Although each of the two is still on an individual pathway over a short period of time, and even though either one of the pair may randomly lead or lag the other at any given point in time, still, they will always be found close together. The distance between them is fairly predictable, thus the pair are said to be cointegrated. Returning now to technical terms, if there are two non-stationary time series, such as a hypothetical set of currency pairs AB and XY, that become stationary when the difference between them is calculated, these pairs are called an integrated first-order series — also call an I 1 series.

Even though neither of these series stays at a constant value, if there is a linear combination of AB and XY that is stationary described as I 0 , then AB and XY are cointegrated. The above simple example consists of only two time series of hypothetical forex pairs. Yet, the concept of cointegration also applies to multiple time series, using higher integration orders… Think in terms of a wandering drunk accompanied by several dogs, each on a different-length leash.

In forex pairs trading, my focus is on capitalizing on the quantitative and predictable relationship between cointegrated pairs of currencies. In practice, a mechanical trading system for forex pairs trading needs to calculate cointegration instead of just relying on the R-squared value between AB and XY.

When using the Engle-Granger method in forex pairs trading, the beta values of the regression are used to calculate the trade sizes for the pairs. When I use my mechanical trading system for forex pairs trading, the setup and execution are fairly simple. Then, I calculate the estimated spreads between the two pairs.

Next, I check for stationarity using a unit-root test or another common method. I make sure that my inbound data feed is working appropriately, and I let my mechanical trading algorithms create the trading signals. It looks like a Bollinger Band indicator, yet in fact the oscillator shows the price differential between the two different currency pairs. When this oscillator moves toward either the high or low extreme, it indicates that the pairs are decoupling, which signals the trades.

Still, to be sure of success I rely on my well-built mechanical trading system to filter the signals with the Augmented Dickey-Fuller test before executing the appropriate trades. Of course, anyone who wants to use cointegration for his or her forex pairs trading, yet lacks the requisite algo programming skills, can rely on an experienced programmer to create a winning expert advisor.

Through the magic of algorithmic trading, I program my mechanical trading system to define the price spreads based on data analysis. My algorithm monitors for price deviations, then automatically buys and sells currency pairs in order to harvest market inefficiencies. Forex pairs trading is not entirely risk-free. Above all, I keep in mind that forex pairs trading using cointegration is a mean-reversion strategy, which is based on the assumption that the mean values will be the same in the future as they were in the past.

I rely on strong risk management rules, which means that my mechanical trading system exits from unprofitable trades if or when the calculated reversion-to-mean is invalidated.

I try to detect drift as soon as possible. When I use my mechanical trading system for forex pairs trading, I use the autoregressive formula mentioned earlier in this article in order to calculate a moving average to forecast the spread. Then, I exit the trade at my calculated error bounds. Using cointegration in forex pairs trading is a market-neutral mechanical trading strategy that lets me trade in any market environment.

Because of its potential use in profitable mechanical trading systems, cointegration for forex pairs trading has attracted interest from both professional traders as well as academic researchers.

There are plenty of recently-published articles, such as this quant-focused blog article, or this scholarly discussion of the subject, as well as plenty of discussion among traders. Cointegration is a valuable tool in my forex pairs trading, and I highly recommend that you look into it for yourself.

Excellent article! Correlation is also applied in stocks equities. What is the difference? Can the above process be applied to stocks? Yes, the same process can be applied to stocks as well as to derivatives.

Since there is such a large universe of stocks when compared with forex pairs, there should be a larger number of potential opportunities for trading.

Hi Eddie, Do you trade intra day or over weeks using this strategy? Also, what programming language would you recommend. R does take time to run calculations and if it is intra day trade, latency comes into play.

Thanks, Harish. I trade using daily charts, and I stay in most trades for a couple of days to a couple of weeks.

Shaun is an expert programmer, and I always trust his judgment to use the best programming language to obtain the best results for a given trading strategy.

In fact, Shaun can create a well-balanced, winning program to leverage cointegration and other factors as well. There is some interest in an implementation of this for MT4. If you can you provide some specifics on your implementation of this strategy in code, please send to czimmer onestepremoved.

Hello Eddie, I am doing a small project on cointegration strategies in FX for my MSc. It's understandable that if we do the test in two steps like in CADF, error accumulates between steps. Johansen test overcomes this by allowing us find hedge ratio and test cointegration at the same time. Another advantage of Johansen test is that it can be extended to more than two stocks. It seems that Johansen test is more strict than the CDAF test regarding to accepting pairs.

It is time to backtest the EWA-EWC pairs trading on the Bollinger-bands strategy. The strategy is very simple. In order to avoid the look-ahead bias caused by using whole dataset for regression, we use a rolling window and re-estimate the linear regression at every step. This is also known as walk forward analysis.

Another approach is to use online regression mechanism such as Kalman filter , which will be covered in the next post. There are also two kinds of spreads: price spread and return spread.

