The L1_filteringa.xlsx Model

L1 Trend Filtering

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Given a series of observations, we want to employ a piecewise linear filter. Although the estimation is similar to that of Hodrick-Prescott (HP) filter, which is basically a L2 filter, the main difference is that penalty parameter lambda here does not determine the smoothness, but the number of breaks.

This is a good example of the use of linearization, which is useful in handling the non-smooth ABS() functions.

Keywords:

Time Series | Filtering | Piecewise Linear | L1 norm | Trend | Hodrick-Prescott |