARIMA Indicator to:
Identify Trends: Detect emerging trends by observing the direction of the ARIMA line.
Spot Reversals: Look for divergences between the ARIMA line and the price to identify potential reversal points.
Generate Trading Signals: Use crossovers between the ARIMA line and the price to generate buy or sell signals.
Filter Noise: Enable the optional smoothing to filter out market noise and focus on significant price movements.
Example Usage Instructions
Add the ARIMA Indicator to your chart.
Adjust the input parameters to suit your trading strategy:
Set the SMA Length (e.g., 14).
Choose the Differencing Period (e.g., 1).
Define the AR Order (p) and MA Order (q) (e.g., 1).
Configure the Smoothing Length if smoothing is desired (e.g., 5).
Enable or disable smoothing as needed.
Observe the ARIMA line (blue) and compare it to the price chart.
Use the ARIMA line to identify trends and potential reversals.
Implement trading decisions based on the ARIMA line’s behavior relative to the price.
mathLibrary "math"
It's a library of discrete aproximations of a price or Series float it uses Fourier Discrete transform, Laplace Discrete Original and Modified transform and Euler's Theoreum for Homogenus White noice operations. Calling functions without source value it automatically take close as the default source value.
Here is a picture of Laplace and Fourier approximated close prices from this library:
Copy this indicator and try it yourself:
import AutomatedTradingAlgorithms/math/1 as math
//@version=5
indicator("Close Price with Aproximations", shorttitle="Close and Aproximations", overlay=false)
// Sample input data (replace this with your own data)
inputData = close
// Plot Close Price
plot(inputData, color=color.blue, title="Close Price")
ltf32_result = math.LTF32(a=0.01)
plot(ltf32_result, color=color.green, title="LTF32 Aproximation")
fft_result = math.FFT()
plot(fft_result, color=color.red, title="Fourier Aproximation")
wavelet_result = math.Wavelet()
plot(wavelet_result, color=color.orange, title="Wavelet Aproximation")
wavelet_std_result = math.Wavelet_std()
plot(wavelet_std_result, color=color.yellow, title="Wavelet_std Aproximation")
DFT3(xval, _dir)
Discrete Fourier Transform with last 3 points
Parameters:
xval (float) : Source series
_dir (int) : Direction parameter
Returns: Aproxiated source value
DFT2(xval, _dir)
Discrete Fourier Transform with last 2 points
Parameters:
xval (float) : Source series
_dir (int) : Direction parameter
Returns: Aproxiated source value
FFT(xval)
Fast Fourier Transform once. It aproximates usig last 3 points.
Parameters:
xval (float) : Source series
Returns: Aproxiated source value
DFT32(xval)
Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float) : Source series
Returns: Aproxiated source value
DTF32(xval)
Combined Discrete Fourier Transforms of DFT3 and DTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float) : Source series
Returns: Aproxiated source value
LFT3(xval, _dir, a)
Discrete Laplace Transform with last 3 points
Parameters:
xval (float) : Source series
_dir (int) : Direction parameter
a (float) : laplace coeficient
Returns: Aproxiated source value
LFT2(xval, _dir, a)
Discrete Laplace Transform with last 2 points
Parameters:
xval (float) : Source series
_dir (int) : Direction parameter
a (float) : laplace coeficient
Returns: Aproxiated source value
LFT(xval, a)
Fast Laplace Transform once. It aproximates usig last 3 points.
Parameters:
xval (float) : Source series
a (float) : laplace coeficient
Returns: Aproxiated source value
LFT32(xval, a)
Combined Discrete Laplace Transforms of LFT3 and LTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float) : Source series
a (float) : laplace coeficient
Returns: Aproxiated source value
LTF32(xval, a)
Combined Discrete Laplace Transforms of LFT3 and LTF2 it aproximates last point by first
aproximating last 3 ponts and than using last 2 points of the previus.
