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To me this looks like an ambiguity in the docs when "Month" is specified as a possible shift because everything else implies a fixed shifting increment. If you really want to shift your data by a calendar month then try this: monthShift[timeSeries_, months_] := Module[{ts = timeSeries}, ts[[2, 2, 1, 1]] = (DatePlus[#1, {months, "Month"}] &) /@ ...

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