I have quite a lot of thoughts on this subject but not much time at the moment.

Correlation essentailly measures the percent that two series move together. Correlation says nothing about the magnitude of the moves. Two series may be positively correlated (move in same direction at same time), negatively correlated (move in opposite direction at same time) or uncorrelated. The scale is +1 to -1 where 1 = perfect positive correlation, 0 = no correlation and -1 = perfect negative correlation.

Cointegration, as was mentioned talks to the long-term relationship of two series. Two series may be cointegrated without being correlated, just as two series may be correlated but not cointegrated. A complex computation that can be performed in R or Matlab can determine if two series are cointegrated. If they are, their long-term prices move together with a certain mathematical relationship that can be modelled.

The third option, that I'm least familiar with and that might be more useful to traders than correlation is covariance. From wikipedia: covariance is a measure of how much two variables change together.

So it seems that while correlation will tell us the % positive / negative movement but not the magnitude, covariance will tell us the magnitude of the comovements of two series, and that perhaps covariance could be used with correlation in an effective manner. I know most econometrics texts cover covariance, but I haven't made it that far yet in my reading!

Basically you need time series that are both correlated and cointegrated.

When they get out of correlation you can use that as a signal. There is a study with price action techniques based on correlation, there are some ideas inside it. I have not really tested it.

But professional traders always, laways check and use multiple pairs for correlation even in their discretionary trading.

One of the ideas is that if you know that two pairs are correlated and you monitor their daily range. So basically based on the daily range you know which pair is leading and which pair is following.

The correlationhas aplace in thetrade. Will ask you towaittoset upamql5,so Itestwithto show youthat there issuch a possibility. Haveopportunities, butneedandappropriate tests.

For a good explanation of cointegration loor ak this site too:

Anyway this is quite complex matter of the statistical arbitrage. I do not have any practical experience and it is quite away from the realm of the common retail trader.

Anyway you ar eright guandi, correlation is an insufficient concept, what really matters is the cointegration. Very good point.

The problem with the Stat arbitrage is that when you have something you are not interested to share it.

The assumption is that if you have an adge and you share that edge the other participants will deny you the possibility to take profit from that edge, or will be quicker than you and as soon as there are many of them the edge would disapear very fast.

On the contrary if you use a directionnal system if there are more users of your system that does not change anything, even it may be good because more people are going to drive the price in the same direction.

That explains why you will not find anything concrete about stat arbitrage just kitchen recepees, but you are on your own. Developping a stat arbitrage strategy is a hell a lot of work. And sharing on internet for free your strategy would be the most stupid thing you may do.

So I mean there is a reason that those techniques are not well known. What is available is just rudimentary pieces of advice. There is a lot more than correlation alone.

Any idea for practical implementation for Forex is welcome. I just cannot implement pair trading with stocks, I do not want to trade stocks. The 7bit composite charts

1. Appear completely artificial to me. They are not formed following a real market relationship (e.g. correlated and cointegrated stocks for pair trading).

2. It makes more complicated the money management as a lot of positions are opened.

3. You have to pay a spread on each one of them. And the cost for spread may become substantial.

I am learning bit by bit.

On the other hand: serious traders rely heaviliy on stat arbitrage for their living. As the stat arbitrage strategies are not giving big winners but are giving you constanly a profit.

Thanks for the link to the stat arb thread. You are correct in your analysis of sharing stat arb strategies vs directional strategies and the dis-incentive to share arb strats.

On 7Bit's thread, watch out for the trend-o-mat. It looks appealilng (upward trending curve presumably cointegrated). But it is full of pitfalls (watch his videos to see what can happen to these artificial combinations.) Arb-o-mat's regression formula appears to be sound. But 7Bit doesn't do the necessary step of running the Augmented Dickey Fuller test to determine if there is a cointegrating relationship. Regressing alone does not guarantee cointegration. Also, these relationships can and do fall apart. The good thing about finding a cointegrated ralationship is that you are guaranteed at least one causal relationship, also known as Granger causality. With correlation alone, there is no guarantee that one thing causes the other to move. The relationship may be simply coincidental.

You might have better luck with EURUSD and GBPUSD instead of AU/NU to find a cointegrated pair. But as you may know whether a given pair is or isn't cointegrated it is dependant on the time frame used and the number of bars in your sample. Also you might find that using 3 or more symbols might make it easier to find cointegrating relationships.

#3 can work if you can determine the causitive lead/lag relationship and trade the lagger to follow the leader where there is Granger causality.

The idea is to have independant probabilities. That is the idea of all the excercise.

The signal from the Directionnal system and its probability would in theory be independant from the signal that results from the pair trading.

I give just an example any pair or combination of pairs can be examined as we rely on directionnal signal we do not care that someone will eat the edge. LOL. Anyway since we do not count of speed of execution there is nothing to warry about from that perspective.

## Comments

wats conintegration

sorry i mean cointegration

wats that?

http://www.tradingmarkets.com/.site/stocks/commentary/quantitative_trading/Cointegration-is-not-the-same-as-correlation.cfm

thank you for the link, John.

I have quite a lot of thoughts on this subject but not much time at the moment.

Correlation essentailly measures the percent that two series move together. Correlation says nothing about the magnitude of the moves. Two series may be positively correlated (move in same direction at same time), negatively correlated (move in opposite direction at same time) or uncorrelated. The scale is +1 to -1 where 1 = perfect positive correlation, 0 = no correlation and -1 = perfect negative correlation.

Cointegration, as was mentioned talks to the long-term relationship of two series. Two series may be cointegrated without being correlated, just as two series may be correlated but not cointegrated. A complex computation that can be performed in R or Matlab can determine if two series are cointegrated. If they are, their long-term prices move together with a certain mathematical relationship that can be modelled.