Parameters:
xval (float) : Source series
a (float) : laplace coeficient
Returns: Aproxiated source value
whitenoise(indic_, _devided, minEmaLength, maxEmaLength, src)
Ehler's Universal Oscillator with White Noise, without extra aproximated src.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
Parameters:
indic_ (float) : Input series for the indicator values to be smoothed
_devided (int) : Divisor for oscillator calculations
minEmaLength (int) : Minimum EMA length
maxEmaLength (int) : Maximum EMA length
src (float) : Source series
Returns: Smoothed indicator value
whitenoise(indic_, dft1, _devided, minEmaLength, maxEmaLength, src)
Ehler's Universal Oscillator with White Noise and DFT1.
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate indicator and thus reducing noise.
Parameters:
indic_ (float) : Input series for the indicator values to be smoothed
dft1 (float) : Aproximated src value for white noice calculation
_devided (int) : Divisor for oscillator calculations
minEmaLength (int) : Minimum EMA length
maxEmaLength (int) : Maximum EMA length
src (float) : Source series
Returns: Smoothed indicator value
smooth(dft1, indic__, _devided, minEmaLength, maxEmaLength, src)
Smoothing source value with help of indicator series and aproximated source value
It uses src and sproxiated src (dft1) to clearly define white noice.
It uses dinamic EMA to aproximate src and thus reducing noise.
Parameters:
dft1 (float) : Value to be smoothed.
indic__ (float) : Optional input for indicator to help smooth dft1 (default is FFT)
_devided (int) : Divisor for smoothing calculations
minEmaLength (int) : Minimum EMA length
maxEmaLength (int) : Maximum EMA length
src (float) : Source series
Returns: Smoothed source (src) series
smooth(indic__, _devided, minEmaLength, maxEmaLength, src)
Smoothing source value with help of indicator series
It uses dinamic EMA to aproximate src and thus reducing noise.
Parameters:
indic__ (float) : Optional input for indicator to help smooth dft1 (default is FFT)
_devided (int) : Divisor for smoothing calculations
minEmaLength (int) : Minimum EMA length
maxEmaLength (int) : Maximum EMA length
src (float) : Source series
Returns: Smoothed src series
vzo_ema(src, len)
Volume Zone Oscillator with EMA smoothing
Parameters:
src (float) : Source series
len (simple int) : Length parameter for EMA
Returns: VZO value
vzo_sma(src, len)
Volume Zone Oscillator with SMA smoothing
Parameters:
src (float) : Source series
len (int) : Length parameter for SMA
Returns: VZO value
vzo_wma(src, len)
Volume Zone Oscillator with WMA smoothing
Parameters:
src (float) : Source series
len (int) : Length parameter for WMA
Returns: VZO value
alma2(series, windowsize, offset, sigma)
Arnaud Legoux Moving Average 2 accepts sigma as series float
Parameters:
series (float) : Input series
windowsize (int) : Size of the moving average window
offset (float) : Offset parameter
sigma (float) : Sigma parameter
Returns: ALMA value
Wavelet(src, len, offset, sigma)
Aproxiates srt using Discrete wavelet transform.
Parameters:
src (float) : Source series
len (int) : Length parameter for ALMA
offset (simple float)
sigma (simple float)
Returns: Wavelet-transformed series
Wavelet_std(src, len, offset, mag)
Aproxiates srt using Discrete wavelet transform with standard deviation as a magnitude.
Parameters:
src (float) : Source series
len (int) : Length parameter for ALMA
offset (float) : Offset parameter for ALMA
mag (int) : Magnitude parameter for standard deviation
Returns: Wavelet-transformed series
LaplaceTransform(xval, N, a)
Original Laplace Transform over N set of close prices
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
Returns: Aproxiated source value
NLaplaceTransform(xval, N, a, repeat)
Y repetirions on Original Laplace Transform over N set of close prices, each time N-k set of close prices
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
repeat (int) : number of repetitions
Returns: Aproxiated source value
LaplaceTransformsum(xval, N, a, b)
Sum of 2 exponent coeficient of Laplace Transform over N set of close prices
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
Returns: Aproxiated source value
NLaplaceTransformdiff(xval, N, a, b, repeat)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
repeat (int) : number of repetitions
Returns: Aproxiated source value
N_divLaplaceTransformdiff(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, with dynamic rotation
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
repeat (int) : number of repetitions
Returns: Aproxiated source value
LaplaceTransformdiff(xval, N, a, b)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
Returns: Aproxiated source value
NLaplaceTransformdiffFrom2(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
repeat (int) : number of repetitions
Returns: Aproxiated source value
N_divLaplaceTransformdiffFrom2(xval, N, a, b, repeat)
N repetitions of Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor, dynamic rotation
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
repeat (int) : number of repetitions
Returns: Aproxiated source value
LaplaceTransformdiffFrom2(xval, N, a, b)
Difference of 2 exponent coeficient of Laplace Transform over N set of close prices, second element has for 1 higher exponent factor
Parameters:
xval (float) : series to aproximate
N (int) : number of close prices in calculations
a (float) : laplace coeficient
b (float) : second laplace coeficient
Returns: Aproxiated source value
Fine-tune Inputs: Fourier Smoothed Volume zone oscillator WFSVZ0Use this Strategy to Fine-tune inputs for the (W&)FSVZ0 Indicator.
