Mean reversion application seems to be one of those universally accepted truths regarding trading schemes. Since the schemes were developed by absolutely brilliant people mere mortals are reluctant to question whether or not any functional use is possible. Reversion is easily observed and occurs consistently. When applied to investment management and trading it seems absolutely useless. Means move. Reversion will occur but most likely at a point and price far from anything with reasonable utility or meaning. Then there is the entire matter of the time slice selected; 10 days, 50 days, 10 months, 20 years? There is a time frame somewhere that demonstrates the reversion to the mean. Unfortunately, it serves no useful purpose. I am hardly endowed with the intellectual gifts possessed by many in the field. However, the long engagement in the business allows recognition of schemes incapable of delivering results or supporting pursuit of informed management decisions.

Larry,

There are analytical tools that are useful in addressing the concerns you mentioned.

(i) There are models / analytical that take account non-stationarity in the mean. These include, for example, the Range-based EGARCH model referred to in the article. The short volatility process returns to a stochastic (non-stationary) long term mean.

Also, there are statistical tests such as Johansen, variants of which allow the user to test for reversion to a mean that incorporates a trend.

(ii) There are specific models, such as Ornstein-Uhlenbeck, that allow you to estimate the speed of mean reversion. This allows you to estimate whether you can anticipate reversion taking place in two days, or twenty years. I make use of this specific model and its properties in constructing mean-reversion strategies. See blog posts for details.

There may be tools that address the concerns but do not erase or mitigate the inherent dysfunction. Nothing is predictive in this business although reasonably probability can be estimated and used as guidance. The emotional element and crowd psychology aspect preclude timing anticipation. There is violence out there and often more than incidental or occasional. Everything reverts to a mean sooner or later. The issues are; what means, where do they meet and what time slice underlies the assumptions embedded in the models. A major problem with regression analysis is that a time slice must be selected in an application. Sadly, the selection matters not due to the inherent dysfunction. When convergence finally occurs it is often a matter of no one caring any longer and the meaning is long lost. Regression supporters offer some strong mathematic argument favoring use but the approach seems unsuitable for financial market application. The fact or idea that a price reverts to a non stationary means offers no constructive use when managing assets and rendering decisions. Events often disrupt the models in a "no one saw that one coming" manner. Then the fact that no one knows what happens next becomes more acutely problematic. Post disruptive events no one can plausibly present a model suggesting high probability patterns or subsequent movement. I respect the work and find it fascinating. Unfortunately, the results produced are no better than the random walk. The drunkard's walk permits him to return to his place of origin if given enough time. A monkey can write Shakespeare on a typewriter if given enough time. All price will revert to a mean if given enough time. Unfortunately, the time element cannot be measured within any reasonably useful or relevant dimension.

A single price process normally does not revert, but sometimes spreads between prices of related securities do.