The Impact of Wavelet-Based Denoising on Beta Regression Model Fit

Abstract

This paper discusses the relevance of wavelet-based denoising in a coupled beta regression for the analysis of the continuous, bounded response variables sensitive to noise. This hybrid approach was performed against both simulation experiments and real-world industrial data. The simulation phase generated data varying sample sizes, precision parameters, and noise levels to investigate the effects of pre-processing the response variable with discrete wavelet transforms – Daubechies, Symlets, and Coiflets – on model fitness, accuracy, and robustness.These wavelets were selected due to their complementary mathematical properties, which offer different equilibria for time-frequency localization, symmetry, and smoothness, and are suitable for denoising bounded response variables before modeling with beta regression. These wavelets were selected due to their complementary mathematical properties, which offer different equilibria for time-frequency localization, symmetry, and smoothness, and are suitable for denoising bounded response variables before modeling with beta regression. The simulation results indicated that wavelet-denoised models consistently outperform the conventional beta regression in noisy conditions. Daubechies and Symlets performed better in simulations overall. For the real data analysis, using 32 observations from a process of production of gasoline, wavelet-based denoising improved model fit, prediction precision, and residual behavior. In this case, the Coiflets wavelet performed better, providing the highest log-likelihood and precision estimates and lowest AIC, BIC, and MSE values. Residual testing confirms better symmetry and reduced variability in wavelet-enhanced models. Wavelet preprocessing is a useful and successful improvement over beta regression for industrial and process data that contain little noise and occasional outliers.