Splinets 1.5.0 -- Periodic Splinets

TL;DR

This paper introduces an efficient method for implementing periodic splines, called splinets, and integrates them into the R package 'Splinets' for analyzing circular data such as wind directions.

Contribution

It presents a novel orthogonal basis for periodic splines, called splinets, and extends the 'Splinets' package to support these for circular data analysis.

Findings

Efficient orthogonal basis for periodic splines developed.

Added periodic splinets to the 'Splinets' R package.

Applied tools to analyze wind direction and speed data.

Abstract

Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects representing such splines and describes how an efficient orthogonal basis can be obtained. The proposed orthonormalized basis is called a periodic splinet in the reference to earlier work where analogous concepts and tools have been introduced for splines on an interval. Based on this methodology, the periodic splines and splinets are added to the earlier version of the R package "Splinets". Moreover, the developed computational tools have been applied to functionally analyze a standard example of functional circular data of wind directions and speeds.