Some Results on ？1 Polynomial Trend Filtering

Abstract ？ 1 polynomial trend filtering, which is a filtering method described as an ？ 1 -norm penalized least-squares problem, is promising because it enables the estimation of a piecewise polynomial trend in a univariate economic time series without prespecifying the number and location of knots. This paper shows some theoretical results on the filtering, one of which is that a small modification of the filtering provides not only identical trend estimates as the filtering but also extrapolations of the trend beyond both sample limits. View Full-Tex