I would imagine that marketing expenditures are for distributed types of results, e.g. you pay for an ad that then runs for days or weeks? This suggests a lagged & distributed respons of sales to a given marketing expenditure. This could perhaps be represented by convolution with an "impulse response" kernel.

Commonly "stationarity" is considered in the context of ARIMA models. This approach should be applicable here, as I believe these models can represent convolutions. However you would have to use the multivariate version. I cannot say what tools would be best to estimate this sort of model, but here is one place to start.

I would imagine that marketing expenditures are for distributed types of results, e.g. you pay for an ad that then runs for days or weeks? This suggests a lagged & distributed respons of sales to a given marketing expenditure. This could perhaps be represented by convolution with an "impulse response" kernel.

Commonly "stationarity" is considered in the context of ARIMA models. This approach should be applicable here, as I believe these models can represent convolutions. However you would have to use the multivariate version. I cannot say what tools would be best to estimate this sort of model, but here is one place to start.