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Z Score Standardized Normal Distribution

This z-score indicator shows the correct z-score of an asset, as it uses the normalized price data for calculation, which is the only correct way. Z-score is only applicable for normal distributed data, therefore not the actual price is considered, but the normalised returns, which were assumed to follow a normal distribution.

Returns are mean reverting and assumed to follow a normal distribution, therefore z-score calculation of returns is more reliable than z-score on price, as price is NOT mean reverting and follow NOT a normal distribution but a log-normal distribution.


Z-score measures the distance to the mean in terms of standard deviation. If z-score is 0 it is equivalent to the mean score, if it is 1.0 the distance is 1 standard deviation from the mean. Therefore, it is important that the underlaying data follows a normal distribution, which the returns are assumed.


This indicator curve is the thick z-score line (coloured blue). It also shows outliers, if the respective line exceeds it individual standard deviation band it changes colour. At the default mode is exceeding 2 SDs. If turning pink it indicates a pre-warning that a bearish reversal could take place. If the Blue line turns “aqua” it indicates a bullish reversal.


How to use: As the returns are mean reverting, it is more likely if the z-score is high, that there will be a reversal back to the mean. So, it is an oscillator in the general sense. The confidence intervals for 90%, 95% and 99%, are also plotted which can act as probability levels, that the z-score will not exceed that level. That means, it can indicate a reversal. For instances if the curve is close to the 99% line, there is only a probability of 1% that the z score will exceed that line, so a reversal is more likely. Also, the colour change of the returns line (default: blue) can indicate a reversal (pink: bearish, aqua: bullish)


The Input Settings:

Sample Size: Default 30, length of periods back to calculated z-score

Multiplier: default 2.0, Multiplier in terms of standard deviation, to show outliers/possible reversals (line colour change)


Remark: Indicator is provided for statistical analysis and showing probabilities only and should not be construed as financial advice.


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The Returns Momentum Oscillator (RMO) shows the difference of exponentially weighted volatility. It is used to find market tops and bottoms. Volatility comes in waves, and as the Returns often front run price action it gives directional prediction of market movement.   The Oscillator signal is RMSed (root mean squared) to make the distribution closer to Gaussian distribution. While the traditional RSI indicators are often stuck in overbought or oversold areas for a long time, RMSing of the sign
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Bollinger Bands based on Returns   This indicator characterizes the price and volatility by providing a channel/band of standard deviations like the Bollinger Bands. In contrary to standard Bollinger Bands which uses price directly, this indicator uses returns due to normalization.   The standard Bollinger Bands based on price directly, were one of the first quant or statistical methods for retail traders available. The issue with these bands, standard deviations can only be calculated, if the u
35 USD
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