I'm working with the ca.jo function in R in order to evaluate cointegration among 4 economic variables (GDP, m1, bank interest rates and currency US dollar-mexican peso) but I still don't have a clear idea on how to correctly interpret the output.
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# Johansen-Procedure #
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Test type: trace statistic , with linear trend
Eigenvalues (lambda):
[1] 0.70039082 0.45734841 0.19752107 0.04859328
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 3 | 1.74 6.50 8.18 11.65
r <= 2 | 9.45 15.66 17.95 23.52
r <= 1 | 30.84 28.71 31.52 37.22
r = 0 | 73.02 45.23 48.28 55.43
Eigenvectors, normalised to first column:
(These are the cointegration relations)
diff.tf.tiie..l4 diff.tf.tipo_cambio..l4 diff.tf.logpib..l4 diff.tf.logm1..l4
diff.tf.tiie..l4 1.000000 1.000000 1.0000 1.00000000
diff.tf.tipo_cambio..l4 -3.616626 -2.639547 -117.1233 -0.04544856
diff.tf.logpib..l4 -391.182869 10.919719 -3348.6089 -16.51841837
diff.tf.logm1..l4 98.884942 7.698052 8735.8534 1.46417115
Basically, we can say we reject null for r=0 and r<=1 and therefore conclude we have 1 cointegration vector. So I have two questions:
1) What does "one cointegration vector" exactly mean? That, for example, all variables are stationary independent and don't share a common trend in the long-term?
2) Does it make sense to construct a new stationary serie using the coefficients from the first column of eigenvectors? If yes, how this can be useful in order to understand the relationship among variables?
new_serie = 1.000000*var1 -3.616626*var2 -391.182869* var3 + 98.884942*var4
I read many posts in this site (some of them below) but I'm still a lot confused. Thanks in advance for any advice and suggestion
