# Testing if linear drift exists in time series data

I have some data $X_1, X_2, ..., X_n$ which shows no apparent sign of linear drift. Nethertheless, I want to conduct some sort of test which I could use in instances which are not so clear.

Is there a way of testing this without assuming normality of error terms etc?

Perhaps a randomisation test of some sort?

My data in particular is measured every day for roughly 100 weeks. There was a weekly trend in the data which I have removed, and so now I have a time series centred at zero. I basically want some sort of test I can apply to data of this type with minimal assumptions that tests whether or not the data has some linear drift.

• This concerns whether the process the data came from is a stationary process or not. A. More advanced treatment of the topic is found in What is the difference between a stationary test and a unit root test? – blackeneth Oct 8 '16 at 7:35
• So if there is some linear drift, suppose say the mean is decreasing, these histograms should show the mean at smaller and smaller points? Is that the idea of the test? Also appreciate the link, will give it a read now. – Patty Oct 8 '16 at 7:40