I am very confused about time series analysis. Let $y$ is the dependent variable, which has an increasing trend. Let $x1$ is a price index for a group of goods. I know that $x1$ creates the general trend of $y$. Both $y$ and $x1$ are $I(1)$. So, I can regress $y$ on $x1$ (cointegration).
However, I also know that there are some other variables that affect $y$. For example, variable $x2$, affects $y$ in short term - it creates some seasonal effects around the trend. And I have also other such variables, which explain the variability of $y$ around the trend.
I am confused about this situation. I can regress $y$ on $x1$, because they are both $I(1)$. However, $x2$ is $I(0)$. So, I can't regress $x2$ on $y$.
How can I model $y$ using $x1$ and $x2$? I will appreciate help or advice on articles on this subject.