1 Trend Filtering

  title={1 Trend Filtering},
  author={Seung-Jean Kim and Kwangmoo Koh and Stephen P. Boyd and Dimitry M. Gorinevsky},
  journal={SIAM Rev.},
The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed $\ell_1$ trend filtering method substitutes a sum of absolute values (i.e., $\ell_1$ norm) for the sum of squares used in H-P filtering to penalize variations in the estimated trend. The $\ell_1$ trend filtering method produces trend estimates that are piecewise linear… Expand
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