Normalized Bollinger Band Distance

This TradingView script calculates and visualizes the Normalized Bollinger Band Distance to analyze the relative spread of Bollinger Bands as a percentage of the moving average. It also determines thresholds based on global statistics to highlight unusual market conditions. Here's a detailed description:

Indicator Overview
Purpose: The indicator measures the normalized distance between the upper and lower Bollinger Bands relative to the Simple Moving Average (SMA). It helps identify periods of high or low volatility.
Visualization: Displays the normalized distance along with dynamic thresholds based on global statistical calculations (mean and standard deviation).
Inputs
Length (length): Defines the period for the SMA and Bollinger Bands calculation. Default is 200.
Standard Deviations (stdDev): Number of standard deviations for the Bollinger Bands. Default is 2.
Calculation
Bollinger Bands:

Upper Band:
SMA
+
(
Standard Deviation
×
stdDev
)
SMA+(Standard Deviation×stdDev)
Lower Band:
SMA
−
(
Standard Deviation
×
stdDev
)
SMA−(Standard Deviation×stdDev)
Normalized Distance:

Normalized Distance
=
Upper Band
−
Lower Band
SMA
Normalized Distance=
SMA
Upper Band−Lower Band
​

Global Statistics:

Global Mean (
𝜇
μ): Average of all normalized distances up to the current bar.
Global Standard Deviation (
𝜎
σ): Standard deviation of all normalized distances up to the current bar.
High Threshold:
𝜇
+
1.5
×
𝜎
μ+1.5×σ
Low Threshold:
𝜇
−
1.5
×
𝜎
μ−1.5×σ
Visualization
Normalized Distance Plot:
The normalized distance is plotted in blue as a percentage for easy interpretation.
Threshold Lines:
High Threshold: Red line to signal unusually high volatility.
Low Threshold: Green line to signal unusually low volatility.
Mean Line: White line indicating the average normalized distance.
Zero Line: Horizontal white line for reference.
Use Case
High Threshold Breach: Indicates an unusual increase in Bollinger Band width relative to the SMA, signaling potential high market volatility.
Low Threshold Breach: Indicates an unusual narrowing of Bollinger Band width, suggesting low volatility and potential consolidation.
Trend Analysis: Observe how the normalized distance evolves over time to anticipate market conditions.