I wonder if two identical time series are cointegrated. Can anyone shed some light on this? Thanks
If I understand your question correctly, you are asking if you take two identical time series (i.e. a time series and a direct copy of it), are these two cointegrated?
If that is your question, then it really reduces to a simpler form: is a time series stationary? As I understand it, cointegration is the phenomenon whereby non-stationary processes have linear combinations that are stationary. If you have two identical time series, then the set of all linear combinations of those time series is equivalent to the set of all scalar multiples of one of them. In this case, if a time series has a scalar multiple of it that is stationary, then the original time series was itself stationary.
I may be way off base, but this seems like the question you're asking, and it doesn't seem to be much more complicated than this. If you intended something more complicated (i.e. a time series and a lagged version of itself), then there may be some more depth here.