📄 bdssig.m
字号:
2.30 2.29 2.29 2.28 2.27 2.29 2.28 2.28 2.29 2.29 2.31 2.33 2.35 2.36
2.79 2.78 2.75 2.78 2.80 2.79 2.81 2.83 2.83 2.81 2.84 2.88 2.92 2.93
3.16 3.15 3.09 3.07 3.13 3.17 3.14 3.18 3.20 3.24 3.22 3.24 3.32 3.36];
% n = 500, eps = 0.5 (c1 ~ 0.28)
quants(1:8, 1:14, 4, 1) = [...
-2.88 -3.01 -3.35 -4.01 -5.05 -6.40 -7.60 -6.95 -5.99 -5.12 -4.43 -3.88 -3.43 -3.07
-2.63 -2.78 -3.04 -3.67 -4.52 -5.92 -7.22 -6.69 -5.74 -4.93 -4.28 -3.74 -3.31 -2.95
-2.22 -2.38 -2.62 -3.09 -3.87 -5.15 -6.55 -6.33 -5.44 -4.66 -4.03 -3.54 -3.11 -2.77
-1.89 -2.01 -2.24 -2.64 -3.32 -4.38 -5.78 -6.00 -5.20 -4.46 -3.85 -3.35 -2.95 -2.63
2.01 2.13 2.37 2.87 3.68 5.25 8.05 13.57 22.54 31.55 -2.28 -2.00 -1.73 -1.51
2.46 2.64 2.92 3.55 4.55 6.61 10.41 17.88 31.94 49.71 -2.08 -1.89 -1.64 -1.43
2.95 3.27 3.72 4.41 5.74 8.50 13.55 23.17 44.46 84.82 133.43 -1.73 -1.53 -1.33
3.32 3.61 4.14 5.03 6.58 9.75 15.80 27.76 55.17 109.55 198.94 264.86 -1.45 -1.27];
% n = 500, eps = 1.0 (c1 ~ 0.52)
quants(1:8, 1:14, 4, 2) = [...
-2.55 -2.52 -2.53 -2.51 -2.46 -2.46 -2.48 -2.54 -2.65 -2.80 -3.01 -3.24 -3.43 -3.47
-2.34 -2.33 -2.30 -2.30 -2.27 -2.27 -2.30 -2.36 -2.47 -2.61 -2.78 -3.01 -3.22 -3.31
-2.01 -2.00 -1.99 -1.96 -1.99 -2.00 -2.03 -2.07 -2.16 -2.28 -2.46 -2.66 -2.91 -3.04
-1.72 -1.72 -1.71 -1.70 -1.73 -1.75 -1.76 -1.81 -1.88 -1.98 -2.14 -2.35 -2.59 -2.80
1.77 1.77 1.77 1.81 1.87 1.93 2.01 2.12 2.25 2.47 2.76 3.16 3.64 4.34
2.14 2.15 2.20 2.26 2.34 2.43 2.55 2.71 2.95 3.21 3.57 4.06 4.74 5.71
2.58 2.62 2.64 2.76 2.89 3.04 3.23 3.47 3.79 4.15 4.58 5.23 6.31 7.75
2.89 2.95 3.00 3.10 3.28 3.50 3.68 4.02 4.41 4.84 5.51 6.24 7.34 9.28];
% n = 500, eps = 1.5 (c1 ~ 0.71)
quants(1:8, 1:14, 4, 3) = [...
