Piecewise Regression Using Cubic Splines

Abstract

Spline theory and piecewise regression theory are integrated to provide a framework in which structural change is viewed as occurring in a smooth fashion. Specifically, structural change occurs at given points through jump discontinuities in the third derivative of a continuous piecewise cubic estimating function. Testing procedures are developed for detecting structural change as well as linear or quadratic segments. Finally, the techniques developed are illustrated empirically in a learning-by-doing model.