Strategy allows you to fine-tune the indicator for 1 TimeFrame at a time; cross Timeframe Input fine-tuning is done manually after exporting the chart data.
I suggest using "Close all" input False when fine-tuning Inputs for 1 TimeFrame. When you export data to Excel/Numbers/GSheets I suggest using "Close all" input as True, except for the lowest TimeFrame.
MEANINGFUL DESCRIPTION:
The Volume Zone oscillator breaks up volume activity into positive and negative categories. It is positive when the current closing price is greater than the prior closing price and negative when it's lower than the prior closing price. The resulting curve plots through relative percentage levels that yield a series of buy and sell signals, depending on level and indicator direction.
The Wavelet & Fourier Smoothed Volume Zone Oscillator (W&)FSVZO is a refined version of the Volume Zone Oscillator, enhanced by the implementation of the Discrete Fourier Transform . Its primary function is to streamline price data and diminish market noise, thus offering a clearer and more precise reflection of price trends.
By combining the Wavalet and Fourier aproximation with Ehler's white noise histogram, users gain a comprehensive perspective on volume-related market conditions.
HOW TO USE THE INDICATOR:
The default period is 2 but can be adjusted after backtesting. (I suggest 5 VZO length and NoiceR max length 8 as-well)
The VZO points to a positive trend when it is rising above the 0% level, and a negative trend when it is falling below the 0% level. 0% level can be adjusted in setting by adjusting VzoDifference. Oscillations rising below 0% level or falling above 0% level result in a natural trend.
HOW TO USE THE STRATEGY:
Here you fine-tune the inputs until you find a combination that works well on all Timeframes you will use when creating your Automated Trade Algorithmic Strategy. I suggest 4h, 12h, 1D, 2D, 3D, 4D, 5D, 6D, W and M.
When I ndicator/Strategy returns 0 or natural trend , Strategy Closes All it's positions.
ORIGINALITY & USFULLNESS:
Personal combination of Fourier and Wavalet aproximation of a price which results in less noise Volume Zone Oscillator.
The Wavelet Transform is a powerful mathematical tool for signal analysis, particularly effective in analyzing signals with varying frequency or non-stationary characteristics. It dissects a signal into wavelets, small waves with varying frequency and limited duration, providing a multi-resolution analysis. This approach captures both frequency and location information, making it especially useful for detecting changes or anomalies in complex signals.
The Discrete Fourier Transform (DFT) is a mathematical technique that transforms discrete data from the time domain into its corresponding representation in the frequency domain. This process involves breaking down a signal into its individual frequency components, thereby exposing the amplitude and phase characteristics inherent in each frequency element.
This indicator utilizes the concept of Ehler's Universal Oscillator and displays a histogram, offering critical insights into the prevailing levels of market noise. The Ehler's Universal Oscillator is grounded in a statistical model that captures the erratic and unpredictable nature of market movements. Through the application of this principle, the histogram aids traders in pinpointing times when market volatility is either rising or subsiding.
DETAILED DESCRIPTION:
My detailed description of the indicator and use cases which I find very valuable.
What is oscillator?
Oscillators are chart indicators that can assist a trader in determining overbought or oversold conditions in ranging (non-trending) markets.
What is volume zone oscillator?
Price Zone Oscillator measures if the most recent closing price is above or below the preceding closing price.
