A data analysis of natural gas prices using penalized median regression splines

Abstract

We carry out a study on a natural gas prices data analysis based on a penalized median regression spline estimator with B-spline and total variation penalty. Once we express the estimator by a linear combination of a linear B-splines, the coefficients are estimated by minimizing a penalized check loss function. A coordinate descent algorithm is introduced to handle the special penalty determined by the B-spline coefficients. In implementation, we adopt the form of an univariate weighted absolute function, which is a convex and piecewise linear function, and find its slope to find the minimum of each coordinate. We also illustrate the performance of the proposed method using some numerical studies and data analysis. The performance of the proposed estimator is studied through both numerical simulations and the natural gas prices data sets.