and how is it used?Thanks to adas...P

Just to get the ball rolling:Unlike correlation, Co-integration refers not to co-movements in returns, but to co-movements in raw asset prices (or exchange rates or yields). If spreads are mean reverting, asset prices are tied together in the long term by some common stochastic trend, and we say the asset prices are ‘co-integrated’. Since the seminal work of Engle and Granger (1987) co-integration has become the prevalent tool of time series econometrics. Co-integration has emerged as a powerful technique for investigating common trends in multivariate time series, and provides a sound methodology for modelling both long-run and short-run dynamics in a system.Co-integration is a two step process: first any long run equilibrium relationships between exchange rates are established, and then a dynamic correlation model of exchange rate returns is estimated. This error correction model (ECM), so called because short term deviations from equilibrium are corrected, reveals the Granger causalities that must be present in a co integrated system. The fundamental aim of co-integration analysis is to detect any common stochastic trends in the price data, and to use these common trends for a dynamic analysis of correlation returns. Thus co-integration analysis is an extension of the simple correlation based analysis. Whereas correlation is based only on return data, co-integration analysis is based on the raw price, exchange rate or yield data as well as the return data. Exchange rate data (as used in this study) is not generally stationary in nature – in fact it is generally integrated of order 1 {sometimes represented as I(1)}. Since it is normally the case that the logarithm of exchange rates will be co-integrated when the actual rates are co-integrated, it is standard to perform co-integration analysis on log exchange rates. In case you were wondering - I lifted the above from my undergraduate econometrics project on exchange rates.

Suppose you have 2 processes, X and Y which are integrated of order 1 (This means that their first differences are zero). If we can determine that some linear relationship between these two processes: Et = Yt - h.Xt is integrated of order 0 - i.e. it is a stationary process, the two processes are cointegrated.

"In case you were wondering - I lifted the above from my undergraduate econometrics project on exchange rates."Really - sounds more like Carol Alexander's Market Models to me. V.

QuoteReally - sounds more like Carol Alexander's Market Models to me. Well spotted. But I did reference the chunk in my project.

Example: income and consumption: [income] - [consumption] is stationary generally. Prices of similar products in different location are co-integrated.Short-term and long-term interest rates are evidently co-integrated generally.

I think a good, related question would be: What's the difference between co-integration and correlation?I don't claim to be an expert at all, and maybe someone can further elaborate, but co-integration generally seems to refer to a reversion to the mean of the differences in asset prices.For instance, CactusMan presented the case of short-term vs. long-term rates. Well the correlation between the two rates may be not super high (I'm thinking 0.7-0.85), meaning day over day they may not move exactly together (and you could lose lots of money exploiting day over day divergences) and can even diverge at times. But they may be highly co-integrated meaning that, though they diverge day over day, one can expect that they will eventually revert to some constant value for the difference. I think this is hidden in adas' post: "because short term deviations from equilibrium are corrected".For applications, if one observes two things to be co-integrated, they well bet on the two products reverting to the constant difference after (how long? that's for the strategist to decided) an appropriate (how much can they diverge before entering the trade? - some discrepancy there again) level of divergence. This guy, http://epchan.blogspot.com/ likes to use it a lot for trading strategies.That's my interpretation anyways, please correct if I'm off.

thanks for providing an explanation in lay man terms. Sometimes, we all get caught up in jargons that we dont the practical aspects of the theory.

Hi adas, Wondering if you could give me some guidance,, how does cointegration contrast to correlation?

google for Carol Alexander papers... the answer is there...