I am working on a time series that contains daily sales data. The aim of the project is to estimate the impact of marketing expenditure on the sales, while accounting for seasonality and trend.
I have subtracted a double seasonality (weekly and yearly) and a trend by using TBATS. Now I plan to regress the marketing expenditure on the residuals.
The problem is that sales are 0 (or almost) every Sunday and on Public Holidays. Sundays are taken into account by the weekly seasonality and for Holidays I added a dummy variable in the regression. However marketing expenditure is not 0 on those days and that could bias the regression.
I was considering the following options, which one would be recommended and/or are there any other suggestions?
- Multiply marketing expenditure by a dummy that is 0 on Sundays and Holidays and 1 otherwise
- Do the same for Holidays, but leave out Sundays altogether from the data