I have a basic question about modelling intraday price relationships. If I "visually " see two instruments that typically move in line with each other intraday, how can I verify that this relationship is stable? Using a price series ( cointegration) or return series (correlation). I am quite new to this, so my understand might be off but from what I know cointegration essentially implies a stationary spread between two I(1) series. Is a relationship established using a cointegration model stable intraday ? From the literature I have read , it seems like it helps in identifying when a deviation from a long-term relationship happens. What do you guys think ?If I use an intra-day return time series to model this relationship , my analysis would be highly dependent on the time scale I use to compute these intra-day returns. How can I attack this problem? Really need some help understanding modelling intraday relationships.

Cointegration is actually is a very weird thing in econometrics. The sure thing is that it accounts for long-run common trend and can't be applied to intraday data. That's been said return series correl seems a good option. Have you thought about building different time blocks and look for change in correlation? Furthermore, I don't know what you aim at will all of this but Granger causality might also be an option. P-S: Dont forget to remove the very high persistence in the data.

Well so I see intra-day co-movement in a certain set of securities. Sometimes when they dont move together, I can see a catch-up of some sort as the day progresses and I want to be able to model this phenomena of "securities moving out of line intraday" so it acts as a trading signal ( buying cheap and selling expensive securities). Cointegration might have been an option, but seems like its too unstable intraday. How can I go about modelling this using returns ? Another question, when dealing with intraday data how do you merge two days together without seeing a jump in returns ?

In this case don't use cointegration. I'm not a specialist in reduced-form models but I'm pretty sure that some of those tackle your problem. In terms of econometrics, GARCH related models seem the best fit for your problem. There is an unlimited supply of these Bollerslev 2008 for a literature review. Multivariate GARCH of all kinds could be a good fit for you. You could look at information curves, asymmetry (ex: EGARCH), DCC, AGDCC, CCC, BEKK. You could also try to come up with a procedure to track the persistence of the data and set up a trading rule based on that. Options are unlimited but none are 100% accurate.

Admittedly I never have applied co-integration in modelling intra-day data but wonder why it can not be applied in modelling so. The definition of "a long term movement" is not absolute idea, rather it is relative, i.e. w.r.t. the frequency of data. Therefore if intra-day data means it is sampled in each minute (or even lesser frequency) then for a particular day you will observe lot of data. Hence still I think the idea of co-integration remains valid here. Here w.r.t. your data frequency, your 'long term' may be 1-day here.Thanks,