Solved – How to know if a list of prices are mean-reverting

cointegrationcorrelationeconometrics

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.

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