Why do EMD‐based methods improve prediction? A multiscale complexity perspective

• Published date: 01 November 2019
• Author: Jichang Dong,Lean Yu,Ling Tang,Wei Dai
• Date: 01 November 2019
• DOI: http://doi.org/10.1002/for.2593

RESEARCH ARTICLE

Why do EMD‐based methods improve prediction? A

multiscale complexity perspective

Jichang Dong

1

| Wei Dai

1,2

| Ling Tang

3

| Lean Yu

4

1

School of Economics and Management,

University of Chinese Academy of

Sciences, Beijing, China

2

JD Digital, Beijing, China

3

School of Economics and Management,

Beihang University, Beijing, China

4

School of Economics and Management,

Beijing University of Chemical

Technology, Beijing, China

Correspondence

Ling Tang, School of Economics and

Management, Beihang University, 37

Xueyuan Road, HaiDian District, Beijing

100191, China.

Email: lingtang@buaa.edu.cn

Funding information

National Natural Science Foundation of

China, Grant/Award Numbers: 71301006,

71433001, 71532013, 71573244 and

71622011; National Program for Support

of Top Notch Young Professionals;

National Science Fund for Outstanding

Young Scholars, Grant/Award Number:

71622011

Abstract

Empirical mode decomposition (EMD)‐based ensemble methods have become

increasingly popular in the research field of forecasting, substantially enhanc-

ing prediction accuracy. The key factor in this type of method is the multiscale

decomposition that immensely mitigates modeling complexity. Accordingly,

this study probes this factor and makes further innovations from a new per-

spective of multiscale complexity. In particular, this study quantitatively inves-

tigates the relationship between the decomposition performance and

prediction accuracy, thereby developing (1) a novel multiscale complexity mea-

surement (for evaluating multiscale decomposition), (2) a novel optimized

EMD (OEMD) (considering multiscale complexity), and (3) a novel OEMD‐

based forecasting methodology (using the proposed OEMD in multiscale

analysis). With crude oil and natural gas prices as samples, the empirical study

statistically indicates that the forecasting capability of EMD‐based methods is

highly reliant on the decomposition performance; accordingly, the proposed

OEMD‐based methods considering multiscale complexity significantly outper-

form the benchmarks based on typical EMDs in prediction accuracy.

KEYWORDS

empirical mode decomposition, energy forecasting, entropy, multiscale complexity, time series

forecasting

1|INTRODUCTION

Empirical mode decomposition (EMD)‐based ensemble

methods with powerful prediction capabilities have

become increasingly popular in the research field of fore-

casting. Three steps are involved in a typical EMD‐based

ensemble method: (1) multiscale decomposition, dividing

complicated original time series data into relatively sim-

ple components based on EMD or an EMD variant (par-

ticularly ensemble EMD (EEMD)), (2) individual

prediction, forecasting each extracted component, and

(3) ensemble prediction, aggregating the individual

results into the final prediction (Tang, Yu, Wang, Li, &

Wang, 2012; Yu, Wang, & Lai, 2008). The superiority of

EMD‐based ensemble methods in analysis and prediction

has been fully confirmed in existing studies. For example,

Tang, Wu, and Yu (2018a) employed EEMD as the

decomposition tool to formulate an EEMD‐based random

vector functional link network for crude oil price fore-

casting, and observed that all the EMD‐based learning

paradigms considered were better than their respective

single counterparts without multiscale decomposition, in

terms of prediction accuracy. Similarly, Sun, Wang,

Zhang, and Zheng (2018) formulated an EEMD‐based

decomposition–clustering–ensemble learning approach

for solar radiation forecasting. Yu, Dai, and Tang (2015)

developed an EEMD‐based extended extreme learning

machine (ELM) to predict crude oil price. Geng, Ji, and

Received: 31 May 2018 Revised: 25 December 2018 Accepted: 8 March 2019

DOI: 10.1002/for.2593

© 2019 John Wiley & Sons, Ltd. Journal of Forecasting. 2019;38:714–731.wileyonlinelibrary.com/journal/for

714

Fan (2016, 2017) employed a series of EEMD‐based corre-

lation analyses to investigate the behavior mechanisms of

natural gas prices from a multiscale perspective. Tang,

Wu, and Yu (2018b) proposed an EEMD‐based ELM for

forecasting various energy prices.

Therefore, why EMD‐based ensemble methods can sig-

nificantly improve prediction is an interesting question.