The third option, that I'm least familiar with and that might be more useful to traders than correlation is covariance. From wikipedia: covariance is a measure of how much two variables change together.

So it seems that while correlation will tell us the % positive / negative movement but not the magnitude, covariance will tell us the magnitude of the comovements of two series, and that perhaps covariance could be used with correlation in an effective manner. I know most econometrics texts cover covariance, but I haven't made it that far yet in my reading!

Basically you need time series that are both correlated and cointegrated.

When they get out of correlation you can use that as a signal. There is a study with price action techniques based on correlation, there are some ideas inside it. I have not really tested it.

But professional traders always, laways check and use multiple pairs for correlation even in their discretionary trading.

One of the ideas is that if you know that two pairs are correlated and you monitor their daily range. So basically based on the daily range you know which pair is leading and which pair is following.

John, do you have the link to the study with price action techniques based on correlation?

thanks.

The correlation has a place in the trade.

Will ask you to wait to set up a mql5, so I test with to show you that there is such a possibility.

Have opportunities, but need and appropriate tests.

Please look at this site:

Free Excel add-in for cointegration:

For a good explanation of cointegration loor ak this site too:

Anyway this is quite complex matter of the statistical arbitrage. I do not have any practical experience and it is quite away from the realm of the common retail trader.

Anyway you ar eright guandi, correlation is an insufficient concept, what really matters is the cointegration. Very good point.

And for statistical arbitrage this is one interesting thread:

http://www.elitetrader.com/vb/showthread.php?s=abe455f33976cba8ec7cf3d6031d31f2&threadid=160969&perpage=6&pagenumber=1

another good thread will be 7bit's thread in FF,

http://www.forexfactory.com/showthread.php?t=262827

The problem with the Stat arbitrage is that when you have something you are not interested to share it.

The assumption is that if you have an adge and you share that edge the other participants will deny you the possibility to take profit from that edge, or will be quicker than you and as soon as there are many of them the edge would disapear very fast.

On the contrary if you use a directionnal system if there are more users of your system that does not change anything, even it may be good because more people are going to drive the price in the same direction.

That explains why you will not find anything concrete about stat arbitrage just kitchen recepees, but you are on your own. Developping a stat arbitrage strategy is a hell a lot of work. And sharing on internet for free your strategy would be the most stupid thing you may do.

So I mean there is a reason that those techniques are not well known. What is available is just rudimentary pieces of advice. There is a lot more than correlation alone.

Yes, only 7bit is the only guy I know who shares something about this.

This is hs own site:

https://sites.google.com/site/prof7bit/

not sure if any of you come across this piece of software. the latest version seem to do cointegration.

www.pairtradefinder.com

Have a look here. There is an excel spreadsheet for Cointegration analysis using Johansen procedure

Any idea for practical implementation for Forex is welcome. I just cannot implement pair trading with stocks, I do not want to trade stocks. The 7bit composite charts

1. Appear completely artificial to me. They are not formed following a real market relationship (e.g. correlated and cointegrated stocks for pair trading).

2. It makes more complicated the money management as a lot of positions are opened.

3. You have to pay a spread on each one of them. And the cost for spread may become substantial.

I am learning bit by bit.

On the other hand: serious traders rely heaviliy on stat arbitrage for their living. As the stat arbitrage strategies are not giving big winners but are giving you constanly a profit.

John,

Thanks for the link to the stat arb thread. You are correct in your analysis of sharing stat arb strategies vs directional strategies and the dis-incentive to share arb strats.

On 7Bit's thread, watch out for the trend-o-mat. It looks appealilng (upward trending curve presumably cointegrated). But it is full of pitfalls (watch his videos to see what can happen to these artificial combinations.) Arb-o-mat's regression formula appears to be sound. But 7Bit doesn't do the necessary step of running the Augmented Dickey Fuller test to determine if there is a cointegrating relationship. Regressing alone does not guarantee cointegration. Also, these relationships can and do fall apart. The good thing about finding a cointegrated ralationship is that you are guaranteed at least one causal relationship, also known as Granger causality. With correlation alone, there is no guarantee that one thing causes the other to move. The relationship may be simply coincidental.

I am thinking about a very simple strategy.

1. Find both correlated and cointegrated pairs. I will test AUD/USD and NZD/USD.

2. Building two separate models for them (everybody has its taste)

3. Taking positions only in direction of the other pair. They can be not simultanious as we do not seek for perfect market neutrality.

In that way:

-we have two separate probabilities that are taking place. pair trading and directionnal probability by your model.

-the money management is easy as there is not any basket of pairs.

- you can add additional filter as taking only positions in direction of the trend if you do not have an opposite signal to achieve market neutrality.

This is just rough idea folks.

You might have better luck with EURUSD and GBPUSD instead of AU/NU to find a cointegrated pair. But as you may know whether a given pair is or isn't cointegrated it is dependant on the time frame used and the number of bars in your sample. Also you might find that using 3 or more symbols might make it easier to find cointegrating relationships.

#3 can work if you can determine the causitive lead/lag relationship and trade the lagger to follow the leader where there is Granger causality.

The idea is to have independant probabilities. That is the idea of all the excercise.

The signal from the Directionnal system and its probability would in theory be independant from the signal that results from the pair trading.

I give just an example any pair or combination of pairs can be examined as we rely on directionnal signal we do not care that someone will eat the edge. LOL. Anyway since we do not count of speed of execution there is nothing to warry about from that perspective.

What I am looking for , is the integration of the pair on itself....