Time-series decomposition to a base level and an effect of another feature 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.
You are describing multivariate time series analysis, modeling the interactions and comovements among a group of time series variables.

You can start with a vector autoregression (VAR) model, one of the most successful, flexible, and easy to use models for
the analysis of multivariate time series. Then work through the decomposition of time series.

You'll have to decide if you want assume if all components time series are stationary and ergodic. Each component will have autocovariances and autocorrelations but there are also cross lead-lag covariances and correlations between all possible pairs of components.