CofG Oscillator w/ Added Normalizations/TransformationsThis indicator is a unique study in normalization/transformation techniques, which are applied to the CG (center of gravity) Oscillator, a popular oscillator made by John Ehlers.
The idea to transform the data from this oscillator originated from observing the original indicator, which exhibited numerous whips. Curious about the potential outcomes, I began experimenting with various normalization/transformation methods and discovered a plethora of interesting results.
The indicator offers 10 different types of normalization/transformation, each with its own set of benefits and drawbacks. My personal favorites are the Quantile Transformation , which converts the dataset into one that is mostly normally distributed, and the Z-Score , which I have found tends to provide better signaling than the original indicator.
I've also included the option of showing the mean, median, and mode of the data over the period specified by the transformation period. Using this will allow you to gather additional insights into how these transformations effect the distribution of the data series.
I've also included some notes on what each transformation does, how it is useful, where it fails, and what I've found to be the best inputs for it (though I'd encourage you to play around with it yourself).
Types of Normalization/Transformation:
1. Z-Score
Overview: Standardizes the data by subtracting the mean and dividing by the standard deviation.
Benefits: Centers the data around 0 with a standard deviation of 1, reducing the impact of outliers.
Disadvantages: Works best on data that is normally distributed
Notes: Best used with a mid-longer transformation period.
2. Min-Max
Overview: Scales the data to fit within a specified range, typically 0 to 1.
Benefits: Simple and fast to compute, preserves the relationships among data points.
Disadvantages: Sensitive to outliers, which can skew the normalization.
Notes: Best used with mid-longer transformation period.
3. Decimal Scaling
Overview: Normalizes data by moving the decimal point of values.
Benefits: Simple and straightforward, useful for data with varying scales.
Disadvantages: Not commonly used, less intuitive, less advantageous.
Notes: Best used with a mid-longer transformation period.
4. Mean Normalization
Overview: Subtracts the mean and divides by the range (max - min).
Benefits: Centers data around 0, making it easier to compare different datasets.
Disadvantages: Can be affected by outliers, which influence the range.
Notes: Best used with a mid-longer transformation period.
5. Log Transformation
Overview: Applies the logarithm function to compress the data range.
Benefits: Reduces skewness, making the data more normally distributed.
Disadvantages: Only applicable to positive data, breaks on zero and negative values.
Notes: Works with varied transformation period.
6. Max Abs Scaler
Overview: Scales each feature by its maximum absolute value.
Benefits: Retains sparsity and is robust to large outliers.
Disadvantages: Only shifts data to the range , which might not always be desirable.
Notes: Best used with a mid-longer transformation period.
7. Robust Scaler
Overview: Uses the median and the interquartile range for scaling.
Benefits: Robust to outliers, does not shift data as much as other methods.
Disadvantages: May not perform well with small datasets.
Notes: Best used with a longer transformation period.
8. Feature Scaling to Unit Norm
Overview: Scales data such that the norm (magnitude) of each feature is 1.
Benefits: Useful for models that rely on the magnitude of feature vectors.
Disadvantages: Sensitive to outliers, which can disproportionately affect the norm. Not normally used in this context, though it provides some interesting transformations.
Notes: Best used with a shorter transformation period.
9. Logistic Function
Overview: Applies the logistic function to squash data into the range .
Benefits: Smoothly compresses extreme values, handling skewed distributions well.
Disadvantages: May not preserve the relative distances between data points as effectively.
Notes: Best used with a shorter transformation period. This feature is actually two layered, we first put it through the mean normalization to ensure that it's generally centered around 0.
10. Quantile Transformation
Overview: Maps data to a uniform or normal distribution using quantiles.
Benefits: Makes data follow a specified distribution, useful for non-linear scaling.
Disadvantages: Can distort relationships between features, computationally expensive.
Notes: Best used with a very long transformation period.
Conclusion
Feel free to explore these normalization/transformation techniques to see how they impact the performance of the CG Oscillator. Each method offers unique insights and benefits, making this study a valuable tool for traders, especially those with a passion for data analysis.
Transformation
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.
Simple Neural Network Transformed RSI [QuantraSystems]Simple Neural Network Transformed RSI
Introduction
The Simple Neural Network Transformed RSI (ɴɴᴛ ʀsɪ) stands out as a formidable tool for traders who specialize in lower timeframe trading.
It is an innovative enhancement of the traditional RSI readings with simple neural network smoothing techniques.
