Johansen Cointegration for More Than Two Price Series in R

# How to construct a cointegrating vector using more than 2 price series in R?


# How to construct a cointegrating vector using more than 2 price series in R?












I use now this code from hier Why does the following data fail my cointegration test? with slightly modification of possibility to load something directly from Dropbox file storage .

```
library(RCurl)
library(zoo)
library(tseries)

x <- getURL("https://dl.dropboxusercontent.com/u/12337149/stat/CBA.csv")
y <- read.csv(text = x)

x1 <- getURL("https://dl.dropboxusercontent.com/u/12337149/stat/WBC.csv")
y1 <- read.csv(text = x1)

##gld <- read.csv("CBA.csv", stringsAsFactors=F)
##gdx <- read.csv("GDX.csv", stringsAsFactors=F)

gld <- y
gdx <- y1

gld <- zoo(gld[,5], as.Date(gld[,1]))
gdx <- zoo(gdx[,5], as.Date(gdx[,1]))

t.zoo <- merge(gld, gdx, all=FALSE)
t <- as.data.frame(t.zoo)

cat("Date range is", format(start(t.zoo)), "to", format(end(t.zoo)), "\n")

m <- lm(gld ~ gdx + 0, data=t)
beta <- coef(m)[1]

cat("Assumed hedge ratio is", beta, "\n")

sprd <- t$gld - beta*t$gdx
ht <- adf.test(sprd, alternative="stationary", k=0)

cat("ADF p-value is", ht$p.value, "\n")

if (ht$p.value < 0.05) {
    cat("The spread is likely mean-reverting\n")
} else {
    cat("The spread is not mean-reverting.\n")
}
```

How to construct a cointegrating vector using more than 2 price series in R?

## Answer by Richard Hardy (score 1, accepted)

https://quant.stackexchange.com/a/24566

Use package "vars" function `ca.jo` for cointegration analysis (the Johansen procedure) of a multivariate time series. Here is a code snippet from the functions' help file:

```
data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
season=4)
summary(sjd.vecm)
```

It loads a dataset `denmark`, extracts four times series into a matrix `sjd`, conducts the Johansen procedure by the function `ca.jo` and prints its summary.

You can extract the cointegrating vectors by addressing the slot `V` by `@V` like `sjd.vecm@V`. This will be a matrix where each column is a cointegrating vector. You can multiply the original multivariate series (like `sjd`) to the `V` matrix to get the error correction terms.

A good introduction is the "vignette" of the "vars" package and Pfaff "Analysis of Integrated and Cointegrated Time Series with R" (a textbook).