 deskquant
Topic Author
Posts: 48
Joined: October 24th, 2010, 2:54 am

### Johansen test dyamically carying coefficients

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$acc) Augmented Dickey-Fuller Testdata: df$accDickey-Fuller = -2.7741, Lag order = 5, p-value = 0.2519alternative hypothesis: stationary> adf.test(df$amb) Augmented Dickey-Fuller Testdata: df$ambDickey-Fuller = -1.9339, Lag order = 5, p-value = 0.6038alternative hypothesis: stationaryI 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 trendEigenvalues (lambda): 0.0501585398 0.0003129906Values of teststatistic and critical values of test: test 10pct 5pct 1pctr <= 1 | 0.06 6.50 8.18 11.65r = 0 | 10.19 12.91 14.90 19.19Eigenvectors, normalised to first column:(These are the cointegration relations) acc.l2 amb.l2acc.l2 1.0000000 1.000000amb.l2 -0.9610573 -2.237141Weights W:(This is the loading matrix) acc.l2 amb.l2acc.d -0.03332428 -0.002576070amb.d 0.03986111 -0.0015912272) First 1000 points####################### Johansen-Procedure #######################Test type: maximal eigenvalue statistic (lambda max) , with linear trendEigenvalues (lambda): 0.019211132 0.001959403Values of teststatistic and critical values of test: test 10pct 5pct 1pctr <= 1 | 1.96 6.50 8.18 11.65r = 0 | 19.36 12.91 14.90 19.19Eigenvectors, normalised to first column:(These are the cointegration relations) acc.l2 amb.l2acc.l2 1.0000000 1.00000amb.l2 -0.8611314 15.76683Weights W:(This is the loading matrix) acc.l2 amb.l2acc.d -0.008993595 -0.0002419353amb.d 0.027935684 -0.00020675233) Whole History####################### Johansen-Procedure #######################Test type: maximal eigenvalue statistic (lambda max) , with linear trendEigenvalues (lambda): 0.0144066813 0.0008146258Values of teststatistic and critical values of test: test 10pct 5pct 1pctr <= 1 | 1.16 6.50 8.18 11.65r = 0 | 20.64 12.91 14.90 19.19Eigenvectors, normalised to first column:(These are the cointegration relations) acc.l2 amb.l2acc.l2 1.0000000 1.00000amb.l2 -0.8051537 -25.42806Weights W:(This is the loading matrix) acc.l2 amb.l2acc.d -0.01003068 7.009487e-05amb.d 0.02128464 6.980209e-05You 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?  