Sequences of time series data with only 1 output classification
With only one output, there is no task for a supervised learning algorithm for classification. Your algorithm can only predict your only one class, you do not give any other situations of other classes for your algorithm to work on; a classification algorithm will need at least two classes. I have strong experience with time-series learning problems, but it seems that your problem has nothing to do with whether your data is time-series.

However, depending on your task, you can implement unsupervised learning which does not require any labels. You can seperate your data into clusters which have similar properties as time-windows. Then you can predict with new (or test) samples that which cluster should it be from, what it is alike.