-2.61 -2.54 -2.54 -2.54 -2.48 -2.45 -2.44 -2.41 -2.37 -2.33 -2.29 -2.29 -2.28 -2.25
-2.37 -2.35 -2.31 -2.30 -2.26 -2.25 -2.23 -2.22 -2.19 -2.17 -2.14 -2.12 -2.10 -2.09
-2.01 -2.02 -2.00 -1.98 -1.98 -1.96 -1.94 -1.93 -1.91 -1.89 -1.89 -1.88 -1.87 -1.85
-1.71 -1.71 -1.71 -1.71 -1.69 -1.69 -1.69 -1.67 -1.67 -1.66 -1.65 -1.65 -1.64 -1.63
1.74 1.72 1.73 1.74 1.74 1.74 1.76 1.76 1.79 1.82 1.85 1.89 1.94 1.98
2.10 2.09 2.12 2.11 2.13 2.15 2.17 2.20 2.23 2.28 2.33 2.40 2.45 2.51
2.50 2.54 2.52 2.57 2.60 2.63 2.65 2.71 2.75 2.85 2.88 2.98 3.09 3.21
2.80 2.86 2.86 2.94 2.93 2.99 3.04 3.05 3.14 3.25 3.33 3.46 3.53 3.68];
% n = 500, eps = 2.0 (c1 ~ 0.84)
quants(1:8, 1:14, 4, 4) = [...
-2.65 -2.65 -2.70 -2.63 -2.62 -2.63 -2.63 -2.64 -2.60 -2.55 -2.52 -2.49 -2.46 -2.46
-2.43 -2.43 -2.45 -2.43 -2.39 -2.40 -2.40 -2.39 -2.40 -2.37 -2.34 -2.31 -2.30 -2.28
-2.09 -2.08 -2.08 -2.09 -2.08 -2.07 -2.07 -2.06 -2.07 -2.05 -2.04 -2.02 -2.01 -1.98
-1.76 -1.78 -1.79 -1.79 -1.79 -1.78 -1.78 -1.78 -1.78 -1.78 -1.78 -1.76 -1.74 -1.73
1.78 1.76 1.74 1.73 1.74 1.75 1.75 1.74 1.74 1.74 1.75 1.77 1.77 1.78
2.13 2.14 2.14 2.13 2.12 2.11 2.10 2.10 2.12 2.15 2.16 2.18 2.19 2.20
2.58 2.57 2.58 2.58 2.55 2.57 2.57 2.56 2.60 2.63 2.66 2.69 2.71 2.75
2.91 2.87 2.88 2.87 2.88 2.87 2.88 2.92 2.92 2.95 2.99 2.99 3.06 3.10];
% n = 750, eps = 1.0 (c1 ~ 0.52)
quants(1:8, 1:14, 5, 2) = [...
-2.52 -2.53 -2.49 -2.48 -2.49 -2.45 -2.44 -2.47 -2.51 -2.61 -2.78 -2.96 -3.24 -3.46
-2.32 -2.31 -2.30 -2.28 -2.29 -2.25 -2.23 -2.28 -2.32 -2.40 -2.55 -2.76 -3.03 -3.24
-1.98 -1.97 -1.98 -1.97 -1.96 -1.94 -1.95 -1.97 -2.04 -2.11 -2.23 -2.42 -2.66 -2.91
-1.68 -1.69 -1.69 -1.69 -1.69 -1.69 -1.70 -1.73 -1.77 -1.83 -1.96 -2.13 -2.34 -2.59
1.72 1.74 1.76 1.79 1.80 1.87 1.91 2.01 2.13 2.29 2.49 2.74 3.13 3.70
2.08 2.13 2.15 2.21 2.27 2.35 2.43 2.52 2.68 2.90 3.17 3.55 4.03 4.71
2.48 2.59 2.65 2.69 2.78 2.88 3.00 3.21 3.46 3.64 4.02 4.53 5.16 6.21
2.78 2.91 2.99 3.09 3.16 3.27 3.50 3.73 3.94 4.22 4.70 5.22 6.06 7.30];
% n = 750, eps = 1.5 (c1 ~ 0.71)
quants(1:8, 1:14, 5, 3) = [...
