Regularization in Quantile Regression based on Empirical Mode Decomposition

Abstract

Quantile regression is considered a robust alternative to ordinary least squares (OLS) regression in the presence of outliers or heavy-tailed error distributions, providing insights into the conditional distribution of the response variable. The empirical mode decomposition (EMD) decomposes nonstationary and nonlinear signals into a finite set of orthogonal decomposition components, which are then used in several studies as new predictor variables in regression models. In this work, we develop the use of lasso, ridge, and elastic net regularizations in quantile regression utilising a modified percentile cross-validation based on empirical mode decomposition (EMD). These proposed methods aim to identify the decomposed components that exhibit the strongest effects and address the multicollinearity among decomposition components to improve the prediction accuracy. The simulation study and numerical examples utilising the stock market applications dataset from three countries are applied. The results showed that the proposed methods outperformed other existing methods at different quantiles by producing a model free from multicollinearity and effectively identifying the decomposition components that have a significant impact on the response variable, with high prediction accuracy.