Explanation of order of integration in the context of cointegration Please explain the meaning of 'order of integration' when talking about cointegration.
An explanation with some examples would be great.
 A: In practice, "order of integration" provides you with the number of times you have to difference a series in order to obtain a covariance-stationary series.  
The use of the term "integration" does have something to do with the usual meaning of the term, but in its discrete incarnation (i.e. with "summation"). It comes from the fact that, looking "upstream", a series integrated of order $1$, $I(1)$, can be represented as the sum of the elements of a series integrated of order $0$:
Consider the stochastic process $\{X_t\}$, and assume that it is $I(0)$. Define the process
$$Z_t = \sum_{i=1}^tX_i$$
Then 
$$\Delta Z_t = Z_t - Z_{t-1} = \sum_{i=1}^tX_i - \sum_{i=1}^{t-1}X_i = X_t$$
So the process $\{\Delta Z_t\}$ is $I(0)$ and then the process $\{Z_t\}$ is $I(1)$, while also being the sum of the elements of $\{X_t\}$.  
And this can continue for higher orders of integration, as you can easily check.
Then why not "order of summation" and "summed of order ..."? Well, the late Clive Granger, apart from a great time-series econometrician, was also a master of attractive scientific name-giving. "Integrated" is so much smoother and catchy a word...
