How to measaure the similarity between two series?
A classical approach for time series similarity computation is Dynamic Time Warping (DTW).

From your description, it may suit your use case:


  In general, DTW is a method that calculates an optimal match between two given sequences (e.g. time series) with certain restriction and rules:
  
  
  Every index from the first sequence must be matched with one or more indices from the other sequence, and vice versa
  The first index from the first sequence must be matched with the first index from the other sequence (but it does not have to be its only match)
  The last index from the first sequence must be matched with the last index from the other sequence (but it does not have to be its only match)
  The mapping of the indices from the first sequence to indices from the other sequence must be monotonically increasing, and vice versa, i.e. if $j&gt;i$ are indices from the first sequence, then there must not be two indices $l&gt;k$ in the other sequence, such that index $i$ is matched with index $l$ and index $j$ is matched with index $k$, and vice versa
  


Some alternatives to DTW can be found in this literature review on time series dissimilarity measures.