Rolling KPSS Statistic [LuxAlgo]

The Rolling KPSS Statistic indicator evaluates the stationarity of price action within a rolling window using the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. This tool helps traders identify whether the current market environment is ranging, trending, or undergoing a structural regime shift by providing a continuous statistical measure of mean reversion.

🔶 USAGE

The indicator is designed to distinguish between stationary price action (where price fluctuates around a mean or trend) and non-stationary price action (where price exhibits random walk or breakout behavior). By applying a rolling window calculation, it provides a real-time assessment of market stability.

The script offers two primary modes of operation tailored to different market conditions:

🔹 Level Mode
This mode tests for stationarity around a constant mean. It is the optimal setting for detecting ranging or mean-reverting environments. When the KPSS statistic is low in this mode, it suggests the market is staying within a defined horizontal corridor.

🔹 Trend Mode
This mode tests for stationarity around a linear trend. It is used to identify if the market is moving consistently within a trending channel. A low KPSS value here indicates that while the price is moving up or down, it is doing so in a mathematically stable "stationary" trend rather than an erratic or parabolic one.

🔶 DETAILS

The KPSS test operates on the null hypothesis that the series is stationary. Unlike other unit root tests (like the Augmented Dickey-Fuller test), a low value in KPSS indicates stationarity, while a high value suggests the presence of a unit root (non-stationarity).

🔹 Critical Levels
The indicator plots three significance thresholds: 10%, 5%, and 1%.

• KPSS < 5% Level: The market is considered stationary. In "Level" mode, this implies a Range. In "Trend" mode, this implies a stable Trend.
  
• KPSS > 5% Level: The null hypothesis is rejected. The market is "Non-Stationary," suggesting a breakout, a trend reversal, or a transition into a random walk state.
  
• KPSS > 1% Level: This indicates a highly significant deviation from stationarity, often seen during impulsive market expansions.
  

🔹 Visual Feedback
The indicator uses a Viridis gradient theme. Brighter colors (yellow/green) represent stationary, mean-reverting behavior, while darker colors (purple/blue) represent non-stationary or trending behavior. A real-time dashboard is also included to provide an immediate summary of the current market state.

🔶 SETTINGS

🔹 Main Settings

• Window Length: The number of bars used for the rolling window. The default of 100 provides a balanced statistical lookback for most timeframes.
  
• Source: The price data used for the calculation (default is Close).
  
• Test Type: Select between "Level" (for ranges) or "Trend" (for trending stationarity).
  
• Newey-West Bandwidth: A lag truncation parameter used to account for serial correlation in the residuals.
  

🔹 Visuals & Dashboard

• Show Critical Levels: Toggles the visibility of the 10%, 5%, and 1% dashed lines.
  
• Dashboard: Enables or disables the on-screen information table.
  
• Position/Size: Controls the location and scale of the dashboard on the chart.