-2.57 -2.56 -2.54 -2.53 -2.50 -2.45 -2.40 -2.39 -2.36 -2.34 -2.31 -2.28 -2.26 -2.23
-2.34 -2.32 -2.33 -2.30 -2.29 -2.27 -2.24 -2.21 -2.17 -2.16 -2.14 -2.10 -2.09 -2.07
-2.01 -1.99 -1.98 -1.98 -1.97 -1.96 -1.95 -1.93 -1.91 -1.90 -1.87 -1.85 -1.84 -1.82
-1.68 -1.69 -1.69 -1.69 -1.71 -1.69 -1.68 -1.67 -1.65 -1.65 -1.63 -1.61 -1.60 -1.60
1.69 1.68 1.68 1.69 1.71 1.72 1.73 1.74 1.75 1.78 1.79 1.80 1.84 1.87
2.02 2.03 2.03 2.06 2.07 2.11 2.12 2.17 2.19 2.23 2.25 2.28 2.32 2.39
2.48 2.50 2.48 2.50 2.54 2.58 2.61 2.63 2.69 2.75 2.84 2.93 2.95 3.04
2.79 2.78 2.77 2.80 2.88 2.91 2.97 3.02 3.08 3.16 3.29 3.33 3.43 3.56];
% n = 750, eps = 2.0 (c1 ~ 0.84)
quants(1:8, 1:14, 5, 4) = [...
-2.66 -2.64 -2.61 -2.65 -2.58 -2.57 -2.55 -2.55 -2.53 -2.51 -2.51 -2.50 -2.49 -2.46
-2.40 -2.40 -2.40 -2.40 -2.37 -2.36 -2.36 -2.36 -2.35 -2.34 -2.31 -2.30 -2.29 -2.25
-2.03 -2.03 -2.05 -2.04 -2.03 -2.03 -2.03 -2.04 -2.04 -2.02 -2.00 -1.99 -1.97 -1.97
-1.72 -1.72 -1.74 -1.74 -1.73 -1.73 -1.73 -1.73 -1.74 -1.72 -1.72 -1.72 -1.71 -1.70
1.75 1.71 1.71 1.69 1.70 1.69 1.69 1.69 1.70 1.71 1.71 1.72 1.73 1.75
2.09 2.09 2.09 2.05 2.05 2.04 2.04 2.06 2.08 2.08 2.09 2.12 2.13 2.14
2.53 2.54 2.49 2.47 2.47 2.48 2.48 2.52 2.55 2.57 2.59 2.60 2.62 2.64
2.86 2.81 2.77 2.78 2.75 2.73 2.77 2.80 2.88 2.88 2.91 2.95 2.97 2.99];
% n = 1000, eps = 0.5 (c1 ~ 0.28)
quants(1:8, 1:14, 6, 1) = [...
-2.66 -2.72 -2.83 -3.17 -3.82 -4.92 -6.63 -8.03 -7.33 -6.36 -5.50 -4.79 -4.21 -3.73
-2.44 -2.48 -2.59 -2.91 -3.51 -4.49 -6.10 -7.69 -7.15 -6.19 -5.35 -4.66 -4.10 -3.62
-2.08 -2.11 -2.24 -2.50 -3.01 -3.90 -5.30 -7.04 -6.85 -5.97 -5.16 -4.49 -3.94 -3.49
-1.77 -1.79 -1.92 -2.16 -2.58 -3.31 -4.59 -6.15 -6.60 -5.76 -4.99 -4.34 -3.81 -3.37
1.87 1.95 2.10 2.36 2.83 3.81 5.53 8.69 14.19 24.40 36.34 -3.02 -2.66 -2.33
2.26 2.37 2.54 2.88 3.46 4.69 6.81 10.86 18.53 32.76 49.56 -2.85 -2.56 -2.25
2.72 2.86 3.12 3.54 4.31 5.75 8.59 13.50 24.27 46.74 89.25 137.59 -2.44 -2.16
3.04 3.25 3.52 4.03 4.82 6.53 9.84 16.19 28.67 56.34 115.13 190.18 -2.25 -2.10];
% n = 1000, eps = 1.0 (c1 ~ 0.52)
quants(1:8, 1:14, 6, 2) = [...
