Triple Z (Geometrical Mean) [ChartPrime]

Triple Z (Geometrical Mean)

Overview
The "Triple Z (Geometrical Mean) [ChartPrime]" indicator calculates three Z-scores of closing prices with different lengths, computes their geometric mean, and visualizes it on the chart with gradient colors and labeled values. Signals are generated when the geometric mean crosses above or below zero.

Geometric Mean:
The geometric mean is the central tendency of a set of numbers, calculated by multiplying them together and then taking the nth root (where n is the count of numbers). It is especially useful for sets of numbers that are products or exponential in nature, providing a more accurate measure of central tendency than the arithmetic mean for growth rates and ratios.

// Geometrical Mean
if barstate.isconfirmed
    geometric_mean := math.pow(( 1 + math.avg(z_1, z_1[1], z_1[2]) / 100) 
                              * (1 + math.avg(z_2, z_2[1], z_2[2]) / 100) 
                              * (1 + math.avg(z_3, z_3[1], z_3[2]) / 100)
                              , 3.0)-1

Key Features:

⯁ Z-Scores Calculation:

• - Three Z-scores with lengths: `length`, `length/2`, and `length/5`.
  

⯁ Geometric Mean:

• - Calculated from the latest Z-scores and plotted on the chart.
  
• - Matrix displays the latest Z-scores and geometric mean below.
  

⯁ Visualization:

• - Lines with gradient colors represent Z-scores.
  
• - Hull Moving Average plotted with gradient color based on the geometric mean.
  
• - Labels show current values.
  
• - Historical Values of Geometrical Mean.
  

⯁ Signals:

• - Diamond shapes indicate when the geometric mean crosses above or below zero.
  

⯁ Usage Break Down:

• - Z score Oscillator above zero > up trend, below zero > down trend
  
• - Slow Z score For longer terms trends, the fastest Z score for fast changes in a market
  
• - Geometrical Mean and matrix is calculated of these three Z scores Oscillators. Geometrical Mean uses Z scores from Matrix, each column contain Z scores of each oscillator (Current at the top, next previous and last before previous Z value).
  
• - The Higher Geometrical Mean the stronger Trend up (above zero), the lower G Mean the stronger Trend Down (below zero)
  
• - Aggregation of these key points creates Ultimate Trend Following Indicator with strength of trends
  

Use this indicator to analyze market trends via Z-scores and their geometric mean. Crossings of the geometric mean can signal potential trend up or trend down. Color gradients provide visual cues on market direction and strength.