Support and Resistance Levels by Different Goodness of Fit Methods to Metalog Distributions
Introduction
The modeling of financial instruments must take into account the unique statistical characteristics of financial markets data.
Financial markets data (“FMD”) are inherently ‘noisy’ and there is difficulty in separating the noise from the true signal.
FMD almost always do not have a good fit into Normal (Gaussian) Distribution. A Normal Distribution is the familiar bell-shaped curve commonly applied in traditional statistical analysis to determine the probability of a variable having a specific value.
FMD have irregular shapes, may have more than one peak, skewed to the right or left, and have long fat tails.
The graphic below illustrates a Probability Density Function (PDF) for a financial instrument that displays long fat tails, skewness, and multiple peaks.)

Long Tails: Indicating higher probabilities of extreme values compared to a normal distribution; much more than the 3 standard deviations that cover 99% of a Normal Distribution.
Skewness: Here, the distribution is shifted towards the right side, and this asymmetry distorts any calculations based on a Normal Distribution.
Kurtosis: Narrow peaks make Mean values less meaningful,
Multiple Peaks: Reflecting the presence of more than one dominant behavior or market regime.
Metalog Distributions (Probability Density Fuctions [PDF])
Metalog Distributions are a new class of unbounded flexible PDF. Unlike traditional distributions that require assumptions about shape parameters, the Metalog Distribution adapts to the empirical data, making it highly versatile for various applications. However, there are several choices for Goodness of Fit crtiteria when you want to fit data to a Distribution. Different criteria will yield different number of terms for the fitting of the Metalog to the data to give you the values at the 5% Quantile and the 95% Quantile We need not bother with the technical formula for calculation of parameters but the common ways to fit a PDF are:
· Akaike Information Criterion (AIC)
· Anderson-Darling
· Maximum Likelihood
· Kolmogorov-Smirnov
The purpose of this post is to list for each of the methods above the values of the PDF at the 5% Quantile and 95% Quantile. In the case of market Indices and stock price data, these form the Support and Resistance levels. We will then evaluate which method of fitting to distribution is most suitable. We use the most recent 240 data points (trading days) of the end-of-day Close of the BSE Sensex data of the Bombay Stock Exchange as of 17 December 2024. The Sensex is a very lively Index due to the participation of retail investors. The data is post-Z-Score normalization, post-ARIMA and post-Monte Carlo Simulation. The input variables are the end-of-day Open, High, Low, and Volume of the Sensex and the output is the Close.
Here is a collage of the BSE Sensex data fitted with different methods to a Metalog PDF, and their resultant different Support(S) and Resistance (R) levels in the format S--->R.

We can see that there is very little difference between the various methods of fitting, except for AIC which yields a narrower band for trading. But the 1-20 steps ahead (trading days ahead) for the BSE Sensex as of 17 Dec shows a gradual upward trend (below) So, the AIC is not appropriate for trading as traders would have to work within a narrower band of cut loss and take profit, which in a rising market is inappropriate and should have more room for risk taking.

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