Hi guys,
I ran ca.jo(data,type="trace", ecdet="none",k=2) i.e. Johansen's Trace test
on R-Studio (package: "urca")and got the output below:
I have 3 questions about this:
A> How do I programmatically access the columns("test", "10pct" etc) in any
row corresponding to, say, r < = 1 in the output? I mean, I shall only
provide the r-value as an input and all the (column name, column value)
pairs will be outputted to me.
B> How do I write a code that will check if the null hypotheses for r =0,
<= 1, <= 2 and so on (in this order) are rejected or not; and in case one
of them is rejected, it checks the next higher value of r and gives the
final inference , something like "Null not rejected for r <= *appropriate
r-value from this table* " or "All nulls rejected" or "No null rejected'.
C> Also, I need to extract the eigen vectors from the Cointegration Matrix
below to get the cointegrated transfoms.
I have attached the data for your perusal. If I need to provide anything
more, please let me know.
Regards,
Preetam
######################
# Johansen-Procedure #
######################
Test type: trace statistic , with linear trend in cointegration
Eigenvalues (lambda):
[1] 7.935953e-01 5.444372e-01 4.985327e-01 2.562245e-01 5.551115e-16
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 3 | 6.81 10.49 12.25 16.26
r <= 2 | 22.68 22.76 25.32 30.45
r <= 1 | 40.77 39.06 42.44 48.45
r = 0 | 77.06 59.14 62.99 70.05
Eigenvectors, normalised to first column:
(These are the cointegration relations)
GDP.l2 HPA.l2 FX.l2 Y.l2 trend.l2
GDP.l2 1.000000000 1.0000000 1.00000000 1.00000000 1.0000000
HPA.l2 2.525511110 0.1569079 0.08077351 -0.22777550 -0.9178250
FX.l2 -8.643729121 -2.5815150 0.17158404 -0.47053012 -4.8528875
Y.l2 0.805229998 -1.4241546 0.07767540 0.02303305 0.5213294
trend.l2 0.006283314 0.0385276 -0.01512016 0.01986813 -0.9516072
Weights W:
(This is the loading matrix)
GDP.l2 HPA.l2 FX.l2 Y.l2 trend.l2
GDP.d 0.03055313 -0.04681978 -0.8376985 -0.04220534 -1.271960e-17
HPA.d -0.22649596 -0.24287691 -1.6358880 2.03813569 -8.002467e-17
FX.d 0.10327579 0.15150469 -0.1649066 0.37449910 -2.570250e-18
Y.d -0.35200485 0.56808024 -5.7829738 0.01000965 1.730461e-16
GDP HPA FX Y
0.514662421 0.635997077 1.37802145 1.773342598
0.936722 3.127683176 1.391916535 3.709809052
0.101482324 1.270555421 0.831157511 0.226267793
0.017548634 2.456061547 1.003945759 9.510258161
0.236462416 0.988324147 0.223682679 5.026671536
0.372005149 2.177631629 0.904226065 4.219235789
0.153915709 4.620341653 0.033410743 3.17396006
0.524887329 1.050861084 0.518201484 7.950098612
0.776616937 0.503349512 0.666089868 3.320938471
0.760074361 3.635853456 0.470220952 6.380945175
0.802986662 1.260738545 0.452674872 1.036040804
0.375145127 0.20035625 1.837306306 6.486871565
0.002568896 3.532359526 0.556752154 8.536594244
0.754309276 3.952381767 0.247402168 8.559081716
0.585966577 4.01463047 1.184382133 0.148121669
0.39767356 1.553753452 0.983129422 5.378373676
0.859898623 4.73191381 0.828795696 3.367809329
0.741376169 4.993350692 1.758051281 5.516460988
0.329240391 3.465836416 1.701655508 1.249497907
0.078661064 3.298298811 0.04575857 5.132921426
0.270971873 0.46627043 1.739487411 4.94697541
0.731072625 0.940642982 0.728747166 7.583041122
0.385038046 3.51048946 0.021866584 7.361148458
0.530760376 1.204422978 0.415530715 1.163503483
0.555323667 4.777712592 1.844184811 8.596644394
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