Volume Zone Oscillator is Volume multiplied by the 1 or -1 depending on the difference of the preceding 2 close prices and smoothed with Exponential moving Average.
What does this mean?
If the VZO is above 0 and VZO is rising. We have a bullish trend. Most likely.
If the VZO is below 0 and VZO is falling. We have a bearish trend. Most likely.
Rising means that VZO on close is higher than the previous day.
Falling means that VZO on close is lower than the previous day.
What if VZO is falling above 0 line?
It means we have a high probability of a bearish trend.
Thus the indicator returns 0 and Strategy closes all it's positions when falling above 0 (or rising bellow 0) and we combine higher and lower timeframes to gauge the trend.
In the next Image you can see that trend is negative on 4h, negative on 12h and positive on 1D. That means trend is negative.
I am sorry, the chart is a bit messy. The idea is to use the indicator over more than 1 Timeframe.
What is approximation and smoothing?
They are mathematical concepts for making a discrete set of numbers a
continuous curved line.
Fourier and Wavelet approximation of a close price are taken from aprox library.
Key Features:
You can tailor the Indicator/Strategy to your preferences with adjustable parameters such as VZO length, noise reduction settings, and smoothing length.
Volume Zone Oscillator (VZO) shows market sentiment with the VZO, enhanced with Exponential Moving Average (EMA) smoothing for clearer trend identification.
Noise Reduction leverages Euler's White noise capabilities for effective noise reduction in the VZO, providing a cleaner and more accurate representation of market dynamics.
Choose between the traditional Fast Fourier Transform (FFT) , the innovative Double Discrete Fourier Transform (DTF32) and Wavelet soothed Fourier soothed price series to suit your analytical needs.
Image of Wavelet transform with FAST settings, Double Fourier transform with FAST settings. Improved noice reduction with SLOW settings, and standard FSVZO with SLOW settings:
Fast setting are setting by default:
VZO length = 2
NoiceR max Length = 2
Slow settings are:
VZO length = 5 or 7
NoiceR max Length = 8
As you can see fast setting are more volatile. I suggest averaging fast setting on 4h 12h 1d 2d 3d 4d W and M Timeframe to get a clear view on market trend.
What if I want long only when VZO is rising and above 15 not 0?
You have set Setting VzoDifference to 15. That reduces the number of trend changes.
Example of W&FSVZO with VzoDifference 15 than 0:
VZO crossed 0 line but not 15 line and that's why Indicator returns 0 in one case an 1 in another.
What is Smooth length setting?
A way of calculating Bullish or Bearish (W&)FSVZO .
If smooth length is 2 the trend is rising if:
rising = VZO > ta.ema(VZO, 2)
Meaning that we check if VZO is higher that exponential average of the last 2 elements.
If smooth length is 1 the trend is rising if:
rising = VZO_ > VZO_
Use this Strategy to fine-tune inputs for the (W&)FSVZO Indicator.
(Strategy allows you to fine-tune the indicator for 1 TimeFrame at a time; cross Timeframe Input fine-tuning is done manually after exporting the chart data)
I suggest using " Close all " input False when fine-tuning Inputs for 1 TimeFrame . When you export data to Excel/Numbers/GSheets I suggest using " Close all " input as True , except for the lowest TimeFrame . I suggest using 100% equity as your default quantity for fine-tune purposes. I have to mention that 100% equity may lead to unrealistic backtesting results. Be avare. When backtesting for trading purposes use Contracts or USDT.
TASC 2024.04 The Ultimate Smoother█ OVERVIEW
This script presents an implementation of the digital smoothing filter introduced by John Ehlers in his article "The Ultimate Smoother" from the April 2024 edition of TASC's Traders' Tips .
█ CONCEPTS
The UltimateSmoother preserves low-frequency swings in the input time series while attenuating high-frequency variations and noise. The defining input parameter of the UltimateSmoother is the critical period , which represents the minimum wavelength (highest frequency) in the filter's pass band. In other words, the filter attenuates or removes the amplitudes of oscillations at shorter periods than the critical period.
According to Ehlers, one primary advantage of the UltimateSmoother is that it maintains zero lag in its pass band and minimal lag in its transition band, distinguishing it from other conventional digital filters (e.g., moving averages ). One can apply this smoother to various input data series, including other indicators.
