Cointegration question.
Please don't repost. If someone has the answer to your question and feels like helping, they will. The most common problem we see in the list archives when questions like this arise is that people are trying to test stationarity and cointegration on prices rather than on returns. However, you haven't actually provided reproducible data with your partial code, so without that I'm just guessing. - Brian
On 06/14/2013 11:09 AM, ganesha0701 wrote:
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?