# if a time series is not stationary at a weekly level, is it also not stationary at quarterly level?

I have time series of sales of many products on weekly level for 2 years. I am interested in forecasting the sales on quarterly (4-months) level for every product.

I also have some exogenous variables for every product, but these are in quarterly level.

I am planning on using a VARMAX model, and to do so I am going to use

from statsmodels.tsa.statespace.varmax import VARMAX


in Python.

VARMAX is suitable for multivariate time series without trend and seasonal components with exogenous variables.

My questions are:

• 1) Is it a good idea to run the model on quarterly frequency (since my exogenous variables are on quarterly level) ? Could it be that I lose too much information by aggregating ?
• 2) When I check for non-stationarity should I check at weekly level, and if so, are the conclusions also valid for the quarterly level (so after aggregation) ?
• 3) If non-stationarity (and/or seasonality) is there, is it sufficient taking the differences so that it becomes stationary, and then use VARMAX ? And if so, should I take the differences on the weekly level or in the quarterly level ?