Concept
Z-score
Z-score, also known as rolling z-score, is a Statistics concept. The Library holds 7 implementations, each one a working definition you can pull into Quant.
Top Z-score indicators
7 total
What is a Z-score?
A z-score expresses how far the current value of a series sits from its recent average, measured in standard deviations. A rolling implementation takes the last N values of any input (price, returns, volume, an oscillator, a spread), computes their mean and standard deviation, then divides the current value's deviation from that mean by the standard deviation. A reading of 0 sits exactly at the mean, +2 is two standard deviations above it, and negative readings mirror below.
The transform matters because it puts unrelated series on one unitless scale, which is the foundation of much mean-reversion and normalization logic: Bollinger Bands are simply the price levels where the z-score equals a chosen multiplier. The usual caution applies. The textbook intuition that roughly 95% of values stay inside ±2 assumes a normal distribution, and market returns are fat-tailed with a drifting mean, so extreme z-scores occur more often than the table suggests and can stay extreme while a trend runs.
How to calculate a Z-score
The rolling calculation needs only a window, a mean, and a standard deviation.
- 1Choose the input series and a lookback window N. Returns and oscillator values are better behaved than raw price, which trends and drags the mean along behind it.
- 2Compute the mean and the standard deviation of the last N values.
- 3Subtract the mean from the current value and divide the result by the standard deviation. The output is the distance from the window average, expressed in standard deviations.
- 4Plot it as an oscillator around zero, typically with reference lines at ±1, ±2, and ±3 marking increasingly rare readings.
How traders use it
- As a mean-reversion trigger: readings beyond a threshold such as ±2 flag statistically stretched values, with entries taken back toward the mean. Thresholds are conventions rather than guarantees, and trending markets can hold a z-score pinned high or low for long stretches, which is why many systems pair the trigger with a trend filter.
- As a common scale for comparison: z-scoring lets momentum, stretch, or relative volume be ranked across different symbols and timeframes on equal footing, since every input becomes 'standard deviations from its own norm'.
- As the engine of spread trading: pairs models z-score the spread between two related instruments and trade its extremes, usually after a cointegration check confirms the spread actually reverts.
- As an outlier flag: a z-scored volume series is one standard way to define a volume spike, and the same treatment isolates unusually wide ranges or gaps.
Z-score vs related concepts
Percentile Rank: Percentile rank counts how many past values sit at or below the current one, using order alone. A z-score measures distance in standard deviations, so it preserves magnitudes but leans on the distribution being roughly normal; percentile rank makes no such assumption and saturates at the window's extremes.
Min-max Scaling: Min-max scaling positions the value between the window's minimum and maximum, so a single outlier stretches the scale and compresses everything else. A z-score is anchored to the mean and standard deviation, which dampens, though does not remove, the influence of one extreme print.
Bollinger Bands: The two are the same mathematics displayed differently: the bands draw the mean plus and minus k standard deviations on the price panel, while the z-score plots the equivalent position as an oscillator. A close on the upper band and a z-score of +k (same window and source) are identical statements.
More Z-score implementations
Related concepts · Normalization & distribution
Concept family
Statistics
45 concepts mapped · 37 in the Library
Z-score FAQ
What is a good z-score threshold for trading signals?
Common conventions are ±2 for stretched and ±3 for extreme, echoing normal-distribution benchmarks. Because returns are fat-tailed and regimes shift, the frequency of those readings varies widely across markets and window lengths. Treat thresholds as parameters to test rather than fixed rules, and expect more ±3 events than a normal table implies.
What lookback period should a rolling z-score use?
There is no universal setting. Short windows adapt quickly but produce noisy standard-deviation estimates; long windows are stable but slow to accept a regime change. A practical approach is to match the window to the horizon of the reversion you trade, then confirm the signal is not hypersensitive to small changes in that length.
Does a z-score above 2 mean price will revert?
No. It says the current value is unusual relative to the recent window, not that a reversal is due. In a strong trend the rolling mean chases price, so the score can stay elevated bar after bar. Most systems require additional confirmation, such as a momentum stall or a level, before fading a stretched reading.
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