Empirical Mode Decomposition Combined with Local Linear Quantile Regression for Automatic Boundary Correction

Abstract

Empirical mode decomposition (EMD) is particularly useful in analyzing nonstationary and nonlinear time series. However, only partial data within boundaries are available because of the bounded support of the underlying time series. Consequently, the application of EMD to finite time series data results in large biases at the edges by increasing the bias and creating artificial wiggles. This study introduces a new two-stage method to automatically decrease the boundary effects present in EMD. At the first stage, local polynomial quantile regression (LLQ) is applied to provide an efficient description of the corrupted and noisy data. The remaining series is assumed to be hidden in the residuals. Hence, EMD is applied to the residuals at the second stage. The final estimate is the summation of the fitting estimates from LLQ and EMD. Simulation was conducted to assess the practical performance of the proposed method. Results show that the proposed method is superior to classical EMD.