[tnecniv]

It depends on your time series, really. If the samples are evenly spaced, e.g., your sensor gives you a reading every millisecond, your measured sequences aren’t partially overlapping, and you don’t have structured discrete events, then time isn’t very useful. You can always rescale time so that it is just the same as the index.

For your calendar example, date information is very useful because patterns tend to exhibit a cyclic nature across years and there’s discrete special events (holidays). With enough data, you probably don’t need to include the date, but it’s informative for smaller data sets.