On Automatic Boundary Corrections Using Empirical Mode Decomposition
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Date
2016-03
Authors
Mohamed Jaber, Abobaker
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Empirical mode decomposition (EMD) is particularly useful in analyzing nonstation-
ary and nonlinear time series. Yet EMD struggle from boundary problems caused by
the application of the EMD to a finite signal. Consequently, large bias at the edges and
artificial wiggles happen when the classical boundary assumptions are not met. This
study introduces two new two-stage methods to automatically decrease the boundary
effects present in EMD namely Empirical Mode Decomposition combined with local
linear quantile regression, EMD-LLQ and Empirical Mode Decomposition combined
with local linear regression, EMD-LL. The accuracy of the method is shown by simu-
lation studies and real example with comparison to other existing imputation methods.
For simulation part: at the first stage, local linear quantile regression (LLQ) and local
linear regression are 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 summa-
tion of the fitting estimates from LLQ and EMD and LL and EMD. Many interesting
features have been noted from the study. One of the most striking points is that the
pro-posed methods EMD-LLQ and EMD-LL are more efficient than traditional
boundary extensions (wave, periodic, symmetric, and even odd) of EMD and its
extension sta-tistical empirical mode decomposition (SEMD) when the boundaries are
present. For the real data application we apply the proposed techniques, EMD-LLQ, and EMD-LL to forecast two closed stock market index. Detailed experiments are carried out for the proposed method, in which EMD-LLQ, EMD, and Holt-Winter methods are com-pared. The proposed EMD-LLQ and EMD-LL methods are determined to be superior to the EMD and Holt-Winter methods in predicting the stock
closing prices.
Description
Keywords
Empirical mode decomposition