Adaptive Nonparametric Regression Using Hybrid Fourier-Wavelet Series: A Generalized Inference Approach for Multiscale Socioeconomic Dynamics

This study proposes a novel approach to nonparametric regression by integrating Fourier and wavelet series, allowing for better adaptability in capturing both global and local variations in data. Traditional Fourier-based models often struggle with abrupt changes, whereas the hybrid Fourier-wavelet model provides a more flexible and accurate estimation framework. The study develops inferential tools, including multivariate hypothesis tests and adjusted t-tests, to enhance its applicability. Empirical validation using regional expenditure data demonstrates a significant improvement in predictive accuracy compared to traditional methods, with a reduction in Mean Square Error (MSE) and an increase in R-squared values. The findings highlight the model’s potential in economic and social data analysis, offering a robust alternative for decision-making in dynamic environments.