I have a little trouble figuring out when both the independent and dependent variables are time series.
E.g I can figure out that monthly returns are time series but what about something like 12 month trailing P/E?
The key to identifying data types is in understanding the experimental unit. Recall, the experimental unit is the object that you take measurements from for the sample. You have a population of experimental units, and you select a sample of experimental units. In order for data to be time series, the experimental unit must be some sort of time. For example, if you are told that a sample of 34 months was taken, you know the experimental unit is a month. If you are told that analysts are trying to predict the annual revenue for firm X, and they sampled 8 years for firm X, you know that a year is the experimental unit. The data are time series in both cases. Another hint is to look for the sequential ordering of the data.
This problem does not involve figuring out if each variable is time series, because the variables come from the same experimental unit. The quickest way to identify the experimental unit and whether or not the data are time series, is to look at the sample (as noted before a sample of _ # _ _ experimental units _, e.g. 34 months).
If you are trying to predict for a unit of time, then you have time series data.
Hope this helps!