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Are there any known techniques or methods to extract and identify decays from a time-series of data?

By "extract and identify" I mean finding similar features as those in the blue boxes in the figure.

Time Series Data

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    $\begingroup$ Pls define decay? It's the case that beauty is in the eye of the beholder. $\endgroup$ – horaceT Apr 8 '17 at 17:15
  • $\begingroup$ If the decay patterns are of same length => seasonality; If the patterns are of different lengths => cycles $\endgroup$ – Ferdi Apr 8 '17 at 17:32

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