Hi Lione,

thanks your sharing,seems interesting,
could you share how did analysis the cointegration in R?

One question I'd ask Lionel: did you perform your cointegration analysis using prices during the period of your backtest (i.e. after 2002-01-03)? If that is the case you algorithm has lookahead bias. For algorithms like this to show valid backtest results you either have to 1) perform the cointegration analysis on prices prior to the backtest period or 2) repeat the cointegration analysis inside the algorithm periodically for dates that are prior to the current date of the algorithm.

I have been playing for a month with cointegration and vecm using implementation here http://econ.schreiberlin.de/software/vecmclass.py. Most times cointegration fails out of sample so if you can put in some checks around that a 1 sharpe strategy is feasible in my experience.

Novice TAI,

I don't know how Lionel did his analysis but you can use the package urca.

Here is a small example:

#for simulation of geometric brownian motion  
require('sde')  
#for cointegration analysis  
require('urca')  
#creation of common stochastic trend (geometric brownian motion)  
GBM <- GBM(x = 100,r = 0.02,sigma = 0.2,T = 1,N = 252)  
#white noise  
u <- rnorm(n = 253,mean = 0,sd = 1)  
v <- rnorm(n = 253,mean = 0,sd = 1)  
#time series of cointegrated prices  
p1 <- GBM + u  
p2 <- GBM + v  
#cointegration analysis  
coRes=ca.jo(data.frame(p1,p2),type="trace",K=2)  
summary(coRes)  

Hi,

I did the cointegration analysis by fitting a linear regression model without intercept on every single pair of Dow Jones stocks (stock1_price = beta*stock2_price + error)

Then perform an Augmented Dickey-Fuller test on the spread (the error term) to test stationarity. I used the series package.

Rudiger is right, there is lookahead biais because i used all the available data on the stocks prices. It was just an easy test of Quantopian platform.

We could also assume that if the spread has been stationary for such a long time until today, it will continue to be stationary in the future.

See you
Lionel

We could also assume that if the spread has been stationary for such a long time until today, it will continue to be stationary in the future.

Haha would that we could! But seriously, one really must not optimize to test data, it's tempting when messing around and the only goal is a pretty back-test, but eventually (hopefully) you're going to be risking real money, so it's better to never get in the habit of cutting corners.

A case in point is GDX (gold miners ETF) and GLD (gold ETF). At some point they were cointegrated, but eventually the relationship broke down, because it turns out that GDX also has exposure to oil prices. So, although pairs appear to be stationary for quite some time, the reality can change in the future.

It is useful as a coding exercise. But never use this to trade directly. Your approach involved two most common problems in research: Look ahead bias and survival bias. If you use more aggressive curve fitting techniques, you can potentially get much better returns. But that means nothing for the real trading.

You're right Alan, it was one.