Estimation of Fourier series regression curve on the open unemployment rate data in Indonesia in multivariable nonparametric regression

The statistical analysis method used to determine the effect between two or more variables is called regression analysis. The pattern of relationships between variables in regression analysis does not always have a parametric pattern. There are some cases where one or more predictor variables do not have a pattern that is called nonparametric and even has a combined pattern of parametric and nonparametric, called semiparametric. Nonparametric regression is a statistical method that is used to identify and modelling the pattern of the relationship between predictor variables and response variables whose function is unknown. One method that is widely used to estimate the regression curve using a nonparametric approach is the Fourier series. The advantage of the Fourier series is this method is quite good for describing curves whose data patterns are repeated. This study will examine the estimation of the nonparametric regression curve of the Fourier series and then modelling the Open Unemployment Rate data in Indonesia with the best model criteria based on the maximum R2 value and the minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). The results of this research shown that with the Fourier series, the minimum GCV is 2.66 with an oscillation number of 3. Then the model goodness value is 91.73% and the MSE model is 2.410.