ABIC Based Method for the Trend Estimation Problem of One Dimensional Data

Abstract

To estimate a smooth trend of one dimensional data, a procedure based on the minimization of ABIC (Akaike's Bayesian Information Criterion) combined with local spline function is proposed. This is the development of Akaike's simple procedure based on the minimization of ABIC with a difference modeling, which only can treat the equidistantly distributed data (Akaike, 1980) . In this paper, the author explaines the theoretical treatment and numerical calculation method of the procedure in detail. A numerical example is also included to show the effectiveness the procedure.