Volume Weighted Intra Bar LR Correlation

This indicator analyzes market character by providing a detailed
view of correlation. It applies a Linear Regression model to
intra-bar price action, dissecting the total correlation of
each bar into three distinct components.

Key Features:

1. **Three-Component Correlation Decomposition:** The indicator
separates correlation based on the 'Estimate Bar Statistics' option.
- **Standard Mode (`Estimate Bar Statistics` = OFF):** Calculates
correlation based on the selected `Source` (this results
mainly in 'Trend' and 'Residual' correlation).
- **Decomposition Mode (`Estimate Bar Statistics` = ON):** The
indicator uses a statistical model ('Estimator') to
calculate *within-bar* correlation.
(Assumption: In this mode, the `Source` input is
**ignored**, and an estimated mean for each bar is used
instead).
This separates correlation into:
- **Trend Correlation (Green/Red):** Correlation explained by the
regression's slope (Directional Alignment).
- **Residual Correlation (Yellow):** Correlation from price
oscillating around the regression line (Mean-Reversion/Cointegration).
- **Within-Bar Correlation (Blue):** Correlation from the
high-low range of each bar (Microstructure/Noise).

2. **Visual Decomposition Logic:** Total Correlation is the
primary metric displayed. Since Correlation Coefficients are not
linearly additive, this indicator plots the *exact* Total
Correlation and partitions the area underneath based on the
Covariance Ratio. This ensures the displayed total correlation
remains mathematically accurate while showing relative composition.

3. **Dual Display Modes:** The indicator offers two modes to
visualize this decomposition:
- **Absolute Mode:** Displays the *total* correlation as a
stacked area chart, partitioned by the ratio of
the three components.
- **Relative Mode:** Displays the direct *energy ratio*
(proportion) of each component relative to the total (0-1),
ideal for identifying the dominant market character.

4. **Calculation Options:**
- **Normalization:** An optional 'Normalize' setting
calculates an **Exponential Regression Curve** (log-space),
making the analysis suitable for growth assets.
- **Volume Weighting:** An option (`Volume weighted`) applies
volume weighting to all regression and correlation calculations.

5. **Correlation Cycle Analysis:**
- **Pivot Detection:** Includes a built-in pivot detector
that identifies significant turning points (highs and lows) in
the *total* correlation line. (Note: This is only visible
in 'Absolute Mode').
- **Flexible Pivot Algorithms:** Supports various underlying
mathematical models for pivot detection provided by the
core library.

6. **Note on Confirmation (Lag):** Pivot signals are confirmed
using a lookback method. A pivot is only plotted *after*
the `Pivot Right Bars` input has passed, which introduces
an inherent lag.

7. **Multi-Timeframe (MTF) Capability:**
- **MTF Correlation Lines:** The correlation lines can be
calculated on a higher timeframe, with standard options
to handle gaps (`Fill Gaps`) and prevent repainting
(`Wait for...`).
- **Limitation:** The Pivot detection (`Calculate Pivots`) is
**disabled** if a Higher Timeframe (HTF) is selected.

8. **Integrated Alerts:** Includes comprehensive alerts for:
- Correlation magnitude (High Positive / High Inverse).
- Correlation character changes/emerging/fading.
- Total Correlation pivot (High/Low) detection.

**Caution! Real-Time Data Behavior (Intra-Bar Repainting)**
This indicator uses high-resolution intra-bar data. As a result, the
values on the **current, unclosed bar** (the real-time bar) will
update dynamically as new intra-bar data arrives. This behavior is
normal and necessary for this type of analysis. Signals should only
be considered final **after the main chart bar has closed.**

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**DISCLAIMER**

1. **For Informational/Educational Use Only:** This indicator is
provided for informational and educational purposes only. It does
not constitute financial, investment, or trading advice, nor is
it a recommendation to buy or sell any asset.

2. **Use at Your Own Risk:** All trading decisions you make based on
the information or signals generated by this indicator are made
solely at your own risk.

3. **No Guarantee of Performance:** Past performance is not an
indicator of future results. The author makes no guarantee
regarding the accuracy of the signals or future profitability.

4. **No Liability:** The author shall not be held liable for any
financial losses or damages incurred directly or indirectly from
the use of this indicator.

5. **Signals Are Not Recommendations:** The alerts and visual signals
(e.g., crossovers) generated by this tool are not direct
recommendations to buy or sell. They are technical observations
for your own analysis and consideration.