█ CALCULATIONS
Ehlers derived the UltimateSmoother using inspiration from the design principles he learned from his experience with analog filters , as described in the original publication. On a technical level, the UltimateSmoother's unique response involves subtracting a high-pass response from an all-pass response . At very low frequencies (lengthy periods), where the high-pass filter response has virtually no amplitude, the subtraction yields a frequency and phase response practically equivalent to the input data. At other frequencies, the subtraction achieves filtration through cancellation due to the close similarities in response between the high-pass filter and the input data.
Kalman Filter by TenozenAnother useful indicator is here! Kalman Filter is a quantitative tool created by Rudolf E. Kalman. In the case of trading, it can help smooth out the price data that traders observe, making it easier to identify underlying trends. The Kalman Filter is particularly useful for handling price data that is noisy and unpredictable. As an adaptive-based algorithm, it can easily adjust to new data, which makes it a handy tool for traders operating in markets that are prone to change quickly.
Many people may assume that the Kalman Filter is the same as a Moving Average, but that is not the case. While both tools aim to smooth data and find trends, they serve different purposes and have their own sets of advantages and disadvantages. The Kalman Filter provides a more dynamic and adaptive approach, making it suitable for real-time analysis and predictive capabilities, but it is also more complex. On the other hand, Moving Averages offer a simpler and more intuitive way to visualize trends, which makes them a popular choice among traders for technical analysis. However, the Moving Average is a lagging indicator and less adaptive to market change, if it's adjusted it may result in overfitting. In this case, the Kalman Filter would be a better choice for smoothing the price up.
I hope you find this indicator useful! It's been an exciting and extensive journey since I began diving into the world of finance and trading. I'll keep you all updated on any new indicators I discover that could benefit the community in the future. Until then, take care, and happy trading! Ciao.
Nasan Rate of Change (ROC)**NOTE: FOR COMPARISON TRADITIONAL ROC IS PLOTTED WITH THE SAME ROC LENGTH OF 9. IT IS NOT PART OF THE INDICATOR"
The Nasan ROC indicator is smoothed version of the of the traditional ROC indicator. The Nasna ROC uses a triple pass moving average differencing strategy. A cumulative sum of the deviations obtained from the moving average differencing provides a smooth "noise free" trend and this cumulative sum of deviations is used for calculating ROC.
Let's break down the components and understand the indicator we discussed earlier:
Sequential Triple Pass Filter:
Three filters with lengths specified by length1, length2, and length3 are applied to the closing prices (close).
The filters involve calculating the cumulative sum of the differences between the closing prices and their respective moving averages.
The idea is to detrend the data and accumulate the deviations from the average over time, emphasizing longer-term trends.
Calculation of Rate of Change (ROC) of Cumulative Sum:
The Rate of Change (ROC) of the cumulative sum (rocCumulativeSum) is calculated using the ta.roc function with a specified length (rocLength).
ROC measures the percentage change in the cumulative sum over a specified period.
The ROC histogram provides insights into the momentum of the detrended series. Positive values suggest increasing momentum, while negative values suggest decreasing momentum.
Pay attention to the color of the histogram bars.
The histogram bars are colored green if the current ROC value is greater than or equal to the previous ROC value, and red otherwise.
This coloring is based on the concept that a positive ROC suggests upward momentum, while a negative ROC suggests downward momentum.
Volatility - Volume Impact:
The Average True Range (ATR) is calculated with a period of 14.
Volume strength is calculated as a factor (VCF) that considers the ratio of the simple moving average (SMA) of the current volume to the SMA of the volume over a longer period (144).
This volume factor (VCF) is then multiplied by ATR, creating a synergy with volatility and volume.
Visualization with Background Color Gradient:
A background color gradient is applied to the chart based on the calculated volume strength (f1).
The gradient color ranges from black (indicating low ATR and volume strength) to purple (indicating high ATR and volume strength). A low value indicates a ranging market with no significant price movements and it is safter to avoid signals generated from ROC histogram in these region.
Synergy of ROC and Volume Strength:
Observe how the ROC signals align with the background color gradient. For example, confirm whether positive ROC aligns with periods of high ATR and volume strength.
