Multi Brownian Forecast

📊 Multi Brownian Forecast (Time-Adaptive, Probabilistic)

This indicator uses a sophisticated Geometric Brownian Motion (GBM) Monte Carlo simulation to project future price paths. It adapts to any chart timeframe and provides quantitative, multi-period probability signals.

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🧠 Core Mathematical Methodology

The model relies on GBM, which is a continuous-time stochastic process that models asset prices.

1. Historical Analysis (Drift & Volatility):
* The script first calculates Logarithmic Returns over a user-defined Historical Lookback (Hours).
* Drift ($\mu$): Computed as the average of the log returns.
* Volatility ($\sigma$): Computed as the standard deviation of the log returns.
* These values are then time-adapted to an hourly step, compensating for the chart's current timeframe (e.g., 5-minute, 1-hour).

2. Monte Carlo Simulation:
* It runs a specified Number of Simulations (e.g., 1000).
* For each simulation, the price is stepped forward hourly using the GBM formula, which incorporates the calculated drift and a random shock drawn from a normal distribution (generated via the Box-Muller transform).

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✨ Key Features

• Probabilistic Quartile Forecast: Plots a dynamic "cone" of probability on the chart. It shows key price percentiles (Q1, Q2/Median, Q3, and Q4/Outer Bound) at the forecast's expiration, visualizing the expected range of price outcomes based on the simulations.
  
• Multi-Period Probability Signals: This is the core signal feature. Users can define multiple, independent forecast periods (e.g., 4h, 16h, 48h) in a comma-separated list.
  * For each period, a Probability Up and Probability Down is calculated based on hitting a custom Target Price Change (%) (e.g., 2%) at a certain confidence level given a simulation over the historical backlook.
  * The probabilities are displayed in a chart table. The cell text turns white if the calculated probability exceeds the user-defined Signal Confidence (%).
  
• Conditional Fibonacci Retracement: Optionally displays a Fibonacci Retracement on the chart. This feature is only activated when one of the multi-period signals reaches its minimum confidence threshold, providing a contextual technical level when a probabilistic edge is found.