This unique blend results in fairly accurate signals, tailored for swift market movements. The ɴɴᴛ ʀsɪ is particularly resistant to the usual market noise found in lower timeframes, ensuring a clearer view of short-term trends.
Furthermore, its diverse range of visualization options adds versatility, making it a valuable tool for traders seeking to capitalize on short-duration market dynamics.
Legend
In the Image you can see the BTCUSD 1D Chart with the ɴɴᴛ ʀsɪ in Trend Following Mode to display the current trend. This is visualized with the barcoloring.
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 which can lead to either a softening momentum in the trend or even a mean reversion situation.
Here you can also see the original Indicator line and the Heikin Ashi transformed Indicator bars - more on that now.
Notes
Quantra Standard Value Contents:
To draw out all the information from the indicator calculation we have added a Heikin-Ashi (HA) Candle Visualization.
This HA transformation smoothens out the indicator values and gives a more informative look into Momentum and Trend of the Indicator itself.
This allows early entries and exits by observing the HA transformed Indicator values.
To diversify, different visualization options are available, either a classic line, HA transformed or Hybrid, which contains both of the previous.
To make Quantra's Indicators as useful and versatile as possible we have created options
to change the barcoloring and thus the derived signal from the indicator based on different modes.
Option to choose different Modes:
Trend Following (Indicator above mid line counts as uptrend, below is downtrend)
Extremities (Everything going beyond the Deviation Bands in a Mean Reversion manner is highlighted)
Candles (Color of HA candles as barcolor)
Reversion (HA ONLY) (Reversion Signals via the triangles if HA candles change state outside of the Deviation Bands)
- Reversion Signals are indicated by the triangles in the Heikin-Ashi or Hybrid visualization when the HA Candles revert
from downwards to upwards or the other way around OUTSIDE of the SD Bands.
Depending on the Indicator they signal OB/OS areas and can either work as high probability entries and exits for Mean Reversion trades or
indicate Momentum slow downs and potential ranges.
Please use another indicator to confirm this.
Case Study
To effectively utilize the NNT-RSI, traders should know their style and familiarize themselves with the available options.
As stated above, you have multiple modes available that you can combine as you need and see fit.
In the given example mostly only the mode was used in an isolated fashion.
Trend Following:
Purely relied on State Change - Midline crossover
Could be combined with Momentum or Reversion analysis for better entries/exits.
Extremities:
Ideal entry/exit is in the accordingly colored OS/OB Area, the Reversion signaled the latest possible entry/exit.
HA Candles:
Specifically applicable for strong trends. Powerful and fast tool.
Can whip if used as sole condition.
Reversions:
Shows the single entry and exit bars which have a positive expected value outcome.
Can also be used as confirmation or as last signal.
Please note that we always advise to find more confluence by additional indicators.
Traders are encouraged to test and determine the most suitable settings for their specific trading strategies and timeframes.
In the showcased trades the default settings were used.
Methodology
The Simple Neural Network Transformed RSI uses a simple neural network logic to process RSI values, smoothing them for more accurate trend analysis.
This is achieved through a linear combination of RSI values over a specified input length, weighted evenly to produce a neural network output.
// Simple neural network logic (linear combination with weighted aggregation)
var float inputs = array.new_float(nnLength, na)
for i = 0 to nnLength - 1
array.set(inputs, i, rsi1 )
nnOutput = 0.0
for i = 0 to nnLength - 1
nnOutput := nnOutput + array.get(inputs, i) * (1 / nnLength)
nnOutput
This output is then compared against a standard or dynamic mean line to generate trend following signals.
Mean = ta.sma(nnOutput, sdLook)
cross = useMean? 50 : Mean
The indicator also incorporates Heikin Ashi candlestick calculations to provide additional insights into market dynamics, such as trend strength and potential reversals.
// Calculate Heikin Ashi representation
ha = ha(
na(nnOutput ) ? nnOutput : nnOutput ,
math.max(nnOutput, nnOutput ),
math.min(nnOutput, nnOutput ),
nnOutput)
Standard deviation bands are used to create dynamic overbought and oversold zones, further enhancing the tool's analytical capabilities.
// Calculate Dynamic OB/OS Zones
stdv_bands(_src, _length, _mult) =>
float basis = ta.sma(_src, _length)
float dev = _mult * ta.stdev(_src, _length)
= stdv_bands(nnOutput, sdLook,sdMult/2)
= stdv_bands(nnOutput, sdLook, sdMult)
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.
For questions or recommendations, please feel free to seek contact in the comments.
