A Novel Multivariate Denoising Method for Improved Index Tracking Based on Empirical Mode Decomposition and Principle Components Analysis

Abstract

Index tracking is a valuable low-cost alternative to active portfolio management which aims at replicating the performance of an index or benchmark by investing in a smaller number of constituent stocks or assets. In real financial market, the fluctuation of stock prices is inevitably contaminated with various noises [3]. However, most of the current arithmetic for index tracking, such as the clustering-selection strategy [6, 8], require very clean data and are extremely sensitive to noise. Therefore, in this paper, we propose a novel multivariate noise removal method called PCA-EMD, which integrates Principle Components Analysis (PCA) and Empirical Mode Decomposition (EMD), to filter the original data and recover hidden useful information from the multichannel noisy stock prices, on a scale-by-scale basis. We further investigate whether the noise eliminated data obtained through PCA-EMD can help to improve the tracking performance of the conventional clustering-selection strategy. The computational results on 5 benchmark instances from OR-library demonstrate the feasibility and effectiveness of the proposed method.