Well it depend on what you are looking for on your result. But precision and accuracy, for any analysis in any estimation of time series parameter such data set must be subjected to a unit root test since you are working on time series methodology which you can now runs your models selection ACF or PACF
Stationarity is a very important assumption in time series studies, therefore for increase precision and accuracy it is expected that a stationarity test is performed for any time series data before analysis is carried out