How to interpret results of Johansen test?
1/The loading matrix is the matrix generaly reffered to as alpha (Check urca documentation). 2/ The critical values: If the null hypothesis (r=0, r<=1) is verified your test statistic follows a known distribution. Given the cumulative distribution you can find where lie 90%, 95%, 99% of the values.
How to use Johansen test for time series analysis?
We then call the ca.jo function applied to a data frame of all three time series. The type parameter tells the function whether to use the trace test statistic or the maximum eigenvalue test statistic, which are the two separate forms of the Johansen test. In this instance we’re using trace.
When does the Johansen test check for no cointegration?
The test checks for the situation of no cointegration, which occurs when the matrix A = 0. The Johansen test is more flexible than the CADF procedure outlined in the previous article and can check for multiple linear combinations of time series for forming stationary portfolios. To achieve this an eigenvalue decomposition of A is carried out.
How is Johansen performed on a data set?
Conducts the Johansen procedure on a given data set. The “trace” or “eigen” statistics are reported and the matrix of eigenvectors as well as the loading matrix. Data matrix to be investigated for cointegration.
Why is the Johansen test less statistical power than CADF?
In the Johansen test the linear combination values are estimated as part of the test, which implies that there is less statistical power associated with the test when compared to CADF. It is possible to run into situations where there is insufficient evidence to reject the null hypothesis of no cointegration despite the CADF suggesting otherwise.
How is the Johansen test based on time series?
The Johansen test is based on time series analysis. The ADF test is based on an autoregressive model, a value from a time series is regressed on previous values from the same time series.