Guassianfilter — Indicators and Strategies

Adaptive Gaussian MA For Loop [BackQuant]Adaptive Gaussian MA For Loop PLEASE Read the following carefully before applying this indicator to your trading system. Knowing the core logic behind the tools you're using allows you to integrate them into your strategy with confidence and precision. Introducing BackQuant's Adaptive Gaussian Moving Average For Loop (AGMA FL) — a sophisticated trading indicator that merges the Gaussian Moving Average (GMA) with adaptive volatility to provide dynamic trend analysis. This unique indicator further enhances its effectiveness by utilizing a for-loop scoring mechanism to detect potential shifts in market direction. Let's dive into the components, the rationale behind them, and how this indicator can be practically applied to your trading strategies. Understanding the Gaussian Moving Average (GMA) The Gaussian Moving Average (GMA) is a smoothed moving average that applies Gaussian weighting to price data. Gaussian weighting gives more significance to data points near the center of the lookback window, making the GMA particularly effective at reducing noise while maintaining sensitivity to changes in price direction. In contrast to simpler moving averages like the SMA or EMA, GMA provides a more refined smoothing function, which can help traders follow the true trend in volatile markets. In this script, the GMA is calculated over a defined Calculation Period (default 14), applying a Gaussian filter to smooth out market fluctuations and provide a clearer view of underlying trends. Adaptive Volatility: A Dynamic Edge The Adaptive feature in this indicator gives it the ability to adjust its sensitivity based on current market volatility. If the Adaptive option is enabled, the GMA uses a standard deviation-based volatility measure (with a default period of 20) to dynamically adjust the width of the Gaussian filter, allowing the GMA to react faster in volatile markets and more slowly in calm conditions. This dynamic nature ensures that the GMA stays relevant across different market environments. When the Adaptive setting is disabled, the script defaults to a constant standard deviation value (default 1.0), providing a more stable but less responsive smoothing function. Why Use Adaptive Gaussian Moving Average? The Gaussian Moving Average already provides smoother results than standard moving averages, but by adding an adaptive component, the indicator becomes even more responsive to real-time price changes. In fast-moving or highly volatile markets, this adaptation allows traders to react quicker to emerging trends. Conversely, in quieter markets, it reduces over-sensitivity to minor fluctuations, thus lowering the risk of false signals. For-Loop Scoring Mechanism The heart of this indicator lies in its for-loop scoring system, which evaluates the smoothed price data (the GMA) over a specified range, comparing it to previous values. This scoring system assigns a numerical value based on whether the current GMA is higher or lower than previous values, creating a trend score. Long Signals: These are generated when the for-loop score surpasses the Long Threshold (default set at 40), signaling that the GMA is gaining upward momentum, potentially identifying a favorable buying opportunity. Short Signals: These are triggered when the score crosses below the Short Threshold (default set at -10), indicating that the market may be losing strength and that a selling or shorting opportunity could be emerging. Thresholds & Customization Options This indicator offers a high degree of flexibility, allowing you to fine-tune the settings according to your trading style and risk preferences: Calculation Period: Adjust the lookback period for the Gaussian filter, affecting how smooth or responsive the indicator is to price changes. Adaptive Mode: Toggle the adaptive feature on or off, allowing the GMA to dynamically adjust based on market volatility or remain consistent with a fixed standard deviation. Volatility Settings: Control the standard deviation period for adaptive mode, fine-tuning how quickly the GMA responds to shifts in volatility. For-Loop Settings: Modify the start and end points for the for-loop score calculation, adjusting the depth of analysis for trend signals. Thresholds for Signals: Set custom long and short thresholds to determine when buy or sell signals should be generated. Visualization Options: Choose to color bars based on trend direction, plot signal lines, or adjust the background color to reflect current market sentiment visually. Trading Applications The Adaptive Gaussian MA For Loop can be applied to a variety of trading styles and markets. Here are some key ways you can use this indicator in practice: Trend Following: The combination of Gaussian smoothing and adaptive volatility helps traders stay on top of market trends, identifying significant momentum shifts while filtering out noise. The for-loop scoring system enhances this by providing a numerical representation of trend strength, making it easier to spot when a new trend is emerging or when an existing one is gaining strength. Mean Reversion: For traders looking to capitalize on short-term market corrections, the adaptive nature of this indicator makes it easier to identify when price action is deviating too far from its smoothed trend, allowing for strategic entries and exits based on overbought or oversold conditions. Swing Trading: With its ability to capture medium-term price movements while avoiding the noise of short-term fluctuations, this indicator is well-suited for swing traders who aim to profit from market reversals or short-to-mid-term trends. Volatility Management: The adaptive feature allows the indicator to adjust dynamically in volatile markets, ensuring that it remains responsive in times of increased uncertainty while avoiding unnecessary noise in calmer periods. This makes it an effective tool for traders who want to manage risk by staying in tune with changing market conditions. Final Thoughts The Adaptive Gaussian MA For Loop is a powerful and flexible indicator that merges the elegance of Gaussian smoothing with the adaptability of volatility-based adjustments. By incorporating a for-loop scoring mechanism, this indicator provides traders with a comprehensive view of market trends and potential trade opportunities. It’s important to test the settings on historical data and adapt them to your specific trading style, timeframe, and market conditions. As with any technical tool, the AGMA For Loop should be used in conjunction with other indicators and solid risk management practices for the best results. Thus following all of the key points here are some sample backtests on the 1D Chart Disclaimer: Backtests are based off past results, and are not indicative of the future. INDEX:BTCUSD INDEX:ETHUSD BINANCE:SOLUSD

