Change-Point Detection (CUSUM) [LuxAlgo]

The Change-Point Detection (CUSUM) indicator is a statistical tool designed to detect structural changes in price trends by accumulating deviations from a mean, allowing for the identification of regime shifts before they become obvious to the naked eye.

🔶 USAGE

The indicator helps traders identify when a market has shifted from its current state (bullish or bearish) by monitoring the cumulative sum of standardized log-returns. Unlike standard trend-following indicators that rely on lagging averages, CUSUM looks for a "tipping point" where price behavior significantly deviates from its recent historical norm.

🔹 Interpreting the Visuals

• Regime Line: The solid horizontal/stepping line represents the price level at which the last change-point was detected. The color indicates the current regime (Green for Bullish, Red for Bearish).
  
• Pressure Bands: The shaded areas extending from the regime line represent the sPos and sNeg accumulators. These visualize how much "pressure" is building up against the current regime.
  
• Markers: Small triangles appear when the accumulated pressure exceeds the user-defined threshold, signaling a change-point and resetting the baseline to the current price.
  

🔶 DETAILS

The script utilizes a modified Cumulative Sum (CUSUM) algorithm, a sequential analysis technique typically used for monitoring change-point detection.

The process follows these steps:

1. Log-Returns & Standardization: The script calculates the log-returns of the price and standardizes them into a Z-Score based on a rolling mean and standard deviation. This ensures the sensitivity of the algorithm remains consistent regardless of the asset's price or volatility.
   
2. Accumulation: Two accumulators (sPos for upward moves and sNeg for downward moves) track the Z-Score.
   
3. The Slack (k): This parameter acts as a filter. Only deviations greater than k are added to the accumulators. This prevents the indicator from triggering on minor noise or sideways price action.
   
4. The Threshold (h): Once an accumulator exceeds the threshold h, a change-point is confirmed. The accumulators are then reset, and a new regime price is established.
   

🔶 SETTINGS

🔹 Algorithm Settings

• Lookback Period: Determines the window used to calculate the rolling mean and standard deviation for the standardization of returns.
  
• Threshold (h): Controls the sensitivity of the detection. A higher threshold requires a more sustained and significant move to trigger a regime change.
  
• Slack (k): Represents the "allowable" deviation. Increasing this value requires price moves to be more aggressive to begin accumulating toward a change-point.
  

🔹 Dashboard

• Enable Dashboard: Toggles the visibility of the on-screen information panel.
  
• Position: Moves the dashboard to different corners of the chart.
  
• Size: Adjusts the scale of the dashboard text and cells.