How can we detect trend in a time series apart from visual observation of time plots? I'm novice in time series analysis and completely lost through reading so..
I have an enormous dataset of discrete time series of aggregated events and I wish to fit each one of them into ARIMA models. Therefore I have to ensure that the time series are stationary, which I do through adf and kpss tests. However I wonder if these tests also ensure that time series do not need to be tested for trend and seasonality. Is there any statistical criterion that reveals that a time series is trending?
Visual inspection of time plots is difficult in this case out of the question* since the dataset is way too big.
Thanks in advance,
btw I'm an R user ;)
-A
 A: When faced with the daunting task of evaluating a "zillion" number of time series for local time trends one could spend a lot of time reviewing graphs which may or may not have unusual data points potentially obfuscating the trend or an embedded auto-regressive structure which could also defeat your "eyeballing". A more efficient approach might be  to perform a computerized search which could be classified as a productivity aid for your bleary eyes. The suggested procedures to detect time trends and other deterministic structure have been all peer-reviewed and have transparency. These are not ad-hoc methods but state-of-the-art procedures to help you in your qwest. Look at my answer and previous references in Fancy detrending of time series
A: I would point you to the paper Testing parametric assumptions of trends of a nonstationary time series (Zhang and Wu, 2011) which can be found here. In this paper the authors test whether the trend has a specific parametric form (which in my opinion is the most interesting case). If all you care about is whether the mean is constant, you can use one of a variety of changepoint detection methods for the mean of a time series.
