Parameters and Knot Points Estimation for Spline Methods Applied in Time Series Data
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The purpose of this study is to investigate and compare several nonparametric regression approaches, including penalized spline methods, B-splines, and smoothing splines. Applying these techniques to simulated and real datasets, such as Iraqi oil export data, focuses on parameter estimation and identifying optimal knot points for predicting periodic and nonlinear trends. The knot points are selected using generalized cross-validation (GCV) to ensure an accurate fit to the data. For time-series data with nonlinearities and periodic patterns in the response variable, this research employs nonparametric regression with sequential explanatory variables. We research simulated data that exhibit periodic patterns similar to economic cycles, as well as nonlinear data that employs complex equations to model interactions among variables. Simulations were conducted across a range of standard deviations and sample sizes. The efficiency of parameter estimation in these synthetic datasets was quantified using the mean absolute average error (MAME). For the empirical application, the parameters of the nonparametric regression models were estimated using monthly Iraqi oil export data, with the MAME employed as the evaluation metric. The effectiveness of these techniques is further evaluated in forecasting future values by calculating the mean absolute percentage error (MAPE). Among the approaches, the penalized spline consistently achieves the lowest average mean squared error across all standard deviation levels and sample sizes in the simulated data, while also demonstrating robust forecasting performance. In contrast, the smoothing spline outperforms the other methods in terms of parameter estimation accuracy.
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