The reason lies in the EMD‐based multiscale decomposi-

tion involved according to the existing literature. On one

hand, EMD‐based ensemble methods are typical

decomposition–ensemble models, incorporating the

decomposition strategy with the main aims of mitigating

modeling difficulty by decomposing the complicated orig-

inal data into relatively simple modes (Yu et al., 2008). On

the other hand, EMD‐based methods adopt emerging

multiscale analysis techniques: the EMD family,

conducting empirical, adaptive decomposition without

fixed bases to capture the instinctive driving factors (in

terms of intrinsic mode functions (IMFs)) in nonlinear

complex systems (Z. Wu & Huang, 2009). For example,

Tang, Lv, Yang, and Yu (2015) demonstrated that the

EEMD‐extracted modes were simple and meaningful in

terms of low‐level complexity and distinctive periodicity,

respectively. With such helpful multiscale decomposition

and corresponding competitive techniques, EMD‐based

methods can alleviate the modeling complexity of original

data, thereby immensely enhancing prediction accuracy.

Thus the secret of the powerful prediction capability of

EMD‐based methods is the multiscale decomposition

involved that significantly reduces the modeling complex-

ity. The term “complexity”describes an intermediate con-

dition between a completely regular system and a

completely random system (Tang, Lv, et al., 2015). A lower

level of complexity indicates that the observed system is

more likely to follow a deterministic process, which can

be more easily captured and predicted; in comparison, a

higher level of complexity reflects that the data dynamics

might otherwise be more difficult to understand. Through

multiscale decomposition, EMD‐based ensemble methods

transform a tough prediction task for original data with a

high‐level complexity into several easy subtasks with a

low‐level multiscale complexity. Here, “multiscale com-

plexity”refers to the integrated complexity across different

decomposed modes at different timescales (or frequency

bands) (Tang, Lv, & Yu, 2017). A lower level of multiscale

complexity relates to a more satisfactory decomposition

performance—that is, a lower modeling complexity.

Therefore, multiscale complexity could be an effective

standard to quantitatively evaluate the decomposition per-

formance of an EMD‐based model.

However, the existing ensemble methods (involving

EMD‐based models) have ignored this promising mea-

surement—that is, multiscale complexity—in model

formulation. Although it is well known that EMD‐based

ensemble methods mainly improve prediction by mitigat-

ing the modeling complexity (as discussed above), quanti-

tative investigation into the relationship between

decomposition and forecasting performances is, to the

best of our knowledge, still lacking. Moreover, consider-

ing the high significance, multiscale decomposition

should be carefully designed in an EMD‐based model

(particularly for decomposition parameters). However,

the related studies are insufficient. For example, the two

key parameters in EEMD—that is, the level of the added

white noise and the number of ensemble members, were

set to fixed values regardless of data samples, such as 0.1

(or 0.2) and 100 (or 200), respectively (Amirat,

Choqueuse, & Benbouzid, 2013; Bao, Xiong, & Hu,

2012; He, Lech, Maddage, & Allen, 2011; Z. Wu & Huang,

2009; Zheng, Cheng, & Yang, 2014). Thus this study

attempts to improve EMD‐based methods, by optimizing

multiscale decomposition with multiscale complexity as

a standard.

Amongst complexity measurements, entropy—a ther-

modynamic quantity that vividly describes the disorder

state of data dynamics—has been extensively applied to

EMD‐based multiscale analysis (Potty & Miller, 2016; Y.

Wang & Wu, 2016). For example, Liu, Wang, Sun, and

Zhen (2015) employed entropy to analyze the EMD‐

derived IMFs for diagnosing circuit breaker faults. Tang

et al. (2017) proposed an EEMD‐based fuzzy entropy to

investigate the multiscale complexity of clean energy

markets. Similarly, J. Wang, Shang, Xia, and Shi (2015)

applied an EMD‐based multiscale entropy to the com-

plexity estimation of traffic signals. Thus this study intro-

duces entropy to formulate a multiscale complexity

measurement for evaluating the decomposition perfor-

mance of an EMD‐based model.

This study aims to probe the powerful prediction capa-

bility of EMD‐based ensemble models, from a new analy-

sis perspective of multiscale complexity. In particular,

given that EMD‐based models mainly improve prediction

through the multiscale analysis involved, this study

attempts to quantitatively investigate the relationship

between decomposition and prediction performances,

and provides the following three innovations:

1. a novel multiscale complexity measurement, to eval-

uate the effectiveness of multiscale decomposition in

terms of alleviating modeling complexity;

2. a novel optimized EMD (OEMD) that optimizes the

multiscale effectiveness with multiscale complexity

as the fitness function; and

3. a novel OEMD‐based forecasting methodology that

uses the proposed OEMD as the multiscale analysis

technique.

DONG ET AL.

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