Correlation vs. Cointegration

Correlation and cointegration, while theoretically similar, are not the same. Let’s look at examples of series that are correlated, but not cointegrated, and vice versa. First let's check the correlation of the series we just generated.
X.corr(Y)
0.951
That’s very high, as we would expect. But how would two series that are correlated but not cointegrated look? A simple example is two series that just diverge.

Two correlated series (that are not co-integrated)
ret1 = np.random.normal(1, 1, 100)
ret2 = np.random.normal(2, 1, 100)
s1 = pd.Series( np.cumsum(ret1), name='X')
s2 = pd.Series( np.cumsum(ret2), name='Y')
pd.concat([s1, s2], axis=1 ).plot(figsize=(15,7))
plt.show()
print 'Correlation: ' + str(X_diverging.corr(Y_diverging))
score, pvalue, _ = coint(X_diverging,Y_diverging)
print 'Cointegration test p-value: ' + str(pvalue)
Correlation: 0.998
Cointegration test p-value: 0.258 > From <https://medium.com/auquan/pairs-trading-data-science-7dbedafcfe5a>