Z-Score Oscillator

The Z-Score Oscillator indicator is a statistical momentum tool that measures how far the current price deviates from its rolling mean in standard deviation units to identify overbought and oversold conditions. It provides a statistically grounded measure of extremity that automatically adapts to changing volatility regimes across any asset or timeframe.

Usage

The Usage section describes how the script can be used to identify market extremes, trend strength, and potential reversals.

• Mean-Reversion: Use the oscillator to identify statistical extremes (overbought/oversold) where the price is likely to return to its average.
• Trend Confirmation: Persistent elevation in the z-score can confirm strong trending behavior.
• Divergence Spotting: Identify potential reversals or trend continuations by spotting discrepancies between price action and momentum.
• Mode Interpretation:
  • Oscillator Mode: Normalizes data into a fixed ±100 range. Readings above +100 or below -100 indicate statistical extremes based on the selected percentiles.
  • Z-Score Mode: Displays the raw number of standard deviations from the mean. This is useful for traders who prefer viewing literal sigma levels (e.g., ±2.0 or ±3.0).
  • Percentile Rank Mode: Displays the rank of the current value within its history, ranging roughly ±50. This mode is distribution-free and ideal for volatile assets.

Details

The script offers two primary calculation methods to define the "center" and "spread" of price:

1. Mean / StDev: The classic approach using arithmetic mean and standard deviation. It is statistically conventional but can be sensitive to large price outliers.
2. Median / MAD: A robust alternative using the median and Median Absolute Deviation. This method is outlier-resistant and recommended for markets with frequent gaps or long wicks, such as cryptocurrencies.

The indicator utilizes a Multi-Period Percentile Blend, which calculates thresholds across three different lookback windows simultaneously. This prevents the overbought/oversold levels from being overly sensitive to short-term spikes while maintaining relevance to recent price action.

Settings

Display & Z-Score Settings

• Mode: Switches between Oscillator, Z-Score, and Percentile Rank displays.
• Calculation Method: Selects between "Mean / StDev" (Classic) or "Median / MAD" (Robust).
• Rolling Window: The lookback period used to calculate the mean and deviation.
• Percentile Lookback: The history used to determine what constitutes an "extreme" value.
• Upper/Lower Percentile: Defines the statistical cutoffs for overbought (default 95%) and oversold (default 5%) levels.

Multi-Period & Smoothing

• Enable Multi-Period Blend: Toggles the weighted blending of three different lookback periods for thresholds.
• Smoothing Type: Provides five options (ALMA, LinReg, Hull MA, Super Smoother, Two-Pole Gaussian) to reduce bar-to-bar noise.
• Smoothing Length: The period for the selected smoothing algorithm.

Divergence

• Enable Divergence Detection: Toggles the detection of Regular (reversal) and Hidden (continuation) divergences.
• Pivot Lookback Right/Left: Sets the number of bars required to confirm a high or low pivot.
• Delay Plot Until Candle Closes: Prevents repainting by waiting for the price bar to finalize before marking a divergence.

FAQ

How do I interpret a Z-Score of +2.0? In Z-Score mode, a +2.0 reading means the price is currently two standard deviations above its rolling average, which is statistically significant in most distributions.

What is the benefit of the Median / MAD method? The Median / MAD method is less affected by extreme "black swan" events or outliers, ensuring that a single massive price spike doesn't distort the indicator's scale for the subsequent periods.

How can I access the Z-Score Oscillator? You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.