I have two historical price lists with the following columns
data – price
Now i have to create the ratio between the prices of these lists:
list A: 01/01/2011 10.50
list B: 01/01/2011 23.89
I compare the date of the lists, if the day is the same I find the ratio, doing:
ratio = 10.50 / 23.89
Ok… I do this division for each price of the lists.
The result should be:
0.4395 0.4400 0.4289 0.4361
Now the question is: How could I check if this serie (ratios) is mean reverting?
Best Answer
The answer below follows the definition taken from J.Exley et al article on Mean reversion: Discrete time mean-reverting process is a stationary process.
Let $R_t$ is your ratio, and $\mu$ is the mean value of this ratio, then mean-reverting process could be expressed as an $AR(1)$ process of the form:
$$ R_t -\mu = \alpha (R_{t-1}-\mu) + \sigma W_t $$
Stationarity tests are many: (A)DF, PP, KPSS tests all are common part in most of the statistical software. If you suspect that the data may have structural changes than you may consider Zivot-Andrews test. For $R$ users an
urca
library is essential in testing for stationarity.