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I have three time series df['a'], df['b'] and df['c'] which I want to test for cointegration using the statsmodels.tsa.vector_ar.vecm.coint_johansen function (and obtain a cointegration vector).

I start by making sure all three time series are I(1) using the ADF test.

ADF test in level: statsmodels.tsa.stattools.adfuller(df['a']) gives a large p-value, so we conclude that the time series is non-stationary. The test gives an optimal lag length of 2 based on AIC. The ADF test on df['b'] and df['c'] similarly give large p-values with optimal lag lengths of 4 and 7, respectively.

ADF test in first difference: statsmodels.tsa.stattools.adfuller(df['a'].diff().dropna()) gives a p-value < 0.05 so we conclude that the time series is stationary in first difference, and is therefore I(1). Similarly, we conclude that df['b'] and df['c'] are I(1).

I'm now ready to test for cointegration using the Johansen test...

result = statsmodels.tsa.vector_ar.vecm.coint_johansen(df[['a','b','c']], det_order=0, k_ar_diff=???)

...but I'm not sure what to use as the lag length. Should it be 2, should it be 4, should it be 7 or should it be determined some other way?

Furthermore, I have a couple of questions about the results of the Johansen test:

enter image description here

  1. Do we conclude from the above results that the cointegration rank is 3 meaning that there are 3 independent cointegration vectors?
  2. If so, how do we choose which cointegration vector to use to form a stationary time series? Is it appropriate to just use the first one coint_vec = result.evec[:,0]?
  3. Finally, are there any steps missing in my analysis? I read something about checking to see if the residuals of the VAR model are not auto-correlated - would we use one of the result.r0t or result.rkt outputs from the Johansen test to do this?
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  • $\begingroup$ It looks like you have screen shot an output of a Pandas dataframe. Note that Pandas dataframes have a .to_markdown method whose output you can print then copy-paste into a stack exchange post. $\endgroup$
    – Galen
    Commented May 14, 2023 at 19:35
  • $\begingroup$ pandas.DataFrame.to_markdown. $\endgroup$
    – Galen
    Commented May 14, 2023 at 20:08

1 Answer 1

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  1. No. It means there is no cointegration at all. You need to reject the middle null hypothesis for cointegration

  2. If you have cointegration you can choose the first values and get weights weights = list(jres.evec.T[0] / jres.evec.T[0][0])

  3. You need to fit VECM next. But not in this data (because lack of cointegration).

vecm.VECM(timeseries, deterministic="n", k_ar_diff=order, coint_rank=rank)

Rank you get from johansen test and order from VAR or using function

vecm.select_order(timeseries, maxlags=max_lag, deterministic="co")

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