Because return spread in theory has to rebalance every day, here we use price spread. The trading logic is posted below. Full code can be found here on github. Cointegration loosely speaking means that two non-stationary time series can be paired up to form a stationary time series. Technically speaking it means there are more unit-root non-stationary components than the number of unit roots in the system.

There are a lot of materials online about this topic but I found some of them hard for beginners to follow. In this appendix I try to convey the basic idea through an example. In other words, there are two price series but there is only one unit root. This is the mathematics behind the pairs trading. From A2 , it's easy to find the pairing strategy as buying one lot of stock one and selling two lots of stock two,. In case we can't find it by eyes, we can use OLS to regress out the coeffficient, which is exactly what we did in the second section.

or in VAR vector format. This is the well-known Engle and Granger Error-Correction representation. To estimate the model in two steps is because one-step regression upon differences will miss the long-term relationship. Also note that this is to find the VAR representation in ECM format. To test for cointegration, it usually performs ADF test on residuals from first step regression. Algorithmic trading: winning strategies and their rationale. Pairs Trading: quantitative methods and analysis.

The author doesn't promise any future profits and doesn't take responsibility for any trading losses. Introduction In last post we examined the mean reversion statistical test and traded on a single name time series. Statistical Testing Let's look at Ernie Chan's [2] EWA and EWC trade.

Cointegrated Augmented Dickey Fuller Test In order to perform ADF test as in last post , we need to know the hedging ratio between the two stocks. stattools as ts ts. fit data[ 'EWC US Equity' ]. reshape -1 , 1 , data[ 'EWA US Equity' ]. Johansen Test It's understandable that if we do the test in two steps like in CADF, error accumulates between steps.

Cointegration in forex pairs trading is a valuable tool. For me, cointegration is the foundation for an excellent market-neutral mechanical trading strategy that allows me to profit in any economic environment.

Whether a market is in an uptrend, downtrend or simply moving sideways, forex pairs trading allows me to harvest gains year-round. A forex pairs trading strategy that utilizes cointegration is classified as a form of convergence trading based on statistical arbitrage and reversion to mean.

This type of strategy was first popularized by a quantitative trading team at Morgan Stanley in the s using stock pairs, although I and other traders have found it also works very well for forex pairs trading, too. Forex pairs trading based on cointegration is essentially a reversion-to-mean strategy. Stated simply, when two or more forex pairs are cointegrated, it means the price spread between the separate forex pairs tends to revert to its mean value consistently over time.

Correlation is a short-term relationship regarding co-movements of prices. Correlation means that individual prices move together. On the other hand, cointegration is a longer-term relationship with co-movements of prices, in which the prices move together yet within certain ranges or spreads, as if tethered together. Basic forex pairs trading strategies are very simple, especially when using mechanical trading systems: I choose two different currency pairs which tend to move similarly.

I buy the under-performing currency pair and sell the out-performing pair. When the spread between the two pairs converges, I close my position for a profit. Forex pairs trading based on cointegration is a fairly market-neutral strategy.

As an example, if a currency pair plummets, then the trade will probably result in a loss on the long side and an offsetting gain on the short side. So, unless all currencies and underlying instruments suddenly lose value, the net trade should be near zero in a worst-case scenario.

By the same token, pairs trading in many markets is a self-funding trading strategy, since the proceeds from short sales can sometimes be used to open the long position. Even without this benefit, cointegration-fueled forex pairs trading still works very well.

Cointegration is helpful for me in forex pairs trading because it lets me program my mechanical trading system based on both short-term deviations from equilibrium prices as well as long-term price expectations, by which I mean corrections and returning to equilibrium. Stated in mathematical jargon, cointegration is a technique for measuring the relationship between non-stationary variables in a time series.

If any two or more time series each have a root value equal to 1, but their linear combination is stationary, then they are said to be cointegrated. As a simple example, consider the prices of a stock-market index and its related futures contract: Although the prices of each of these two instruments may wander randomly over brief periods of time, ultimately they will return to equilibrium, and their deviations will be stationary.

Therefore, there is no cointegration between their movements. In contrast, consider the idea that an individual drunk is wandering homeward while accompanied by his dog on a leash. In this case, there is a definite connection between the pathways of these two poor creatures.

Although each of the two is still on an individual pathway over a short period of time, and even though either one of the pair may randomly lead or lag the other at any given point in time, still, they will always be found close together.

The distance between them is fairly predictable, thus the pair are said to be cointegrated. Returning now to technical terms, if there are two non-stationary time series, such as a hypothetical set of currency pairs AB and XY, that become stationary when the difference between them is calculated, these pairs are called an integrated first-order series — also call an I 1 series. Even though neither of these series stays at a constant value, if there is a linear combination of AB and XY that is stationary described as I 0 , then AB and XY are cointegrated.

The above simple example consists of only two time series of hypothetical forex pairs. Yet, the concept of cointegration also applies to multiple time series, using higher integration orders… Think in terms of a wandering drunk accompanied by several dogs, each on a different-length leash.

