Geometric Momentum Breakout with Monte Carlo

Overview
This experimental indicator uses geometric trendline analysis combined with momentum and Monte Carlo simulation techniques to help visualize potential breakout areas. It calculates support, resistance, and an aggregated trendline using a custom Geo library (by kaigouthro). The indicator also tracks breakout signals in a way that a new buy signal is triggered only after a sell signal (and vice versa), ensuring no repeated signals in the same direction.

Important:
This script is provided for educational purposes only. It is experimental and should not be used for live trading without proper testing and validation.

Key Features
Trendline Calculation:
Uses the Geo library to compute support and resistance trendlines based on historical high and low prices. The midpoint of these trendlines forms an aggregated trendline.

Momentum Analysis:
Computes the Rate of Change (ROC) to determine momentum. Breakout conditions are met only if the price and momentum exceed a user-defined threshold.

Monte Carlo Simulation:
Simulates future price movements to estimate the probability of bullish or bearish breakouts over a specified horizon.

Signal Tracking:
A persistent variable ensures that once a buy (or sell) signal is triggered, it won’t repeat until the opposite signal occurs.

Geometric Enhancements:
Calculates an aggregated trend angle and channel width (distance between support and resistance), and draws a perpendicular “breakout zone” line.

Table Display:
A built-in table displays key metrics including:

Bullish probability
Bearish probability
Aggregated trend angle (in degrees)
Channel width
Alerts:
Configurable alerts notify when a new buy or sell breakout signal occurs.

Inputs
Resistance Lookback & Support Lookback:
Number of bars to look back for determining resistance and support points.

Momentum Length & Threshold:
Period for ROC calculation and the minimum percentage change required for a breakout confirmation.

Monte Carlo Simulation Parameters:

Simulation Horizon: Number of future bars to simulate.
Simulation Iterations: Number of simulation runs.
Table Position & Text Size:
Customize where the table is displayed on the chart and the size of the text.

How to Use
Add the Script to Your Chart:
Copy the code into the Pine Script editor on TradingView and add it to your chart.

Adjust Settings:
Customize the inputs (e.g., lookback periods, momentum threshold, simulation parameters) to fit your analysis or educational requirements.

Interpret Signals:

A buy signal is plotted as a green triangle below the bar when conditions are met and the state transitions from neutral or sell.
A sell signal is plotted as a red triangle above the bar when conditions are met and the state transitions from neutral or buy.
Alerts are triggered only on the bar where a new signal is generated.
Examine the Table:
The table displays key metrics (breakout probabilities, aggregated trend angle, and channel width) to help evaluate current market conditions.

Disclaimer
This indicator is experimental and provided for educational purposes only. It is not intended as a trading signal or financial advice. Use this script at your own risk, and always perform your own research and testing before using any experimental tools in live trading.

Credit
This indicator uses the Geo library by kaigouthro. Special thanks to Cryptonerds and Hazzantazzan for their contributions and insights.