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Z-Score (Standard Score)

by QuantShare, 2560 days ago
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If you want to compare a certain value of a time-series for a particular security to the value of other securities for the same date, then you should use the z-score. You will need to standardize data in order to use the z-score or the standard score.

The standard score, which is commonly referred to as the z-score, represents the distance between the score or the value and the observation or indicator mean for all the population (U.S. stocks) in units of the standard deviation. The population does not have to be normally distributed.

For each date, you will need to get every security time-series value (The time-series could be the share price, the volume or any indicator), and then calculate the mean and the standard deviation of these values. The end result should be two time-series, one that contains the standard deviation values and the other that contains the mean values.

This can be easily done using the composite plug-in. Mean and Standard deviation - Z-Score is an example on how to do that. This item calculates the one-day rate of return mean and standard deviation of all securities and for every trading bar.

The final step will be to use the following formula to calculate the standard score (z-score):
z = (x - mean) / (standard deviation)

Where z is the z-score for a particular bar and for a specific security and x is the security indicator's value for that bar.

The formula is named "zscore"; it accepts two parameters. The first one is the indicator or time-series for which you want to get the z-score values, and the second parameter is the composite symbol name.
Example:
score = zscore(roc(close, 1), "_RETURN SDV");

Let us take Google (GOOG) and the 25/01/2010 bar for example; a negative z-score value means that the one-bar rate of return of Google on 25/01/2010 was lower than the average one-bar rate of return of all U.S. stocks. A z-score value higher than two means that the one-bar rate of return of Google on 25/01/2010 was two standard deviations above the average one-bar rate of return of all U.S. stocks.

In case the indicator values follow a normal distribution, you can use the standard score and the statistical tables to calculate the percentile rank.


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Object ID: 382


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