In this paper we describe a technique for monitoring and checking temporal logic assertions augmented with real-time and time-series constraints, or Metric Temporal Logic Series (MTLS). The method is based on Remote Execution and Monitoring (REM) of temporal logic assertions. We describe the syntax and semantics of MTLS and a monitoring technique based on alternating finite automata that is efficient for a large set of frequently used formulae and is also an on-line technique. We investigate the run-time data-structure size for several interesting assertions taken from the Kansas State specification patterns.