Stationarity & Efficiency Tests

What are Stationarity & Efficiency Tests?

Stationarity and efficiency tests ask two related questions of a series: do its statistical properties (mean, variance) stay stable through time, and does the series follow a random walk, with returns that carry no usable memory? Unit-root tests answer the first. The augmented Dickey-Fuller (ADF) test takes non-stationarity (a unit root) as its null hypothesis, so rejection is evidence of stationarity, mean-reverting behavior in trading terms; the KPSS test flips the logic and takes stationarity as its null. Efficiency tests answer the second: the variance-ratio test compares the variance of k-period returns to k times the one-period variance, which are equal under a random walk. Ratios persistently below one point toward mean reversion, above one toward trending behavior.

Traders use these tests as regime instruments. Mean-reversion logic (fading a z-score, trading a pairs spread) presumes the traded series is roughly stationary, which raw price levels usually are not; spreads built through cointegration are candidates precisely because a stationary combination is the goal. Rolling versions of ADF, KPSS, or variance ratios are plotted as trend-versus-reversion gauges alongside the Hurst exponent. The honest caveats: these tests have limited power in short windows, verdicts flip with lag and window choices, and stationarity measured in the past is not a property the future is obliged to keep.

How traders use it

• Gating mean reversion: run a rolling ADF (or KPSS) on a spread or detrended series and allow reversion entries only while the test favors stationarity, standing aside when the spread starts behaving like a random walk.
• Regime classification: a rolling variance ratio above one supports momentum tactics, below one supports fading extremes; many workflows require agreement with an independent regime measure before switching playbooks.
• Input validation: checking that series fed to statistical or machine-learning models (returns, spreads, oscillator inputs) are approximately stationary, since many estimators quietly assume it.