# How to decompose seasonality of a time series with a limited time span?

I am working on a time series that contains daily sales data over 2 and a half years. The aim of the project is to estimate the impact of marketing expenditure on the sales, while accounting for seasonality and trend.

A plot of the data reveals a strong weekly seasonality. There also seems to be yearly seasonality. However, as there is only 2 and a half years of data available, I was wondering what the best method(s) would be to take the yearly seasonality into account without sacrificing too much of the data for testing the impact of marketing expenditure on?

I am more confortable in Python, but if need be I can use R as well.

• You may want to look at TBATS models, although their original form (and the implementation in the forecast package for R) does not allow for covariates, like your marketing expenditures. Maybe you can remove the multiple seasonalities using a TBATS model, then regress the deseasonalized series on marketing expenditure. – Stephan Kolassa Dec 27 '17 at 20:19
• Thank you very much for the advice. Looking into TBATS I found a blog post from Hyndsight suggesting to use auto.arima with multiple Fourier terms as covariates for the double seasonality. I will try out both and see what works best! – Technologic Dec 27 '17 at 22:33