currently I'm working on a project where I want to test effects of external indicators on internal sales data.

So I already collected a lot of data and now want to compare two time series. But there are some things I'm not sure about:

- Is it recommendable to decompose each time series in advance? So basically I would test the random component of time series 1 against the random part of time series 2? Thus I dont attribute an effect to the "predictor" that is just based on high seasonality / trend for both time series?
- If some data is only available on a quarterly basis, is it ok from a statistical point of view to divide that time series by 3 in order to get monthly data?
- When data preprocessing is done: I'd conduct a cross correlation test to account for time-shifted correlation, what measurements should I take to ensure those findings are valid (ACF, PACF)?

Best regards,

Markus