Should-Read: Perhaps the most remarkable thing is that neither Robert Hodrick nor Ed Prescott ever came up with any arguments for why the filter was something you ought to use. Never. Not one:
James D. Hamilton: Why You Should Never Use the Hodrick-Prescott Filter: "Here's why. (1) The HP filter produces series with spurious dynamic relations that have no basis in the underlying data-generating process... http://www.nber.org/papers/w23429
...(2) Filtered values at the end of the sample are very different from those in the middle, and are also characterized by spurious dynamics. (3) A statistical formalization of the problem typically produces values for the smoothing parameter vastly at odds with common practice, e.g., a value for λ far below 1600 for quarterly data. (4) There's a better alternative. A regression of the variable at date t+h on the four most recent values as of date t offers a robust approach to detrending that achieves all the objectives sought by users of the HP filter with none of its drawbacks...