Z-Score
Definition
Z-score is the number of standard deviations a value is from the mean. In trading, z-scores measure how unusual a current value is relative to historical distribution — high z-scores indicate extreme conditions (overbought/oversold, abnormal volatility, regime stress). Z-score analysis underlies many mean-reversion and statistical arbitrage strategies.
In-depth: Z-Score
Z-scores translate raw values into a standardised scale that lets traders compare conditions across different instruments and timeframes. The transformation is statistical and assumes the underlying distribution is approximately normal — a problematic assumption for financial data but a useful approximation for many practical purposes.
Z-score computation:
• z = (current value − rolling mean) ÷ rolling standard deviation • Rolling window typically 20, 50, or 100 periods • Result is dimensionless; comparable across instruments
Z-score interpretation:
• |z| < 1: normal range; current value within one standard deviation of mean • |z| 1-2: somewhat unusual; ~32% of normal-distribution values fall in this range • |z| 2-3: unusual; ~5% of normal-distribution values • |z| > 3: very unusual; ~0.3% of normal-distribution values; potential outlier or regime shift
Z-score applications in forex trading:
• **Mean-reversion signals**: when an indicator's z-score exceeds threshold (e.g. RSI z-score > +2), expect mean reversion. Combined with directional confirmation, generates trade signals • **Statistical arbitrage**: monitor price spread between historically-correlated instruments; trade when spread z-score exceeds threshold • **Regime classification**: extreme z-scores on volatility metrics (ATR z-score > +2) indicate volatile regime; near-zero z-scores indicate calm regime • **Anomaly detection**: monitor performance metrics' z-scores during live deployment; large z-score deviations from baseline suggest strategy decay or regime shift
Limitations of z-score analysis:
• **Normal-distribution assumption**: financial data has fat tails; |z| > 3 events occur more often than 0.3% normal distribution predicts. Z-scores systematically underestimate tail probability • **Non-stationarity**: rolling means and standard deviations themselves shift over time; z-scores computed against shifting baseline have different meaning across time • **Regime sensitivity**: during regime shifts, z-scores can show extreme values not because the current value is unusual but because the baseline reflects a different regime • **Single-pair limitation**: z-scores work on individual series; multi-pair or cross-asset correlations require more sophisticated multivariate methods
For EA buyer evaluation: EAs using z-score logic (statistical arbitrage, mean-reversion, regime classification) should document the rolling window length and threshold values. Vendors who specify these signal genuine implementation; vendors using z-score terminology without parameter disclosure are typically using it as marketing.