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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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This Oscillator describes the drift of an asset, as part of the geometric Brownian Motion (GBM). As a data basis the mean reverting log returns of the asset price is considered. It gives the percentile of drift directional. For instance, a value of 0.05 means a drift of 5%, based on the selected sample size. If the value is positive, drift to higher asset values is determined.  This indicator should be used in confluence with other indicators based on volatility, probability and statistics. L
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Percentile of Historical Volatility and Correlation Coefficient shows if the asset is cheap or expensive based on the volatility. It is used to determine a good entry point. It has two indicators built in: Historical Volatility is ranked percentile wise and its correlation to price action which gives an indication of the direction of a possible future move. Together the both indicators can give good entries and direction.   Historical Volatility is a statistical measure of the dispersion of retu
The indicator ‘Probability Range Bands’ gives a prediction of the amount, how much the asset is moving from its current price. The range bands give probabilities, that the candle close will not exceed this certain price level. It is also called the expected move for the current candle close.   This Indicator is based on statistical methods, probabilities and volatility. Asset price is assumed to follow a log-normal distribution. Therefore, log returns are used in this indicator to determine the
The RSI2.0 indicator uses normalized price data and signal processing steps to get a normal distributed oscillator with no skew (mean is zero). Therefore, it can give much better reads than the traditional RSI.   Areas/Levels of reversal: Overbought or oversold levels from traditional RSI have no statistical significance, therefore the standard deviation bands are implemented here, which can be used in similar way as possible reversal points.   Divergence: As the indicator is nearly normal dist
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
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
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