I seem to have a multivariate time-series causal problem. I am trying to forecast revenue based on variables that may have affected this revenue. I have a dataset containing marketing spend and marketing data through time for various campaigns and social media sites, for example, on the first week of April, the company spent 1M on Twitter marketing, spent $ 3M on Facebook, received 300M of Facebook impressions, and so forth. The dataset also contains any other causal variables such as whether a given day was a bank holiday or whether the day was a holiday season. The business question is what will be the effect on revenue if we increased Facebook spend on this given week by 10%.
What tools can I employ to help solve such a task? It seems to be a causal question, so linear regression may not be of help?