# Cointegration between daily time series and intraday time series

I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments as 'a' and 'b'. When I check for cointegration between A and B my results tell me that the series are indeed cointegrated, but when checking their intraday series, a and b, my analysis shows no cointegration unless I apply some form of differencing to the series ( ie. taking returns of a and b , or log(a) and log(b) ).

Is the conclusion here as simple as declaring that intraday the series are not cointegrated, but over longer time frames they are? Or can I reach some generalized conclusion that I should be able to expect some degree of mean reversion intraday of a and b due to the daily cointegration between A and B.

I am mainly having a hard time connecting whether or not there are implications to be drawn from daily results -> intraday data, or vice versa in general.

• Hi There's nothing necessarily with differencing two variables and then finding thast they are cointegrated but ONLY IF THAT DIFFERENCING DOESN"T MAKE THEM I(0). II the differenced variables are I(0), then it's not possible for them to be co-integrated by definition. I would be careful testing for intraday cointegration.. It's an unstable beast to being with and then try to test it intraday probably just makes it more unstable. Finally, testing for I(1) of intraday seres seems like an exercise in futility because the respective seriies doesn't necessarily have time to trend. – mark leeds Oct 17 '18 at 8:52
• please see Verbeek (2012) $A$ $guide$ $to$ $modern$ $econometrics$ for an excellent discussion on cointegration. – user22485 Oct 26 '18 at 9:08