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

Table 4

The MSE of the classical EMD and proposed method under variety of boundary solution noise structure, different values of quantile 𝜏 (0.25, 0.50, and 0.75), and sample size = 100.

Test function 3
Quantiles	𝜏=0.25			𝜏=0.50			𝜏=0.75
Errors	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)
EMD (none)	0.034744	0.037490	0.06867	0.035888	0.035473	0.0708678	0.03540	0.0375	0.07260
EMD-LLQ	0.01494	0.01827	0.04637	0.0142052	0.0168427	0.04288602	0.014913	0.0197	0.048020
Wilcoxon test; 𝑉=	453610	426890	371062	740664	435835	415746	455217	420619	393951
𝑃-value<2.2𝑒^−16
Test function 3
Quantiles	𝜏=0.25			𝜏=0.50			𝜏=0.75
Errors	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)
EMD (periodic)	0.01495	0.01601	1.46184	0.014931	0.017672	1.475389	0.01513	0.0173	1.44361
EMD-LLQ	0.01201	0.01425	0.14555	0.010031	0.016859	0.0967748	0.01176	0.0157	0.10338
Wilcoxon test; 𝑉=	142798	167295	500426	159630	193475	500491	133946	170435	500474
𝑃-value<2.2𝑒^−16
Test function 3
Quantiles	𝜏=0.25			𝜏=0.50			τ=0.75
Errors	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)
EMD (symmetric)	0.856264	0.938382	1.01019	0.853808	0.928291	0.9873542	0.86854	0.9322	0.96783
EMD-LLQ	0.11334	0.12452	0.14649	0.065446	0.056100	0.09569597	0.06553	0.06180	0.104910
Wilcoxon-test; 𝑉=	500489	499304	500420	500500	500498	500474	500500	500485	500463
𝑃-value<2.2𝑒^−16
Test function 3
Quantiles	𝜏=0.25			𝜏=0.50			𝜏=0.75
Errors	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)	N~(0,1)	𝑇(100,3)	AR(0.5)
EMD (wave)	1.19549	1.19853	1.22884	1.180275	1.200136	1.217799	1.193706	1.20841	1.236941
EMD-LLQ	0.11508	0.12732	0.14624	0.063552	0.055484	0.094623	0.06860	0.20362	0.110907
Wilcoxon test; 𝑉=	500500	500500	500500	500500	500500	500500	500500	499500	500500
𝑃-value<2.2𝑒^−16