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

Table 3

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 2
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)	13.71622	8.517261	7.290762	7.818736	8.094024	6.974746	7.168348	8.445187	7.364002
EMD-LLQ	2.200657	2.148026	2.063819	2.147824	0.8982332	0.847309	1.68474	1.69877	1.57035
Wilcoxon test; 𝑉=	467459	463117	500260	499774	498875	489150	482567	483765	489150
𝑃-value<2.2𝑒^−16
Test function 2
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)	7.430924	6.976339	6.77826	7.135594	6.982454	6.827251	7.226472	6.865929	6.725184
EMD-LLQ	2.118629	2.145495	2.052055	0.904618	0.9031342	0.8702984	1.672161	1.691775	1.598264
Wilcoxon test; 𝑉=	498562	497328	495251	500441	500350	500203	498068	496900	496766
𝑃-value<2.2𝑒^−16
Test function 2
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)	8.693953	8.800117	8.678484	8.679718	8.902223	8.76185	8.623087	8.756977	8.718655
EMD-LLQ	2.121942	2.142339	2.059669	0.918506	0.8823274	0.8637991	1.655741	1.670038	1.571081
Wilcoxon test; 𝑉=	500500	500500	500500	500500	500500	500500	500500	500500	500500
𝑃-value<2.2𝑒^−16
Test function 2
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)	7.243865	7.493569	7.341059	7.138806	7.430882	7.449	7.124459	7.374468	7.302789
EMD-LLQ	2.12519	2.149727	2.053073	0.908747	0.9056965	0.8560205	1.653102	1.704716	1.552656
Wilcoxon test; 𝑉=	500500	500500	500500	500500	500500	500500	500500	500497	500500
𝑃-value<2.2𝑒^−16