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Table 7 97.5%-VaR backtesting analysis for total period

From: Testing expected shortfall: an application to emerging market stock indices

Distributions Normal Student’s t Skewed-t
Country index EV v VR Coverage test Indep test v VR Coverage test Indep test v VR Coverage test Indep test
Brazil 82 103 1.24 4.84 (0.02) 0.56 (0.45) 88 1.06 0.36 (0.54) 0.05 (0.81) 54 0.65 4.84 (0.03) 0.56 (0.45)
Chile 82 97 1.17 2.47 (0.11) 0.43 (0.50) 94 1.13 1.57 (0.21) 1.71 (0.19) 57 0.69 2.47 (0.11) 0.43 (0.51)
Colombia 65 102 1.56 18.46 (0.00) 7.08 (0.00) 95 1.46 12.45 (0.00) 6.78 (0.01) 70 1.07 18.46 (0.00) 7.08 (0.00)
Mexico 82 97 1.17 2.47 (0.11) 0.30 (0.58) 96 1.16 2.15 (0.14) 0.01 (0.90) 66 0.80 2.47 (0.11) 0.30 (0.58)
Peru 82 79 0.95 0.15 (0.69) 1.94 (0.16) 80 0.96 0.07 (0.78) 1.83 (0.17) 81 0.98 0.15 (0.69) 1.94 (0.16)
Czech 82 87 1.05 0.24 (0.62) 2.55 (0.11) 82 1.00 0.00 (0.95) 3.27 (0.07) 68 0.82 0.24 (0.62) 2.55 (0.11)
Egypt 77 103 1.32 7.81 (0.00) 17.47 (0.00) 91 1.17 2.28 (0.13) 10.14 (0.00) 75 0.96 7.81 (0.00) 17.47 (0.00)
Greece 82 72 0.87 1.43 (0.23) 1.08 (0.30) 78 0.94 0.25 (0.61) 2.00 (0.15) 64 0.77 1.43 (0.23) 1.08 (0.30)
Hungary 82 75 0.90 0.72 (0.39) 0.84 (0.35) 71 0.86 1.72 (0.19) 0.21 (0.64) 74 0.89 0.72 (0.39) 0.84 (0.36)
Poland 82 82 1.00 0.00 (0.95) 1.56 (0.21) 89 1.07 0.51 (0.47) 0.94 (0.33) 79 0.95 0.00 (0.95) 1.56 (0.21)
Qatar 82 99 1.20 3.18 (0.07) 4.28 (0.04) 106 1.28 6.30 (0.01) 1.74 (0.18) 108 1.32 3.18 (0.07) 4.28 (0.04)
Russia 82 91 1.10 0.86 (0.35) 0.11 (0.73) 85 1.03 0.07 (0.78) 0.84 (0.35) 66 0.80 0.86 (0.35) 0.11 (0.73)
South Africa 82 82 1.00 0.00 (0.95) 0.41 (0.51) 86 1.03 0.07 (0.78) 0.28 (0.59) 55 0.66 0.00 (0.95) 0.41 (0.51)
Turkey 82 78 0.94 0.25 (0.61) 6.31 (0.01) 72 0.87 1.43 (0.23) 7.79 (0.00) 72 0.87 0.25 (0.61) 6.31 (0.01)
China 67 86 1.27 4.79 (0.03) 0.23 (0.63) 77 1.14 1.31 (0.25) 0.01 (0.22) 79 1.17 4.79 (0.03) 0.23 (0.63)
India 82 87 1.05 0.24 (0.62) 0.20 (0.64) 83 1.00 0.00 (0.95) 1.46 (0.04) 69 0.83 0.24 (0.62) 0.20 (0.65)
Indonesia 82 99 1.20 3.18 (0.07) 1.23 (0.26) 100 1.21 3.56 (0.06) 4.11 (0.12) 74 0.89 3.18 (0.07) 1.23 (0.26)
Korea 75 107 1.42 12.39 (0.00) 2.32 (0.12) 94 1.25 0.31 (0.57) 2.38 (0.15) 52 0.69 12.3 (0.00) 2.32 (0.13)
Malaysia 81 92 1.14 1.56 (0.21) 3.43 (0.06) 90 1.11 1.06 (0.30) 2.05 (0.00) 87 1.07 1.56 (0.21) 3.43 (0.06)
Philippines 82 82 1.00 0.00 (0.95) 7.98 (0.00) 95 1.15 1.85 (0.17) 7.26 (0.00) 91 1.10 0.00 (0.95) 7.98 (0.00)
Taiwan 82 98 1.18 2.81 (0.09) 0.00 (0.96) 105 1.27 5.80 (0.01) 0.03 (0.84) 77 0.93 2.81 (0.09) 0.00 (0.96)
Thailand 82 84 1.01 0.02 (0.86) 0.78 (0.37) 82 1.00 0.00 (0.95) 0.67 (0.41) 75 0.90 0.02 (0.87) 0.78 (0.37)
  1. EV expected violations. v violations according to the model (normal), Student’s t or skewed-t. VR violations ratio (v/EV)
  2. P-value for different statistics in parentheses. For P-values ≤ 0.05, the coverage or independent test fails