An investigation of export–import ratios in Turkey using spline regression models

Abstract

This paper examines the use of spline functions in linear, squared, and cubic spline regression models and exhibits the estimation of spline parameters from data by ordinary least squares. Determination of the number and the location of knots is central to spline regression. In this paper, we initially propose a method based on the coefficient of determination R2 related to the estimation of knots in spline regression. This proposed method as applied to export–import ratio distributions in Turkey for the years 1923–2010 determines the knots, and linear, quadratic, and cubic spline regression models are established accordingly. Results reveal that spline regression models offer better results than polynomial regression models, and that the quadratic spline regression model is the best explanatory model for export–import ratio distributions in the smoothest spline regression models.