-2.52 -2.53 -2.47 -2.45 -2.43 -2.42 -2.40 -2.40 -2.44 -2.52 -2.65 -2.87 -3.07 -3.33
-2.28 -2.29 -2.26 -2.22 -2.20 -2.22 -2.21 -2.21 -2.25 -2.34 -2.48 -2.63 -2.86 -3.11
-1.96 -1.96 -1.93 -1.94 -1.92 -1.90 -1.92 -1.93 -1.97 -2.06 -2.15 -2.31 -2.51 -2.77
-1.68 -1.67 -1.66 -1.65 -1.65 -1.65 -1.65 -1.68 -1.71 -1.80 -1.88 -2.00 -2.20 -2.44
1.68 1.70 1.72 1.75 1.78 1.82 1.88 1.95 2.04 2.12 2.28 2.50 2.79 3.19
2.03 2.07 2.11 2.15 2.19 2.25 2.31 2.40 2.54 2.66 2.87 3.13 3.52 4.07
2.43 2.50 2.56 2.57 2.66 2.73 2.82 3.00 3.15 3.35 3.62 3.94 4.44 5.20
2.74 2.78 2.86 2.89 2.99 3.13 3.25 3.39 3.64 3.84 4.25 4.63 5.21 5.94];
% n = 1000, eps = 1.5 (c1 ~ 0.71)
quants(1:8, 1:14, 6, 3) = [...
-2.53 -2.54 -2.50 -2.50 -2.47 -2.46 -2.44 -2.41 -2.38 -2.34 -2.31 -2.27 -2.26 -2.23
-2.33 -2.34 -2.30 -2.28 -2.27 -2.24 -2.22 -2.21 -2.19 -2.17 -2.15 -2.12 -2.09 -2.07
-2.00 -1.99 -2.01 -1.99 -1.97 -1.95 -1.94 -1.92 -1.92 -1.91 -1.89 -1.87 -1.86 -1.83
-1.69 -1.71 -1.71 -1.71 -1.71 -1.67 -1.67 -1.66 -1.66 -1.65 -1.63 -1.63 -1.62 -1.61
1.68 1.69 1.68 1.68 1.70 1.71 1.73 1.73 1.74 1.75 1.77 1.79 1.81 1.83
2.01 2.02 2.03 2.04 2.06 2.08 2.12 2.16 2.16 2.19 2.22 2.25 2.27 2.31
2.43 2.46 2.45 2.48 2.49 2.53 2.55 2.58 2.65 2.69 2.73 2.78 2.84 2.90
2.70 2.74 2.78 2.81 2.82 2.87 2.89 2.89 2.93 3.01 3.07 3.16 3.23 3.30];
% n = 1000, eps = 2.0 (c1 ~ 0.84)
quants(1:8, 1:14, 6, 4) = [...
-2.70 -2.65 -2.62 -2.59 -2.58 -2.57 -2.58 -2.60 -2.56 -2.53 -2.51 -2.49 -2.47 -2.46
-2.40 -2.41 -2.39 -2.37 -2.37 -2.37 -2.35 -2.36 -2.35 -2.33 -2.30 -2.28 -2.26 -2.25
-2.05 -2.04 -2.04 -2.05 -2.04 -2.04 -2.05 -2.04 -2.03 -2.02 -2.00 -2.00 -1.98 -1.96
-1.73 -1.72 -1.74 -1.74 -1.73 -1.74 -1.74 -1.74 -1.73 -1.72 -1.73 -1.73 -1.71 -1.71
1.70 1.68 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.70 1.71 1.72 1.73 1.73
2.04 2.04 2.04 2.05 2.04 2.04 2.06 2.07 2.07 2.07 2.08 2.08 2.09 2.11
2.45 2.47 2.45 2.47 2.46 2.47 2.51 2.51 2.50 2.52 2.52 2.55 2.57 2.58
2.77 2.76 2.80 2.79 2.77 2.76 2.80 2.82 2.83 2.85 2.88 2.87 2.90 2.93];
% n = 2500, eps = 0.5 (c1 ~ 0.28)
quants(1:8, 1:14, 7, 1) = [...
