Estimating Mean-Reversion Time with an Ornstein–Uhlenbeck Model

Summary

The answer points to the Ornstein–Uhlenbeck process as a simple model for mean-reverting behavior and explains how its parameters relate to the process. In particular, the reversion-strength parameter indicates how quickly deviations tend to decay, with its reciprocal commonly used as a characteristic mean-reversion time. The model also includes a parameter for the scale of random variation.

For estimating parameters from a time series, the answer identifies least squares as an intuitive approach and maximum likelihood as a more exact alternative, and references an external tutorial. It does not derive either estimator, apply them to data, or calculate the expected time until a path crosses its long-term mean. The reciprocal reversion rate is a characteristic timescale, not a guarantee of when an individual process will cross its mean; crossing-time estimates depend on the model assumptions and the path's current state. The discussion also cautions that mean-reversion trading can refer to many different approaches.

Key ideas

• The Ornstein–Uhlenbeck process is a simple model for continuous mean-reverting behavior.
• Its reversion-strength parameter controls how quickly deviations tend to decay.
• The reciprocal of reversion strength is commonly treated as a characteristic reversion timescale.
• Least squares and maximum likelihood are possible approaches for estimating model parameters from time series.
• A characteristic reversion timescale does not by itself determine when a particular path will cross its mean.

Tags

# Mean reversion time estimation


# Mean reversion time estimation












I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.

## Answer by Alex C (score 10)

https://quant.stackexchange.com/a/17973

Well, "mean reversion trading" could mean a lot of things, I am not qualified to describe it in full generality.

However, there is a simple model of mean reversion called the Ornstein Uhlenbeck process that is often seen. It has two parameters $\lambda$ and $\sigma$, where $\lambda$ is the strength of the mean reversion (so one over $\lambda$ is the mean reversion time).

Here is a nice web site that covers the estimation of OU process parameters from time series data using two methods: least squares (most intuitive) and max likelihood (more exact).

http://www.sitmo.com/article/calibrating-the-ornstein-uhlenbeck-model/

Hope this helps.

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