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List: r-sig-finance
Subject: [R-SIG-Finance] Questions on stationarity and johansen test.
From: ganesha0701 <ganesha0701 () gmail ! com>
Date: 2013-06-14 9:07:47
Message-ID: CA+j8qo26XWGyVL11etHiauuVkDKFMxigMi0LLx5GwdEpdcRXpA () mail ! gmail ! com
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Hi all, I am a newbie and looking to seek some help.
I have two time series that I am investigating, acc and amb, the time
frequency is daily data. They are both non stationary, as evidenced by the
follows.
adf.test(df$acc)
Augmented Dickey-Fuller Test
data: df$acc
Dickey-Fuller = -2.7741, Lag order = 5, p-value = 0.2519
alternative hypothesis: stationary
> adf.test(df$amb)
Augmented Dickey-Fuller Test
data: df$amb
Dickey-Fuller = -1.9339, Lag order = 5, p-value = 0.6038
alternative hypothesis: stationary
I am looking to test for cointegration between the two time series but the
problem I am running into is that the cointegrating vector seems to change
in time.
1)* First 200 points*
######################
# Johansen-Procedure #
######################
Test type: maximal eigenvalue statistic (lambda max) , with linear trend
Eigenvalues (lambda):
[1] 0.0501585398 0.0003129906
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 1 | 0.06 6.50 8.18 11.65
r = 0 | 10.19 12.91 14.90 19.19
Eigenvectors, normalised to first column:
(These are the cointegration relations)
acc.l2 amb.l2
acc.l2 1.0000000 1.000000
amb.l2 -0.9610573 -2.237141
Weights W:
(This is the loading matrix)
acc.l2 amb.l2
acc.d -0.03332428 -0.002576070
amb.d 0.03986111 -0.001591227
2) *First 1000 points*
######################
# Johansen-Procedure #
######################
Test type: maximal eigenvalue statistic (lambda max) , with linear trend
Eigenvalues (lambda):
[1] 0.019211132 0.001959403
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 1 | 1.96 6.50 8.18 11.65
r = 0 | 19.36 12.91 14.90 19.19
Eigenvectors, normalised to first column:
(These are the cointegration relations)
acc.l2 amb.l2
acc.l2 1.0000000 1.00000
amb.l2 -0.8611314 15.76683
Weights W:
(This is the loading matrix)
acc.l2 amb.l2
acc.d -0.008993595 -0.0002419353
amb.d 0.027935684 -0.0002067523
3)* Whole History*
######################
# Johansen-Procedure #
######################
Test type: maximal eigenvalue statistic (lambda max) , with linear trend
Eigenvalues (lambda):
[1] 0.0144066813 0.0008146258
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 1 | 1.16 6.50 8.18 11.65
r = 0 | 20.64 12.91 14.90 19.19
Eigenvectors, normalised to first column:
(These are the cointegration relations)
acc.l2 amb.l2
acc.l2 1.0000000 1.00000
amb.l2 -0.8051537 -25.42806
Weights W:
(This is the loading matrix)
acc.l2 amb.l2
acc.d -0.01003068 7.009487e-05
amb.d 0.02128464 6.980209e-05
You can see the marginal change the coefficient values, from -0.96 to -0.86
to -0.80.
My question is how to interpret this, what is the optimal look back period,
what is the true relationship I should use for future prediction?
Many thanks.
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