This synergy can provide confirmation or divergence signals, adding another layer of analysis.
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.
ATR Adaptive RSI OscillatorThe " ATR Adaptive RSI Oscillator " is a versatile technical analysis tool designed to help traders make informed decisions in dynamic market conditions. It combines the Relative Strength Index (RSI) with the Average True Range (ATR) to provide adaptive and responsive insights into price trends.
Key Features :
Adaptive RSI Periods : The indicator introduces the concept of adaptive RSI periods based on the ATR (Average True Range) of the market. When enabled, it dynamically adjusts the RSI calculation period, offering longer periods during high volatility and shorter periods during low volatility. This adaptability enhances the accuracy of RSI signals across varying market conditions.
Volume-Based Smoothing : The indicator includes a smoothing feature that computes a time-decayed weighted moving average of RSI values over the last two bars, using volume-based weights. This approach offers a time-sensitive smoothing effect, reducing noise for a clearer view of trend strength compared to the standard RSI.
Divergence Detection : Traders can enable divergence detection to identify potential reversal points in the market. The indicator highlights regular bullish and bearish divergences, providing valuable insights into market sentiment shifts.
Customizable Parameters : Traders have the flexibility to customize various parameters, including RSI length, adaptive mode, ATR length, and divergence settings, to tailor the indicator to their trading strategy.
Overbought and Oversold Levels : The indicator includes overbought (OB) and oversold (OS) boundary lines that can be adjusted to suit individual preferences. These levels help traders identify potential reversal zones.
The "ATR Adaptive RSI Oscillator" is a powerful tool for traders seeking to adapt their trading strategies to changing market dynamics. Whether you're a trend follower or a contrarian trader, this indicator provides valuable insights to support your decision-making process.
Discrete Fourier Transformed Money Flow IndexThe Discrete Fourier Transform Money Flow Index indicator integrates the Money Flow Index (MFI) with Discrete Fourier Transform (credit to author wbburgin - May 26 2023 ) smoothing to offer a refined and smoothed depiction of the MFI's underlying trend. The MFI is calculated using the formula: MFI = 100 - (100 / (1 + MR)), where a high MFI value indicates robust buying pressure (signaling an overbought condition), and a low MFI value indicates substantial selling pressure (signaling an oversold condition).
Why is the DFT and MFI combined?
The aim of this combination between DFT and MFI is to effectively filter out short-term fluctuations and noise, enabling a clearer assessment of the overall trend. This smoothing process enhances the reliability of the MFI by emphasizing dominant and sustained buying or selling pressures. This script executes a full DFT but only uses filtering from one frequency component. The choice to focus on the magnitude at index 0 is significant as it captures the dominant or fundamental frequency in the data. By analyzing this primary cyclic behavior, we can identify recurring patterns and potential turning points more easily. This streamlined approach simplifies interpretation and enhances efficiency by reducing complexity associated with multiple frequency components. Overall, focusing on the dominant frequency and applying it to the MFI provides a concise and actionable assessment of the underlying data.
Note: The FMFI indicator provides both smoothed and non-smoothed versions of the MFI, with the option to toggle the original non-smoothed MFI on or off in the settings.
Application
FMFI functions as a trend-following indicator. Bullish trends are denoted by the color white, while bearish trends are represented by the color purple. Circles plotted on the FMFI indicate regular bull and bear signals. Additionally, red arrows indicate a strong negative trend, while green arrows indicate a strong positive trend. These arrows are calculated based on the presence of regular bull and bear signals within overbought and oversold zones. To enhance its effectiveness, it is recommended to combine this indicator with other complementary technical analysis tools and integrate it into a comprehensive trading strategy. Traders are encouraged to explore a wide range of settings and timeframes to align the indicator with their unique trading preferences and adapt it to the current market conditions. By doing so, traders can optimize the indicator's performance and increase their potential for successful trading outcomes.
Utility
Traders and investors can employ this indicator to enhance their trend-following strategies. The white-colored components of the FMFI can help identify potential buying zones, while the purple-colored components can assist in identifying potential selling points. The red and green arrows can be used to pinpoint moments of strong bull or bear momentum, allowing traders to position themselves advantageously in their trading activities. Please note that future performance of any trading strategy is fundamentally unknowable, and past results do not guarantee future performance.
