The Use of Spline Techniques in the Nonparametric Regression Analysis for the Sequence Data with a Random Walk Process

This study evaluates and compares various spline techniques in the nonparametric regression analysis, specifically focusing on the smoothing spline regression, the natural spline regression, the B-spline regression, and the penalized spline regression. The dependent variable in this analysis is time series data generated by a random walk process, while the independent variable is represented as sequential data. The simulation data, derived from a random walk process with diverse variances and sample sizes, ensures an absence of fixed patterns in the variable's changes. In addition, real-world data from the monthly trading volume of the SET (Stock Exchange of Thailand) index is used for practical application. The criterion for model efficiency estimation is based on minimizing the average mean square error for the simulation and SET index data. At the same time, predictive performance for future values is assessed through the minimum of average mean absolute percentage error. Among the models tested, the natural spline regression achieved the minimum average mean square error in all simulations due to SET index data estimation, excelling in model fit. However, the B-spline regression proved highly effective for forecasting future values.