R: A Simple Replication of Cointegration Test Results

This post is a straightforward replication of the Johansen cointegration test results from Johansen and Juselius (1990) using R urca package.

Johansen cointegration test using R

Johansen Test Result from Johansen and Juselius (1990)

I will not cover cointegration theory here, as there are many excellent books on the topic, such as Analysis of Financial Time Series by Ruey S. Tsay. Instead, I will demonstrate how to replicate the cointegration test results from Johansen and Juselius (1990), as it can serve as a starting point or reference for further research.

In their influential paper, two datasets are utilized: Danish and Finnish data. Both datasets are analyzed using 2 lags and a quarterly seasonal dummy. The Danish dataset includes a constant in the cointegration equation, whereas the Finnish dataset does not use either a constant or a trend.

The target result is Table 3 on page 183 of Johansen and Juselius (1990), as presented below.

R code

Using the urca R package, the above results can be implemented as follows:

# Load the necessary package for cointegration
library(urca)
 
# Load the 'denmark' dataset 
data(denmark)
 
# select data 
data <- as.matrix(denmark[,c(2,3,5,6)])
 
#=====================================================
# Perform the Johansen cointegration test
#=====================================================
# - type  = "trace" runs the trace test 
#           alternatively, 
#           use "eigen" for the max-eigenvalue test
#
# - ecdet = "none" for no intercept in cointegration, 
#           "const" for constant term in cointegration
#           "trend" for trend variable in cointegration.
#
# - K     = The lag order of the series (levels) in the VAR.
#        ex) K = 2 sets the lag length (1 lag difference)
#=====================================================
 
test_tr <- ca.jo(data, type = "trace", ecdet = "const", 
                 K = 2, season = 4)
test_eg <- ca.jo(data, type = "eigen", ecdet = "const", 
                 K = 2, season = 4)
 
result1 = data.frame(trace=round(test_tr@teststat,2), 
                    trace_95=test_tr@cval[,2],
                    lamax=round(test_eg@teststat,2), 
                    lamax_95=test_eg@cval[,2])
 
 
# Load the 'finland' dataset 
data(finland)
data2 <- as.matrix(finland)
 
test_tr2 <- ca.jo(data2, type = "trace", ecdet = "none", 
                  K = 2, season = 4)
test_eg2 <- ca.jo(data2, type = "eigen", ecdet = "none", 
                  K = 2, season = 4)
 
result2 = data.frame(trace=round(test_tr2@teststat,2), 
                     trace_95=test_tr2@cval[,2],
                     lamax=round(test_eg2@teststat,2), 
                     lamax_95=test_eg2@cval[,2])
 
print("The Danish data")
result1
 
print("The Finnish data")
result2

We can see that this replication closely matches the original results, as shown in the output below.

Reference

Johansen, S. and Juselius, K. (1990), Maximum Likelihood Estimation and Inference on Cointegration – with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 2, 169–210. 

Originally posted on SHLee AI Financial Model blog.

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