-2.51 -2.53 -2.59 -2.74 -3.00 -3.67 -4.78 -6.51 -8.74 -8.85 -7.73 -6.77 -5.93 -5.24
-2.31 -2.33 -2.37 -2.55 -2.77 -3.35 -4.41 -6.00 -8.28 -8.68 -7.63 -6.66 -5.84 -5.16
-1.97 -1.99 -2.06 -2.16 -2.39 -2.89 -3.82 -5.23 -7.22 -8.41 -7.45 -6.51 -5.71 -5.05
-1.69 -1.70 -1.74 -1.85 -2.04 -2.46 -3.21 -4.52 -6.35 -8.19 -7.29 -6.38 -5.60 -4.93
1.73 1.75 1.79 1.94 2.18 2.66 3.53 5.18 8.20 13.75 24.50 32.59 -4.41 -3.95
2.07 2.11 2.21 2.36 2.68 3.19 4.27 6.32 10.24 17.79 31.87 60.12 95.19 -3.85
2.45 2.54 2.69 2.93 3.22 3.93 5.28 7.70 12.65 22.49 43.30 83.54 131.83 -3.66
2.78 2.85 3.02 3.26 3.60 4.36 5.93 8.69 14.35 26.23 52.23 105.70 216.13 339.65];
% n = 2500, eps = 1.0 (c1 ~ 0.52)
quants(1:8, 1:14, 7, 2) = [...
-2.58 -2.52 -2.47 -2.46 -2.42 -2.40 -2.40 -2.38 -2.42 -2.44 -2.47 -2.50 -2.61 -2.81
-2.35 -2.27 -2.26 -2.24 -2.22 -2.20 -2.20 -2.22 -2.22 -2.22 -2.25 -2.31 -2.41 -2.63
-1.97 -1.94 -1.91 -1.91 -1.90 -1.91 -1.90 -1.89 -1.90 -1.92 -1.97 -2.02 -2.11 -2.29
-1.66 -1.66 -1.64 -1.63 -1.63 -1.64 -1.64 -1.63 -1.62 -1.65 -1.68 -1.74 -1.83 -1.99
1.67 1.70 1.69 1.71 1.75 1.76 1.78 1.79 1.83 1.88 1.95 2.07 2.21 2.39
2.02 2.06 2.08 2.10 2.12 2.16 2.18 2.20 2.24 2.31 2.39 2.53 2.72 2.97
2.47 2.50 2.53 2.55 2.54 2.57 2.66 2.74 2.83 2.88 3.02 3.17 3.35 3.77
2.78 2.77 2.81 2.88 2.89 2.91 3.04 3.13 3.23 3.25 3.43 3.68 3.99 4.31];
% n = 2500, eps = 1.5 (c1 ~ 0.71)
quants(1:8, 1:14, 7, 3) = [...
-2.55 -2.54 -2.53 -2.49 -2.50 -2.45 -2.43 -2.42 -2.40 -2.40 -2.39 -2.36 -2.36 -2.32
-2.34 -2.32 -2.31 -2.29 -2.27 -2.23 -2.21 -2.22 -2.20 -2.18 -2.16 -2.16 -2.15 -2.13
-1.98 -1.96 -1.95 -1.94 -1.94 -1.92 -1.92 -1.92 -1.90 -1.89 -1.88 -1.88 -1.86 -1.84
-1.65 -1.66 -1.66 -1.64 -1.64 -1.63 -1.64 -1.64 -1.63 -1.63 -1.63 -1.62 -1.61 -1.59
1.60 1.60 1.61 1.63 1.64 1.64 1.65 1.67 1.67 1.68 1.69 1.71 1.72 1.75
1.95 1.91 1.92 1.93 1.95 1.98 2.00 2.01 2.02 2.04 2.07 2.11 2.14 2.17
2.36 2.34 2.34 2.34 2.32 2.35 2.36 2.38 2.38 2.42 2.47 2.54 2.58 2.63
2.59 2.60 2.56 2.61 2.58 2.59 2.62 2.67 2.73 2.74 2.77 2.80 2.84 2.89];
% n = 2500, eps = 2.0 (c1 ~ 0.84)
quants(1:8, 1:14, 7, 4) = [...