Gaussian Price Filter [BackQuant]Gaussian Price Filter Overview and History of the Gaussian Transformation The Gaussian transformation, often associated with the Gaussian (normal) distribution, is a mathematical function characteristically prominent in statistics and probability theory. The bell-shaped curve of the Gaussian function, expressing the normal distribution, is ubiquitously employed in various scientific and engineering disciplines, including financial market analysis. This transformation's core utility in trading and economic forecasting is derived from its efficacy in smoothing data series and highlighting underlying trends, which are pivotal for making strategic trading decisions. The Gaussian filter, specifically, is a type of data-smoothing algorithm that mitigates the random "noise" of market price data, thus enhancing the visibility of crucial trend changes and patterns. Historically, this concept was adapted from fields such as signal processing and image editing, where precise extraction of useful information from noisy environments is critical. 1. What is a Gaussian Transformation? A Gaussian transformation involves the application of a Gaussian function to a set of data points. The function is applied as a filter in the context of trading algorithms to smooth time series data, which helps in identifying the intrinsic trends obscured by market volatility. The transformation is characterized by its parameter, sigma (σ), representing the standard deviation, which determines the width of the Gaussian bell curve. The breadth of this curve impacts the degree of smoothing: a wider curve (higher sigma value) results in more smoothing, beneficial for longer-term trend analysis. 2. Filtering Price with Gaussian Transformation and its Benefits In the provided Script, the Gaussian transformation is utilized to filter price data. The filtering process involves convolving the price data with Gaussian weights, which are calculated based on the chosen length (the number of data points considered) and sigma. This convolution process smooths out short-term fluctuations and highlights longer-term movements, facilitating a clearer analysis of market trends. Benefits: Reduces noise: It filters out minor price movements and random fluctuations, which are often misleading. Enhances trend recognition: By smoothing the data, it becomes easier to identify significant trends and reversals. Improves decision-making: Traders can make more informed decisions by focusing on substantive, smoothed data rather than reacting to random noise. 3. Potential Limitations and Issues While Gaussian filters are highly effective in smoothing data, they are not without limitations: Lag introduction: Like all moving averages, the Gaussian filter introduces a lag between the actual price movements and the output signal, which can delay decision-making. Feature blurring: Over-smoothing might obscure significant price movements, especially if a large sigma is used. Parameter sensitivity: The choice of length and sigma significantly affects the output, requiring optimization and backtesting to determine the best settings for specific market conditions. 4. Extending Gaussian Filters to Other Indicators The methodology used to filter price data with a Gaussian filter can similarly be applied to other technical indicators, such as RSI (Relative Strength Index) or MACD (Moving Average Convergence Divergence). By smoothing these indicators, traders can reduce false signals and enhance the reliability of the indicators' outputs, leading to potentially more accurate signals and better timing for entering or exiting trades. 5. Application in Trading In trading, the Gaussian Price Filter can be strategically used to: Spot trend reversals: Smoothed price data can more clearly indicate when a trend is starting to change, which is crucial for catching reversals early. Define entry and exit points: The filtered data points can help in setting more precise entry and exit thresholds, minimizing the risk and maximizing the potential return. Filter other data streams: Apply the Gaussian filter on volume or open interest data to identify significant changes in market dynamics. 6. Functionality of the Script The script is designed to: Calculate Gaussian weights (f_gaussianWeights function): Generates the weights used for the Gaussian kernel based on the provided length and sigma. Apply the Gaussian filter (f_applyGaussianFilter function): Uses the weights to compute the smoothed price data. Conditional Trend Detection and Coloring: Determines the trend direction based on the filtered price and colors the price bars on the chart to visually represent the trend. 7. Specific Actions of This Code The Pine Script provided by BackQuant executes several specific actions: Input Handling: It allows users to specify the source data (src), kernel length, and sigma directly in the chart settings. Weight Calculation and Normalization: Computes the Gaussian weights and normalizes them to ensure their sum equals one, which maintains the original data scale. Filter Application: Applies the normalized Gaussian kernel to the price data to produce a smoothed output. Trend Identification and Visualization: Identifies whether the market is trending upwards or downwards based on the smoothed data and colors the bars green (up) or red (down) to indicate the trend direction.

Bollinger Bands (Nadaraya Smoothed) | Flux Charts Ticker: 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.