I've got a time-series data (let's denote it as `y`) and some feature (let's denote it as `x`). `y` is dependent on `x`, but `x` is often equal to `0`. Even then, `y` is not `0`, so we can assume that there's a base level in `y` which is independent of `x`. Additionally, we can observe some seasonality in `y`. I need to decompose `y` into base level and an effect of `x`. And I need some hint about methodology. I have googled and found plenty of methods to decompose time-series data into trend, seasonality and random noise. However, my case is different, because I have an additional feature `x` and I would like just to extract its effect, and leave trend, seasonality and noise alltogether. What I have in mind can be represented on a plot below, where turquoise area represents base level of `y` and red area represents an effect of `x`. What method would allow to make such a split? I would also appreciate any links or materials.

[![enter image description here](https://i.stack.imgur.com/RU71M.png)](https://i.stack.imgur.com/RU71M.png)