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I am trying to run a Johansen-Procedure in a set of macroeconomic variables (GDP, credit outstanding and industrial production). I am working with them in level.

How should I interpret the following result?

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

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

Eigenvalues (lambda):
[1]  6.999273e-01  3.188663e-01  1.303763e-01  5.099467e-02 -6.157574e-17

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct
r <= 3 |  3.04  7.52  9.24 12.97
r <= 2 |  8.10 13.75 15.67 20.20
r <= 1 | 22.27 19.77 22.00 26.81
r = 0  | 69.82 25.56 28.14 33.24

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

               pib.l1       pim.l1     pmca.l1   credpf.l1    constant
pib.l1       1.000000    1.0000000   1.0000000   1.0000000   1.0000000
pim.l1       3.837837    1.4510004  -1.8089739  -0.5802552  -0.3392558
pmca.l1     -1.521082   -0.7640412  -1.2570908  -1.3764531  -0.6812554
credpf.l1   -0.334400   -0.5162337   0.9390526   0.3000718  -0.1507749
constant  -318.355047 -149.2844982 -37.8967674 -39.9517618 -42.5839669

Weights W:
(This is the loading matrix)

              pib.l1      pim.l1     pmca.l1  credpf.l1      constant
pib.d     0.01887772 -0.20780832 -0.02013903 0.03625849  1.835250e-14
pim.d    -0.04717478 -0.24886913 -0.01666137 0.03942148  4.796621e-14
pmca.d    0.05566538 -0.03881974 -0.01206322 0.11316466 -9.723535e-15
credpf.d  0.02345645 -0.08972929 -0.20632548 0.12360292  2.783076e-14

My goal is to estimate the best VEC model so I can forecast those variables.

Thank you very much!

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    $\begingroup$ I can see 4 variables in the output and you only mention three. I would recommend looking up the Johansen procedure ("eigenvalue" and "trace" statistics) here: faculty.washington.edu/ezivot/econ589/manual.pdf . Also, make sure the choice (no constant or trend in cointegration equation is appropriate). $\endgroup$
    – Tomas
    Dec 26, 2019 at 19:12
  • $\begingroup$ Thank you @Tomas! I'll take a look at this paper! I also have retail sales in there. The variables I used are not the main issue right now for me, my main issue is understanding the output of the test so I can chose the VECM that fits those variables. $\endgroup$ Dec 26, 2019 at 19:40

1 Answer 1

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I think we need to look at cointegration first. There is a good article for that and the subject you ask. Johansen Test For Cointegrating Time Series

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