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Z-Score

Z-Score of an asset's price.

Indicator appearance.

Indicator appearance.

Description​

The standard score (Z-Score) is a measure of relative dispersion of an observed or measured value. It shows how many standard deviations the value lies from the mean.

How Z-Score is calculated​

The Z-Score indicator measures how far the current price deviates from its moving average, in standard deviations.

Moving average of the closing price over \( n \) periods:

MAt=∑i=0n−1Ct−inMA_t = \frac{ \sum_{i=0}^{n-1} C_{t-i} }{n}

where:

  • MAtMA_t — moving average of the closing price,
  • CtC_t — closing price,
  • nn — number of periods.

Standard deviation of the closing price over \( n \) periods:

σt=1n∑i=0n−1(Ct−i−MAt)2\sigma_t = \sqrt{ \frac{1}{n} \sum_{i=0}^{n-1} (C_{t-i} - MA_t)^2 }

where:

  • σt\sigma_t — standard deviation of the closing price over nn periods.

Z-Score calculation:

Zt=Ct−MAtσtZ_t = \frac{C_t - MA_t}{\sigma_t}

where:

  • ZtZ_t — Z-Score, which shows how far the current price is from the mean in units of standard deviation.