Mean reversion is the statistical tendency of a specified time series or constructed relationship to move back toward a stable long-run level or equilibrium after a deviation. In a simple autoregressive model, X(t) − μ = φ[X(t−1) − μ] + ε(t), |φ| < 1 makes the process stationary around μ and causes the effect of a shock to decay rather than persist indefinitely. For 0 < φ < 1, deviations decay toward the mean without changing sign in expectation; for −1 < φ < 0, the adjustment oscillates around it. The reverting object must therefore be identified: it might be a price spread, valuation ratio, volatility measure, inventory deviation or another transformed series. A market price that sometimes reverses direction is not, by that fact alone, a mean-reverting price process.
What is actually reverting?
A random walk has no stationary long-run level around which deviations decay: shocks to its level persist. This makes stationarity central to many statistical applications of mean reversion and creates an important testing boundary. Rejecting a random-walk model does not automatically prove that a series is stationary or mean-reverting, because nonstationary alternatives can also generate such a rejection. Negative return autocorrelation can likewise indicate short-horizon reversal without establishing that the underlying price level is anchored to a stable mean.
Relative-value research adds another layer. Two price series may each be nonstationary while a particular linear combination is stationary. In that case, the combination—not necessarily either price by itself—can represent the long-run equilibrium. For example, suppose a nearby futures contract trades at 80 while a deferred contract trades at 76, producing a calendar spread of +4. Later the contracts trade at 86 and 77, widening the spread to +9. If research establishes that this spread has a stable equilibrium near +4, the mean-reversion hypothesis concerns the +9 spread moving back toward that equilibrium; it does not require either contract to return to 80 or 76. Cointegration formalizes an important version of this idea: the economically meaningful reverting variable may need to be constructed rather than observed directly.
Speed is part of the claim
Mean reversion also concerns how quickly deviations decay. In autoregressive or Ornstein–Uhlenbeck specifications, researchers often summarize that rate with a mean-reversion coefficient or estimated half-life. Those estimates depend on sampling frequency, model form and estimation window, and become fragile when persistence is close to a unit root. A historical equilibrium can also shift after structural change, so treating yesterday's mean as permanent may mistake a regime change for a temporary dislocation.
For market research, the practical question is therefore not simply whether a series “comes back.” It is whether the chosen variable has a defensible equilibrium, whether deviations show statistically stable decay, and whether that relationship survives out-of-sample and across relevant regimes.