In my recent post I wrote the code to download historical data for companies included in S&P500 index. Today I would like to perform statistical procedures to identify whether certain pair of stocks is co-integrated or not.

Since there are approximately 500 companies that means I will need to perform ${{500}\choose{2}} = 124 750$ calculations of testing. First of all I will divide my data into two parts: learning period and testing period. I will find co-integrated pairs in learning period and test the pair-trading strategy in testing period.

Secondly, I will use linear regression to calculate the spread (residuals) of the two corresponding stocks. To find out whether this two stocks are co-integrated or not I will perform the Augmented Dickey-Fuller Unit Root Test on spread to reject or not the hypothesis of stationarity. I will save the p-value of this test to the matrix. I will use the ADF test from fUnitRoots package.

And finally, I will apply this procedure on all the pairs. Uff.. that means a lot of computational time.. so take a break and have a cup of great coffee. See you in the next part of this tutorial.

Feel free to use the source code. Your valuable comments are more than welcome!

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rm(list = ls(all = TRUE))
 
library(quantmod)
library(tseries)
library(timeDate)
library(fUnitRoots)
 
 
load(file = "/home/robo/workspace/R-Test/abcdeXXX.RData")
ht <- matrix(data = NA, ncol = nrStocks, nrow = nrStocks)
beta <- matrix(data = NA, ncol = nrStocks, nrow = nrStocks)
sprd <- list()
 
z_old <- z;
nDays <- length(z[,1])
 
# seting learning and testing periods
testPeriod <- 250
learningPeriod <- 500
 
testDates <- (nDays-testPeriod):nDays
learningDates <- (nDays - testPeriod - learningPeriod):(nDays - testPeriod)
 
data <- z		
z <- z[learningDates,]
zTest <- data[testDates,]
 
# here we go! let's find the cointegrated pairs
for (j in 1:(nrStocks-1)) {
	for (i in (j+1):nrStocks) {
 
		cat("Calculating ", j, " - ", i , "\n")
		if (length(na.omit(z[, i])) == 0 || length(na.omit(z[, j])) == 0) {
			beta[j,i] <- NA
			ht[j,i] <- NA
			next
		}
 
 
		m <- lm(z[, j] ~ z[, i] + 0)
		beta[j,i] <- coef(m)[1]
 
		sprd <- resid(m)
 
		ht[j,i] <- adfTest(na.omit(coredata(sprd)), type="nc")@test$p.value
 
	}
}
 
#save(list = ls(all=TRUE), file = "/home/robo/Dropbox/work/FX/PairTrading/cointeg.RData")
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