Ehlers Data Sampling Relative Strength Indicator [CC]The Data Sampling Indicator was created by John Ehlers (Stocks and Commodities Mar 2023) and this is a genius method to reduce noise in the market data but also doesn't introduce any lag while doing so. The way this works is because traditionally, people have always relied on the close price as the default input for many indicators such as the RSI or MACD as examples. Since the open is usually virtually identical to the previous close, it has been ignored by most people but Ehlers discovered that if you do a simple average of open and close for the input on any indicator, you can remove much of the noise without any added lag. I have used the RSI as he did in his example and plotted both to show the difference between the traditional RSI and using Ehlers' process as the new Data Sampling RSI. You can clearly see that this new RSI follows the price fluctuations much closer and is much smoother than the traditional RSI. As usual, I have included different colors to show the strength of the buy or sell signals so darker colors mean it is a very strong signal and lighter colors means it is a normal signal. Buy when the line turns green and sell when it turns red.
Feel free to try out this method to replace the input for any indicator and let me know how this works for you! And of course let me know if you would like me to publish any indicator script.
Renko Ichimoku CloudThis script utilizes its source from a non-repainting renko closing price. Renko charts focus solely on price movement and minimize the impacts of time and the extra noise time creates. Employing the renko close helps smooth out the Ichimoku Cloud. Insignificant price movements will not cause a change in the plotted lines of the indicator unless a new threshold is breached or a "brick" is created.
This Ichmoku Cloud includes all standard lines with standard lengths. These include:
Tenken Sen
Kiju Sen
Senkou A/B
Chikou Span
We have also included plotted marks for when there is a Tenken Sen/ Kiju Sen cross and for the Kumo cloud twist.
There are two methods for selecting the box size. Box size is critical for the overall function and efficacy of the plots you will visually see with this indicator. Box size is set automatically using the Average True Range "ATR" or manually using the "Traditional" setting. The simplest way to determine a manual box six is to take the ATR of the given instrument and round it to the nearest decimal place. As an example, if the ATR for the asset is 0.017, you would round that number to 0.02 and utilize this as your traditional box size.
NET BSP NET BSP derived from Buying & Selling Pressure which is a volatility indicator that monitors average metrics of green and red candles separately.
We could navigate more confidently through market with projected market balance.
BSP allowed us to track and analyze the ongoing performance of bullish and bearish impulsive waves and their corrections.
Due to unintuitive way of measuring decline with SP going up, I decided to remake it into more intuitive version with better precision.
When we encounter the fall it's better to have declining values of tool to be able to cover it visually with ease.
One of the solutions was to create a sense of balance of Buying Pressure against Selling Pressure.
Since we are oriented by growth, it'd be more logical to summarize the market balance with BP - SP
Comparison:
When Buying and Selling Pressure are equal, NET BSP would be at 0.
NETBSP > 0 and NETBSP > NETBSP = 🟢
NETBSP > 0 and NETBSP < NETBSP = 🟡
NETBSP < 0 and NETBSP < NETBSP = 🔴
NETBSP < 0 and NETBSP > NETBSP = 🟡
Hence, we get visualized stages of uptrends and downtrends which allows to evaluate chances and estimations of upcoming counter-waves.
Also, it is worth to note that output clearly shows how one wave is derived from another in terms of sizing.
Feel free to adjust NET BSP arguments to adapt sensitivity to the timeframe you're working on.
Library_SmoothersLibrary "Library_Smoothers"
CorrectedMA(Src, Len)
CorrectedMA The strengths of the corrected Average (CA) is that the current value of the time series must exceed a the current volatility-dependent threshold, so that the filter increases or falls, avoiding false signals when the trend is in a weak phase.
Parameters:
Src
Len
Returns: The Corrected source.
EHMA(src, len)
EMA Exponential Moving Average.
