Analysis of two time series when one is stationary and another one isnt

Hi there. I have a persistent question. I'm currently using VAR to estimate the relationship between (primarily) two time series: central bank rates and inflation. The problem is: according to ADF test, inflation is stationary and central bank rates are integrated of order 1.

In this case, I cannot use cointegration test since my time series are I(0) and I(1) each. On the other hand, i know It is not much recommended to aply First differences to my I(1).

So... How am i supposed to know If my estimation is not spurious? I mean. It WILL be spurious because my central bank rates clearly show a trend. But turning them stationary also has a cost.

(Bibliographic references for dealing with this issue specifically is very welcome. But It would be also satisfactory to read your opinions)