In forex pairs trading, my focus is on capitalizing on the quantitative and predictable relationship between cointegrated pairs of currencies. In practice, a mechanical trading system for forex pairs trading needs to calculate cointegration instead of just relying on the R-squared value between AB and XY.

When using the Engle-Granger method in forex pairs trading, the beta values of the regression are used to calculate the trade sizes for the pairs.

When I use my mechanical trading system for forex pairs trading, the setup and execution are fairly simple. Then, I calculate the estimated spreads between the two pairs.

Next, I check for stationarity using a unit-root test or another common method. I make sure that my inbound data feed is working appropriately, and I let my mechanical trading algorithms create the trading signals. It looks like a Bollinger Band indicator, yet in fact the oscillator shows the price differential between the two different currency pairs. When this oscillator moves toward either the high or low extreme, it indicates that the pairs are decoupling, which signals the trades.

Still, to be sure of success I rely on my well-built mechanical trading system to filter the signals with the Augmented Dickey-Fuller test before executing the appropriate trades. Of course, anyone who wants to use cointegration for his or her forex pairs trading, yet lacks the requisite algo programming skills, can rely on an experienced programmer to create a winning expert advisor.

Through the magic of algorithmic trading, I program my mechanical trading system to define the price spreads based on data analysis. My algorithm monitors for price deviations, then automatically buys and sells currency pairs in order to harvest market inefficiencies. Forex pairs trading is not entirely risk-free. Above all, I keep in mind that forex pairs trading using cointegration is a mean-reversion strategy, which is based on the assumption that the mean values will be the same in the future as they were in the past.

I rely on strong risk management rules, which means that my mechanical trading system exits from unprofitable trades if or when the calculated reversion-to-mean is invalidated. I try to detect drift as soon as possible. When I use my mechanical trading system for forex pairs trading, I use the autoregressive formula mentioned earlier in this article in order to calculate a moving average to forecast the spread. Then, I exit the trade at my calculated error bounds.

Using cointegration in forex pairs trading is a market-neutral mechanical trading strategy that lets me trade in any market environment. Because of its potential use in profitable mechanical trading systems, cointegration for forex pairs trading has attracted interest from both professional traders as well as academic researchers. There are plenty of recently-published articles, such as this quant-focused blog article, or this scholarly discussion of the subject, as well as plenty of discussion among traders.

Cointegration is a valuable tool in my forex pairs trading, and I highly recommend that you look into it for yourself. Excellent article!

Correlation is also applied in stocks equities. What is the difference? Can the above process be applied to stocks? Yes, the same process can be applied to stocks as well as to derivatives. Since there is such a large universe of stocks when compared with forex pairs, there should be a larger number of potential opportunities for trading. Hi Eddie, Do you trade intra day or over weeks using this strategy? Also, what programming language would you recommend. R does take time to run calculations and if it is intra day trade, latency comes into play.

Thanks, Harish. I trade using daily charts, and I stay in most trades for a couple of days to a couple of weeks. Shaun is an expert programmer, and I always trust his judgment to use the best programming language to obtain the best results for a given trading strategy.

In fact, Shaun can create a well-balanced, winning program to leverage cointegration and other factors as well. There is some interest in an implementation of this for MT4. If you can you provide some specifics on your implementation of this strategy in code, please send to czimmer onestepremoved. Hello Eddie, I am doing a small project on cointegration strategies in FX for my MSc. I believe you ran cointegration tests on a lot of currency pairs. Which ones did you find to be statistically significantly cointegrated?

Thanks, Sasha. The article is intended to be an overall guide to the concept, but not quite to the point of being a bona fide strategy.

Has anyone implemented a backtest code using mean reversion strategy? Should I ajust pip values between two forex pairs? Has anyone added commission cost to backtest code and got profitable results? The only cointegration is between EUR and CHF and between AUD and NZD since are the only intimate trade and economics between this countries and central banks are creating this cointegration.

Hello Eddie. Excellent article. Thanks so much for writing this. Thanks for your time. Sincerely Robert J. The main broker that I use is Pepperstone and STO via TopTradr.

Hello Shaun I have been trading this strategy manually. Do have software to automate this? Shoot me an email with your entry and exit rules to get an estimate.

info onestepremoved. Robert — Thanks for your good feedback. Shaun has the right tools to implement this type of trading strategy, and I entirely agree with his broker recommendations, Thanks again for commenting!

When I use my mechanical trading system for forex pairs trading, I use the autoregressive formula mentioned earlier in this article in order to calculate a moving average to forecast the spread. My algorithm monitors for price deviations, then automatically buys and sells currency pairs in order to harvest market inefficiencies. The trading logic is posted below. In other words, we accept that EWA and EWC are cointegrated with the hedging ratio given by the linear regression. If any two or more time series each have a root value equal to 1, but their linear combination is stationary, then they are said to be cointegrated. Stated simply, when two or more forex pairs are cointegrated, it means the price spread between the separate forex pairs tends to revert to its mean value consistently over time. com and quantbar.

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