Selecting Optimal Knot Points and Oscillation Parameters Using Generalized Cross-validation and Unbiased Risk Method in Nonparametric Regression of Combined Spline Truncated and Fourier Series

A nonparametric regression approach is suitable for the cases in which the shape of the pattern between the response variables and the predictor variables is not known. There are several methods in nonparametric regression, such as spline truncated and Fourier series. In both methods, determining the optimal knot point is crucial. Optimal knot points and oscillation parameters can be selected using the generalized cross-validation (GCV) and unbiased risk (UBR) methods. This study aimed to examine the GCV and UBR methods to select optimal knot point and oscillation parameters on the data on Indonesia’s economic growth rate in 2022. The estimation method used is ordinary least square (OLS). The results obtained used the GCV method because it has MSE value 1.42, which is smaller than MSE of UBR method of 10.614. The coefficient of determination for the GCV method is 89.34%. The optimal number of knot points and oscillation parameters are three and three for nonparametric regression estimator combined of spline truncated and Fourier series.