好久没思考过类似问题了，我试着回答一下，说错了请见谅。首先要看两列数据是否是在同一个时间窗口，difference的本质是随着推移t得到稳定预测，不管线性和非线性都如此。都做diff没什么不可以的。其实计算VAR不一定要这么复杂，EVT也也可以呀。当然如果你是计算portfolio risk, 时间上一定要统一。

It is a rather subtle topic. As a statistical analysis method, PCA does NOT require all variables in the same unit. In some cases you just cannot. For example, the variables include interest rate, oil price and S&P500 index.

However, as xtang60 pointed out, there is an option to use either cor or covar matrix. Each option has pros and cons. There are lots of discussions and debates on which one should be used. The most commonly used approach is to use covar matrix when the variables are on similar scale and the cor matrix when variables are on different scales. For example, use covar matrix when the variables are the treasury yields, while use cor matrix when the variables are the return of different stocks.

Which option is better is somewhat subjective. It is possible that two options give very different results. In this case, you probably want to identify what is the root cause before jumping into either one of them. It will help you better understand the problem and pick the right one to use.

Are you referring to vector autoregression? I am not an expert on that, but I believe you can, but you do not have to, take the diff on the stationary variable. They are equivalent by transforming the coefficient matrices from one way to the other.