-2.56 -2.57 -2.55 -2.54 -2.56 -2.56 -2.54 -2.53 -2.51 -2.51 -2.50 -2.47 -2.46 -2.44
-2.33 -2.33 -2.32 -2.30 -2.32 -2.33 -2.31 -2.29 -2.28 -2.25 -2.26 -2.26 -2.24 -2.24
-1.96 -2.00 -2.00 -1.99 -1.98 -1.98 -1.98 -1.98 -1.96 -1.96 -1.95 -1.94 -1.92 -1.91
-1.67 -1.70 -1.70 -1.70 -1.70 -1.70 -1.71 -1.71 -1.71 -1.69 -1.68 -1.67 -1.66 -1.65
1.69 1.70 1.69 1.68 1.68 1.69 1.69 1.70 1.71 1.71 1.71 1.70 1.71 1.72
2.06 2.08 2.03 2.01 2.03 2.03 2.04 2.07 2.07 2.07 2.06 2.07 2.07 2.07
2.47 2.44 2.45 2.45 2.44 2.42 2.45 2.42 2.44 2.45 2.45 2.47 2.51 2.49
2.72 2.71 2.76 2.74 2.74 2.69 2.70 2.71 2.70 2.72 2.76 2.81 2.78 2.79];
%%%%%%%%%%%%%%%%%%%%%%%%%% Look-up of the appropriate quantiles %%%%%%%%%%%%%%%%%%%%%%%%%%
% Determine in between which two sample sizes tabulated the current n lies:
lower = sum(n >= ncases);
upper = 8 - sum(n <= ncases);
% Fix some special cases; for samples of less than 50, use the values for 50:
if lower == 0
lower = 1;
% and since there are no tabulated values for n = 750, eps = 0.5, reference to the
% corresponding part of the quantile table must be avoided:
elseif eps == 0.5
if lower == 5
lower = 4;
end
if upper == 5
upper = 6;
end
end
% Determine the significance level in turn for each BDS statistic contained in W:
for i = 1 : length(w)
% Find the eight quantile values each for the lower and upper sample sizes:
lowerqus = reshape(quants(1:8, m(i)-1, lower, eps*2), 8, 1);
if n <= 2500
upperqus = reshape(quants(1:8, m(i)-1, upper, eps*2), 8, 1);
else % i.e. approaching standard normality:
upperqus = norminv(siglevels([1:4 6:9]))';
ncases = [ncases 5000];
end
% Interpolate the quantile values for the actual sample size from the quantile
% values of the surrounding sample sizes; note that this method may slightly
% increase the size of a type I error for sample sizes which are not close to one
% of the tabulated cases; this problem could be mitigated by a response surface
% yet to be developed.
if lower ~= upper
qus = lowerqus + (upperqus - lowerqus) * (n - ncases(lower)) /...
(ncases(upper) - ncases(lower));
else
qus = lowerqus;
end
% Find the matching significance levels; at least one of the terms must be 1, or
% both, so their product yields the overall one-sided significance level:
sig(i) = siglevels(5 - sum(w(i)<=qus(1:4))) * siglevels(5 + sum(w(i)>=qus(5:8)));
end
%%%%%%%%%%%%%%%%%%%%%%%%% Otherwise use standard-normal look-up %%%%%%%%%%%%%%%%%%%%%%%%%
else
qus = [norminv(siglevels(1:4)) norminv(1 - siglevels(6:9))]';
for i = 1 : length(w)
sig(i) = siglevels(5 - sum(w(i)<=qus(1:4))) * siglevels(5 + sum(w(i)>=qus(5:8)));
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% REFERENCES:
%
% Kanzler, Ludwig (1998), "Very Fast and Correctly Sized Estimation of the BDS Statistic",
% Oxford University, Department of Economics, working paper, available on
% http://users.ox.ac.uk/~econlrk
% End of file.
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -