A New Method for Specifying the Tuning Parameter of ℓ1 Trend Filtering

Because Hodrick–Prescott (HP) filtering and l1 trend filtering are expressed as penalized least squares problem, both of them require the specification of their tuning parameter. For HP filtering, we have accumulated knowledge for selecting the value of its tuning parameter. However, we do not have similar knowledge for l1 trend filtering. This paper presents a new method for specifying the tuning parameter of l1 trend filtering so that the sum of squared residuals of HP filtering and that of l1 trend filtering may be equivalent.