Mean reversion

In statistical terms, a series is mean reverting when it is stationary: it has a fixed long run average and a tendency to be pulled back towards it, so the further it sits from that average the more likely the next move is towards it. That is a testable property, not an assumption, and standard tests exist for it. The central value is usually estimated by an average of recent observations, most often a moving average, which means the mean being reverted to is itself moving.

Where practitioners disagree is which market series have the property. The strongest cases sit in relationships rather than in outright prices: the difference between two closely related instruments, a yield spread, or a ratio between two prices tied together by an arbitrage. Outright prices behave differently in different regimes, and a series that reverted to a mean for months can trend away from it for months afterwards, which is the observation behind the point that a range bound market and a trending market are not the same object described in two moods.

A great many indicators embed the assumption without stating it. Anything scaled between fixed limits and read as overbought or oversold is a mean reversion instrument by construction, as are bands drawn a number of standard deviations either side of an average. The recurring error is treating a distance from the mean as a statement about what happens next: a series with no fixed mean can travel a long way from its recent average and simply keep going, and no distance is a bound.