Ambark, Ali Saleh Al-Massri
(2024)
Penalized Quantile Regression Methods And Empirical Mode Decomposition For Improving The Accuracy Of The Model Selection.
PhD thesis, Universiti Sains Malaysia.
Abstract
In this study, in several scientific studies, the variables of interest are often represented by time series processes, and such time series data are frequently non-stationary and non-linear, resulting in low accuracy of the resulting regression models and less reliable conclusions. In addition, the ordinary least squares method is sensitive to outliers and heavy-tailed errors in data, and several predictors may suffer from multicollinearity problems. Moreover, selecting the relevant variables when fitting the regression model is critical. Therefore, three methods based on a combination of the empirical mode decomposition (EMD) algorithm and penalized quantile regression have been proposed in this study. The EMD algorithm decomposes the non-stationary and non-linear time series data into a finite collection of approximately orthogonal components called intrinsic mode functions and residual components. In several studies, these components have been employed as novel predictor variables to study the behaviour of the response variable. This study aims to apply the proposed EMD-QRR, EMD-QR, and EMD-QREnet methods to identify the influence of the decomposition components of the original predictor variables on the response variable to build a model that has the best fit and improve prediction accuracy. Furthermore, this study deals with the multicollinearity issue between the decomposition components. To verify the prediction performance of the proposed methods, the proposed methods are compared with three existing regression methods used in previous studies. Simulation studies and empirical analysis of the real data were carried out in this study.
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