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

Table 2

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 1
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)	0.269175	0.310785	0.32917	0.261690	0.3027736	0.3190445	0.2552796	0.306369	0.3223
EMD-LLQ	0.11712	0.122119	0.145831	0.06343	0.058571	0.010130	0.070048	0.067575	0.10510
Wilcoxon test; 𝑉=	451927	459306	449112	49589	497928	480711	493926	494605	479475
Test function 1
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)	1.38123	1.40508	1.45777	1.42545	1.43629	1.47529	1.40223	1.41718	1.44426
EMD-LLQ	0.11287	0.12451	0.14150	0.06375	0.05967	0.09826	0.06509	0.06284	0.10475
Wilcoxon test; 𝑉=	500496	50076	500427	500500	500076	500477	500493	500490	500476
𝑃-value<2.2𝑒^−16
Test function 1
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)	0.86598	0.91897	1.005607	0.87603	0.916301	1.005788	0.8820793	0.92558	0.96602
EMD-LLQ	0.11656	0.12304	0.14698	0.8760	0.05816	0.09760	0.070185	0.06459	0.10498
Wilcoxon test; 𝑉=	500500	499701	500456	500498	499540	500497	500500	500497	500492
𝑃-value<2.2𝑒^−16
Test function 1
Quantiles	𝜏=0.25			𝜏=0.50			𝜏=0.75
Errors	N~(0,1)	𝑇(100,3)	AR(0.5)	errors	N~(0,1)	𝑇(100,3)	AR(0.5)	Errors	N~(0,1)
EMD (wave)	1.20811	1.18084	1.250195	1.19274	1.20855	1.226365	1.199136	1.20274	1.22829
EMD-LLQ	0.11318	0.11967	0.14845	0.06456	0.06173	0.098486	0.066864	0.06339	0.10583
Wilcoxon test; 𝑉=	500500	500500	500500	500500	500500	500500	500500	500500	500500