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z-score

How many standard deviations an observation sits from its mean. The common currency for comparing signals across instruments with different volatilities.

z = (x - mean) / standard deviation. A spread trading two points above a 20-day mean with a 0.8-point standard deviation has z = 2.5, which is comparable with a different pair whose numbers are in entirely different units.

Mean-reversion systems typically enter at |z| above some threshold and exit near zero. The threshold is a parameter like any other and should be checked for a parameter-plateau: if 2.0 works and 2.2 does not, you have fitted noise.

Caution: z-scores assume the mean and standard deviation are meaningful, which fails when the series is trending or non-stationary. On a trending series the z-score is permanently stretched in the direction of the trend, and the system sells strength forever.

Related: normalisation, mean-reversion, stationarity, trading-signal

Educational only, not advice. Spotted an error? Post in Site Feedback.