# augemnted Dickey-Fuller test

In the first Mean Reversion and Cointegration post, I explored mean reversion of individual financial time series using techniques such as the Augmented Dickey-Fuller test, the Hurst exponent and the Ornstein-Uhlenbeck equation for a mean reverting stochastic process. I also presented a simple linear mean reversion strategy as a proof of concept. In this post, I’ll explore artificial stationary time series and will present a more practical trading strategy for exploiting mean reversion. Again this work is based on Ernie Chan's Algorithmic Trading, which I highly recommend and have used as inspiration for a great deal of my own research. Go easy on my design abilities... In presenting my results, I have purposefully shown equity curves from mean reversion strategies that go through periods of stellar performance as well as periods so bad that they would send most traders broke. Rather than cherry pick the good performance, I want to demonstrate what I think is of utmost importance in this type of trading, namely that the nature of mean reversion for any financial time series is constantly changing. At times this dynamism can...

This series of posts is inspired by several chapters from Ernie Chan's highly recommended book Algorithmic Trading. The book follows Ernie's first contribution, Quantitative Trading, and focuses on testing and implementing a number of strategies that exploit measurable market inefficiencies. I'm a big fan of Ernie's work and have used his material as inspiration for a great deal of my own research. My earlier posts about accounting for randomness (here and here) were inspired by the first chapter of Algorithmic Trading. Ernie works in MATLAB, but I'll be using R and Zorro. Ernie cites Daniel Kahneman's interesting example of mean reversion in the world around us: the Sports Illustrated jinx, namely that "an athlete whose picture appears on the cover of the magazine is doomed to perform poorly the following season" (Kahneman, 2011). Performance can be thought of as being randomly distributed around a mean, so exceptionally good performance one year (resulting in the appearance on the cover of Sports Illustrated) is likely to be followed by performances that are closer to the average. Mean reversion also exists in, or can be constructed from, financial time series...