BTC/Gold Power-Law Bands + Quantile Oscillator

Description
This indicator visualizes a set of statistically derived Power-Law bands for the BTC/Gold ratio.
The model is based on a log–log regression of the BTC/Gold ratio over time and a weighted quantile regression that captures the distributional structure of the ratio across several long-term quantiles.

It provides a historical context for where the ratio currently lies relative to these mathematically estimated zones.

This indicator does not perform any new model fitting; it only displays the pre-computed band structure derived from the full historical dataset.

How the model works
This indicator is based on a statistical Power-Law model of the BTC/Gold ratio.
A long-term trend was estimated using a log–log OLS regression, and the deviations from this trend were analyzed through a rolling multi-year volatility measure.

The inverse of this volatility served as the weight for several quantile regression fits, producing robust long-term bands at multiple distribution levels (0.1%, 12.5%, 50%, 80%, 95%, 99.5%).
These quantile curves represent the historical valuation zones of the BTC/Gold ratio.

All final regression coefficients are fixed and embedded into the Pine script, which reconstructs the bands directly on the chart.

The extension of the bands into the future is based solely on the mathematical form of each curve and does not use any future market data.

What the indicator displays
• Six Power-Law quantile bands (0.1%, 12.5%, 50%, 80%, 95%, 99.5%) displayed as stacked colored zones
• BTC/Gold Ratio line
• Future-offset projection curves (mathematical extrapolation of the fitted Power-Laws, not based on future prices)
• Quantile Oscillator: A normalized representation of where the current ratio lies relative to the quantile structure.

How to use it
This indicator is not a timing tool.

It provides a structural, long-term statistical context for the BTC/Gold ratio, showing:
• how extreme a current valuation is relative to long-term history
• where the ratio sits within the Power-Law quantile spectrum
• long-term distribution zones derived from the quantile regressions
• a volatility-weighted representation of historical deviations

It may be useful for long-term cycle studies or ratio-based valuation comparisons, but there is no guarantee that this historical relationship will persist.

Important notes
• This indicator does not repaint.
• All projections are non-predictive mathematical extrapolations.
• This script is designed only for the symbol: BTCUSD/TVC:GOLD (BTC/Gold Ratio)
• It does not provide trading signals, recommendations, or financial advice.

Why closed-source?
The underlying regression model, weighting logic, and quantile estimations were produced externally using Python and constitute the core intellectual component of the study. The Pine version contains only the pre-calculated parameters and the visualization logic.