This paper presents a method for separating signal (trend) from noise in a set of measured bivariate data when there is no mathematical model for that signal. The algorithm models the signal with a smoothing spline for which the number and location of the knots are chosen to optimize the separation into deterministic and random components. This is done by generating a collection of different trial splines and determining which gives residuals with statistical properties most consistent with random noise, in which even autocorrelation is detected. It describes a computer program spline2 which implements the algorithm and applies it to three real world example problems.
nonparametric fitting, signal and noise, smoothing splines
and Rust, B.
Freestyle Data Fitting and Global Temperatures, Computing in Science & Engineering, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50869
(Accessed December 3, 2023)