Volatility-Adjusted Trend Deviation Statistics (C-Ratios)

The Pine Script logic provided generates and displays a table with key information derived from VWMA, EMA, and ATR-based "C Ratios," alongside stochastic oscillators, correlation coefficients, Z-scores, and bias indicators. Here’s an explanation of the logic and what the output in the table informs:

Key Calculations and Their Purpose
VWMA and EMA (Smoothing Lengths):

Multiple EMAs are calculated using VWMA as the source, with lengths spanning short-term (13) to long-term (233).
These EMAs provide a hierarchy of smoothed price levels to assess trends over various time horizons.
ATR-Based "C Ratios":

The C Ratios measure deviations of smoothed prices (a_1 to a_7) from the source price relative to ATR at corresponding lengths.

These values normalize deviations, giving insight into the price's relative movement strength and direction over various periods.
Stochastic Oscillator for C Ratios:

Calculates normalized stochastic values for each C Ratio to assess overbought/oversold conditions dynamically over a rolling window.
Helps identify short-term momentum trends within the broader context of C Ratios.
Displays the average stochastic value derived from all C Ratios.
Text: Shows overbought/oversold conditions (Overbought, Oversold, or ---).
Color: Green for strong upward momentum, red for downward, and white for neutral.
Weighted and Mean C Ratio:

The script computes both an arithmetic mean (c_mean) and a weighted mean (c_mean_w) for all C Ratios.
Weighted mean emphasizes short-term values using predefined weights.
Trend Bias and Reversal Detection:

The script calculates Z-scores for c_mean to identify statistically significant deviations.
It combines Z-scores and weighted C Ratio values to determine:
Bias (Bullish/Bearish based on Z-score thresholds and mean values).
Reversals (Based on relative positioning and how the weighted c_mean and un-weighted C_mean move. ).
Correlation Coefficient:

Correlation of mean C Ratios (c_mean) with bar indices over the short-term length (sl) assesses the strength and direction of trend consistency.
Table Output and Its Meaning
Stochastic Strength:

Long-term Correlation:
List of Lengths: Define the list of lengths for EMA and ATR explicitly (e.g., [13, 21, ..., 233]).

Calculate Mean C Ratios: For each length in the list, calculate the mean C Ratio

Average these values over the entire dataset.

Store Lengths and Mean C Ratios: Maintain arrays for lengths and their corresponding mean C Ratios.

Correlation: compute the Pearson correlation between the list of lengths and the mean C Ratios.
Text: Indicates Uptrend, Downtrend, or neutral (---).
Color: Green for positive (uptrend), red for negative (downtrend), and white for neutral.

Z-Score Bias:

Assesses the statistical deviation of C Ratios from their historical mean.
Text: Bullish Bias, Bearish Bias, or --- (neutral).
Color: Green or red based on the direction and significance of the Z-score.
C-Ratio Mean:

Displays the weighted average C Ratio (c_mean_w) or a reversal condition.
Text: If no reversal is detected, shows c_mean_w; otherwise, a reversal condition (Bullish Reversal, Bearish Reversal).
Color: Indicates the strength and direction of the bias or reversal.
Practical Insights
Trend Identification: Correlation coefficients, Z-scores, and stochastic values collectively highlight whether the market is trending and the trend's direction.
Momentum and Volatility: Stochastic and ATR-normalized C Ratios provide insights into the momentum and price movement consistency across different timeframes.
Bias and Reversal Detection: The script highlights potential shifts in market sentiment or direction (bias or reversal) using statistical measures.
Customization: Users can toggle plots and analyze specific EMA lengths or focus on combined metrics like the weighted C Ratio.