时间序列分析的数据必须是平稳的，非平稳数据必须通过差分或其他形式变为平稳序列才能进行分析；如果同阶协整可以对原始数据进行VAR分析，注意是同阶（如果一个一阶单整，另一个二阶单整，是没有意义的伪回归）；在做实证前进行ADF检验，只是为了说明数据是平稳的，是实证基础。不做这些检验，是论文不严密，甚至是错误的。

I suggest you to do stationary test first. If stationary, you can try LCF/PCF to see the what is the optimal lag to use in autoregression.
In VAR, you can put the optimal leg in equation, say, y(t)=y(t-1)+y(t-2)...
you have to look at residual and check the co-variance matrix of your residuals. If the co-variance matrix is not independent, you have to decompose it and use GLM. Indeed, you DCF test is for the stationary of the time series. you don't need to redo it if you change the VAR.
Hope this helps.

VAR模型应该用平稳序列完成。

但有特殊情况，某些变量理论上是平稳的，但在实际样本选择可能是不平稳的，例如汇率这种维纳过程差分，应该理解为平稳的，但如果你截取的样本期是持续上升或下降的时间段，可能导致差分后的序列在统计上不平稳，但你也可以用这个不平稳的序列去做回归的。

I think you need to make sure that the TS is stationary. From my experience, taking difference may not work very well or a reasonable approach to go with all the time. Try to remove any seasonality and/or trend from your data before you do the difference. And don't too rely on testing, because if you have a large sample size, all testings tend to reject. To choose the model, also include prediction performance.

关于你的这个问题，我觉得应该是这样的。最好是同价单整，但是如果确实是一个一阶单整，一个二阶单整，你就要考虑一下换另外的一些变量了。时间序列分析的数据必须是平稳的，非平稳数据必须通过差分或其他形式变为平稳序列才能进行分析；如果同阶协整可以对原始数据进行VAR分析，注意是同阶（如果一个一阶单整，另一个二阶单整，是没有意义的伪回归）；在做实证前进行ADF检验，只是为了说明数据是平稳的，是实证基础。不做这些检验，是论文不严密，甚至是错误的。