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Reply To: Issue with JohansenTest

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#2922
hao.ding
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Hi kevin,

The method “r” in JohansenTest returns the number of stationary vectors, which are linear combination of input time series.

For example, if we are testing m time series, the value of r could be 0,1,…,m.
r=0: The m time series are not cointegrated.
1<=r 1" when the number of time series is 2. Therefore the test is equivalent to "johansenTest.r(coint, level) == 2", because the largest value r could get is 2. In SuanShu, the procedure to compute r is: step 1: compute the statistics when r=0 and r=1. step 2: compute the asymptotic Johansen distribution when r=0 and r=1. step 3: based on the input significant level, compute the quantile of the distribution when r=0 and r=1. step 4: compare the statistic of r=0 with quantile from distribution of r=0. - If the statistics is larger than quantile, then null hypothesis r=0 is rejected. And we move on to consider the case r=1. - Else we output r=0. -If we are considering r=1 and we can reject the null hypothesis r=1, then r=2. -Else we output r=1. So to answer your question, the results from SuanShu are consistent. To get r=2, we need to compare two statistics, one is the statistics when r=0, and the other is the statistics when r=1. The vector you get from "johansenTest.getStats(coint)" are two statistics. The first value in the vector is the statistics when r=0. And the second value in the vector is for r=1. For example, consider data set A, the statistics is 23.02 and 10.38. when r=0, we will compare 23.02 with the quantile from Johansen distribution for r=0. If r=0 could be rejected, then we will compare 10.38 with the quantile from the Johansen distribution for r=1. If r=1 could be rejected, we conclude that r=2. Hope this helps.