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][1]" kernel.

Commonly "stationarity" is considered in the context of [ARIMA][2] 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][3] is one place to start.

  [1]: https://en.wikipedia.org/wiki/Impulse_response
  [2]: https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average
  [3]: http://stats.stackexchange.com/questions/94443/is-there-any-tool-that-can-do-vector-arima-modeling-in-time-series