# VECM interpretation - Johansen-Procedure

#### TheMonkster

##### New Member
X1 , X2 , X3 and X4 are time series which are stationary at level.I want to establish long term relation between them.I am planning to use it as forecasting model for my work.I want to create this model in terms of equation.I have tested all of them for KPSS test and got p=0.01 for all of them.After reading few articles,I decided to go with VECM instead of VAR (Though I was not 100% sure) .I implemented that code in R and got below result.could someone please help me to interpret this result?how can I put below result in equation or do I need to perform another operation to achieve equation.Please let me know if my pproach is wrong.

> mysample <- cbind(X1,X2,X3,X4)
> myvecm <- ca.jo(mysample, ecdet = "const", type="eigen", K=2, spec="longrun")
> myvecm

#####################################################
# Johansen-Procedure Unit Root / Cointegration Test #
#####################################################

The value of the test statistic is: 1.4814 6.8852 10.1941 19.0711

> summary(myvecm)

######################
# Johansen-Procedure #
######################

Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration

Eigenvalues (lambda):
 6.219413e-02 3.374104e-02 2.291576e-02 4.975326e-03 5.899570e-18

Values of teststatistic and critical values of test:

test 10pct 5pct 1pct
r <= 3 | 1.48 7.52 9.24 12.97
r <= 2 | 6.89 13.75 15.67 20.20
r <= 1 | 10.19 19.77 22.00 26.81
r = 0 | 19.07 25.56 28.14 33.24

Eigenvectors, normalised to first column:
(These are the cointegration relations)

X1.l2 X2.l2 X3.l2 X4.l2 constant
X1.l2 1.0000000 1.00000000 1.000000e+00 1.0000000 1.00000
X2.l2 -13.4606755 0.05012407 -4.229465e-01 0.2062215 168.98883
X3.l2 14.6636224 -0.25491299 -6.044102e-03 -3.1153455 29.80024
X4.l2 -0.7271033 0.52004658 -1.627988e-01 2.2019219 -192.13799
constant -1118.6413405 -905.29920115 -2.449373e+02 90.7496618 -1410.17106

Weights W: