L1 Filtering
Posted: Tue Aug 27, 2013 11:35 am
This does an example from Kim, Koh, Boyd, Gorinevsky(2009), "L1 Filtering", SIAM Review, vol 51, pp 339-360. The L1 filter is a piecewise linear filter similar to the H-P filter. An exact solution for the problem requires a specialized set of optimization software, but it can be very closely approximated with "off-the-shelf" iterated Kalman smoothing as is done here.
One problem (as noted in the comments) with the L1 filter as described in the paper is that the tuning parameter lambda is scale-dependent because one of the terms in the optimand is squared and one is absolute value (unlike the H-P filter, where both are squared). This is set to use a tuning parameter which is scale-independent.
One problem (as noted in the comments) with the L1 filter as described in the paper is that the tuning parameter lambda is scale-dependent because one of the terms in the optimand is squared and one is absolute value (unlike the H-P filter, where both are squared). This is set to use a tuning parameter which is scale-independent.