For purposes of postwar business cycles, the 1600 number was the first tried and seem to mimic well the smooth curve people typically fit throughout the data. As a year is four quarters, reducing it by four squared, that is by factor of 16, resulted in the same amount of variation in trend being permitted. Some good people tried to develop some formal theory, that made connections between different length time periods. But this is a data representation exercise, not a measurement or estimation procedure. An efficient HP-filter.
Any comments are welcome.
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