# Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller test.

Example: Whiting Petroleum Corporation (WLL) vs Approach Resources, Inc. (AREXQ)

Time period: 01 Jan 2012 - 01 Jan 2013

Source: Yahoo Finance

Spread = Y-βX


β is obtained from performing OLS LinearRegression().fit using scikit in Python

If I choose Y = AREXQ and X = WLL, I get β = 0.13470899 And the ADF results:

Results of Dickey-Fuller Test:
Test Statistic                 -3.069995
p-value                         0.028855
#Lags Used                      0.000000
Number of Observations Used    89.000000
Critical Value (1%)            -3.506057
Critical Value (5%)            -2.894607
Critical Value (10%)           -2.584410
This Time Series is STATIONARY


If I swap the tickers, Y = WLL and X = AREXQ, I get β = 5.85042859 And the ADF results:

Results of Dickey-Fuller Test:
Test Statistic                 -2.739417
p-value                         0.067462
#Lags Used                      0.000000
Number of Observations Used    89.000000
Critical Value (1%)            -3.506057
Critical Value (5%)            -2.894607
Critical Value (10%)           -2.584410
This Time Series is NON-STATIONARY


One is stationary and the other is not. Am I doing or understanding something wrong? Is there a criteria that I should only choose a certain pair to be Y or X?

Or if there's one result that returns stationary, then i should assume it's stationary and apply the beta (hedge ratio) to long/short the pair instead?

Example if hedge ratio = 0.13470899, I should LONG 0.135 WL and short 1 AREXQ whenever it hits the lower Zscore boundary.

Thank you

• This question has already been asked quant.stackexchange.com/questions/38456/… although none of the two answers were approved. So the question is still open and I am looking forward to an answer from the experts in Pairs Trading. Jul 2 '20 at 17:25
• Thanks for the link @noob2. Paul Teetor was facing the exact same issue and from his paper, i feel much more comfortable using TLS instead of OLS because it's symmetrical. However I stumbled upon a recent blogpost that compares the OLS,TLS and ODR statistically (not in a trading sense): towardsdatascience.com/…. The summary is TLS>OLS but is prone to error when the variance is large and ODR>TLS>OLS. However, realistically, we still need to backtest these methods out and compare the returns vs its robustness Jul 3 '20 at 1:10