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.

# Normal

STDev BandsReally simple script for dynamic support and resistance. Takes means over last 1440 bars (1440 minutes in a day) and calculates seven stdevs up and down.

Outlier Detector with N-Sigma Confidence IntervalsA detrended series that oscilates around zero is obtained after first differencing a time series (i.e. subtracting the closing price for a candle from the one immediately before, for example). Hypothetically, assuming that every detrended closing price is independent of each other (what might not be true!), these values will follow a normal distribution with mean zero and unknown variance sigma squared (assuming equal variance, what is also probably not true as volatility changes over time for different pairs). After studentizing, they follow a Student's t-distribution, but as the sample size increases (back periods > 30, at least), they follow a standard normal distribution.
This script was developed for personal use and the idea is spotting candles that are at least 99% bigger than average (using N = 3) as they will cross the upper and lower confidence interval limits. N = 2 would roughly provide a 95% confidence interval.

Sectors Relative Strength Normal DistributionI wrote this indicator as an attempt to see the Relative Strengths of different sectors in the same scale, but there is also other ways to do that.
This indicator plots the normal distribution for the 10 sectors of the SPY for the last X bars of the selected resolution, based on the selected comparative security. It shows which sectors are outperforming and underperforming the SPY (or any other security) relatively to each other by the given deviation.