Parameters:
src : Source to act upon
len
Returns: EMA of source
FRAMA(src, len, FC, SC)
FRAMA Fractal Adaptive Moving Average
Parameters:
src : Source to act upon
len : Length of moving average
FC : Fast moving average
SC : Slow moving average
Returns: FRAMA of source
Jurik(src, length, phase, power)
Jurik A low lag filter
Parameters:
src : Source
length : Length for smoothing
phase : Phase range is ±100
power : Mathematical power to use. Doesn't need to be whole numbers
Returns: Jurik of source
SMMA(src, len)
SMMA Smoothed moving average. Think of the SMMA as a hybrid of its better-known siblings — the simple moving average (SMA) and the exponential moving average (EMA).
Parameters:
src : Source
len
Returns: SMMA of source
SuperSmoother(src, len)
SuperSmoother
Parameters:
src : Source to smooth
len
Returns: SuperSmoother of the source
TMA(src, len)
TMA Triangular Moving Average
Parameters:
src : Source
len
Returns: TMA of source
TSF(src, len)
TSF Time Series Forecast. Uses linear regression.
Parameters:
src : Source
len
Returns: TSF of source
VIDYA(src, len)
VIDYA Chande's Variable Index Dynamic Average. See www.fxcorporate.com
Parameters:
src : Source
len
Returns: VIDYA of source
VAWMA(src, len, startingWeight, volumeDefault)
VAWMA = VWMA and WMA combined. Simply put, this attempts to determine the average price per share over time weighted heavier for recent values. Uses a triangular algorithm to taper off values in the past (same as WMA does).
Parameters:
src : Source
len : Length
startingWeight
volumeDefault : The default value to use when a chart has no volume.
Returns: The VAWMA of the source.
WWMA(src, len)
WWMA Welles Wilder Moving Average
Parameters:
src : Source
len
Returns: The WWMA of the source
ZLEMA(src, len)
ZLEMA Zero Lag Expotential Moving Average
Parameters:
src : Source
len
Returns: The ZLEMA of the source
SmootherType(mode, src, len, fastMA, slowMA, offset, phase, power, startingWeight, volumeDefault, Corrected)
Performs the specified moving average
Parameters:
mode : Name of moving average
src : the source to apply the MA type
len
fastMA : FRAMA fast moving average
slowMA : FRAMA slow moving average
offset : Linear regression offset
phase : Jurik phase
power : Jurik power
startingWeight : VAWMA starting weight
volumeDefault : VAWMA default volume
Corrected
Returns: The MA smoothed source
KG StabilizerThis is a personal experimental stabilizer , which utilizes multitiered highest and lowest levels to hold an average with historical levels where the source value has a bias direction.
Settings
Smoothing ema length
Lines count for additional passes (forming a pseudo ribbon)
User choice of 2 colors to fade between
Bias choice input to either follow a mid-level, or to pull strongly towards either high or low values.
You can use any source input of your own to pass through this. it works especially well on Oscillators.
There is a Output of the average for 'indicator on indicator' outputs to chain.
Demonstration shows the difference between the bottom indicator, and the middle indicator being applied on top of it.
The Top indicator is simply applied on the close value.
Smooth EMA/DEMA/TEMA/EHMA (SEMA)This is my attempt at smoothing the exponential moving average any its cousins. I literally just smoothed the source and alpha and this is what we got. I really like this because you get a nice smooth yet fast acting moving average that works better than a traditional simple moving average. This script also included directional alerts.
Smooth EMA
Smooth DEMA
Smooth TEMA
Smooth EHMA
Adaptive Fisherized ROCIntroduction
Hello community, here I applied the Inverse Fisher Transform, Ehlers dominant cycle determination and smoothing methods on a simple Rate of Change (ROC) indicator
You have a lot of options to adjust the indicator.
Usage
The rate of change is most often used to measure the change in a security's price over time.
That's why it is a momentum indicator.
When it is positive, prices are accelerating upward; when negative, downward.
It is useable on every timeframe and could be a potential filter for you your trading system.
IMO it could help you to confirm entries or find exits (e.g. you have a long open, roc goes negative, you exit).
If you use a trend-following strategy, you could maybe look out for red zones in an in uptrend or green zones in a downtrend to confirm your entry on a pullback.
Signals
ROC above 0 => confirms bullish trend
ROC below 0 => confirms bearish trend
ROC hovers near 0 => price is consolidating
Enjoy! 🚀
