A Note on the Predicted Responses in Cubic Splines

Abstract

One of the most used statistical methods in economic and business studies involving time series is related to predicted responses (ỹ values), which can be estimated with two different approaches, namely cubic spline regression method (CSR) and prediction sum of squares statistic (PRESS). This study aims to set and discuss the relation between these two approaches in estimation of predicted responses. In first approach estimated ỹ values are determined from the derived restricted model. According to the second approach, they are estimated with prediction sum of squares statistic (PRESS), and it argues that the use of this technique performs is better for cubic spline regression method (CSR). This study while introducing and discussing the relation between these approaches, also addresses to note the estimation of predicted ỹ values theoretically. The study concludes that same predicted responses can be received by employing both methods. For examining and testing this argument empirically real exchange rates data for Turkey in the period of 1987-2008 are used. Additionally another subject searched and discussed in the study was, how economic crises can be defined with spline methods. Because of the advantages provided by them in reaching minimum residual sum of squares, and achieving the result by using real economic data without changing their nature in time series analysis.