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Table 8 97.5%-VaR backtesting analysis for pre-crisis 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 35 46 1.31 3.23 (0.07) 0.15 (0.69) 37 1.05 0.11 (0.73) 0.00 (0.98) 24 0.68 3.97 (0.04) 0.62 (0.43)
Chile 35 43 1.22 1.75 (0.18) 1.70 (0.19) 41 1.17 1.00 (0.31) 0.47 (0.49) 34 0.97 0.02 (0.86) 0.03 (0.85)
Colombia 27 52 1.89 17.81 (0.00) 2.28 (0.13) 44 1.60 8.61 (0.00) 2.33 (0.12) 29 1.05 0.08 (0.77) 1.57 (0.21)
Mexico 35 45 1.28 2.69 (0.10) 0.20 (0.65) 42 1.20 1.35 (0.24) 0.06 (0.80) 30 0.85 0.76 (0.38) 0.17 (0.67)
Peru 35 45 1.28 2.69 (0.10) 3.33 (0.07) 41 1.17 1.00 (0.31) 2.06 (0.15) 43 1.22 1.75 (0.18) 3.85 (0.05)
Czech 35 35 1.00 0.00 (1.00) 0.01 (0.89) 31 0.88 0.48 (0.48) 0.13 (0.71) 30 0.85 0.76 (0.38) 1.31 (0.25)
Egypt 30 32 1.06 0.13 (0.71) 0.02 (0.87) 30 1.00 0.00 (1.00) 0.07 (0.77) 33 1.10 0.29 (0.58) 0.00 (0.92)
Greece 35 35 1.00 0.00 (1.00) 0.01 (0.89) 33 0.94 0.11 (0.72) 0.06 (0.80) 28 0.80 1.53 (0.21) 0.29 (0.59)
Hungary 35 26 0.74 2.60 (0.10) 0.44 (0.50) 24 0.68 3.97 (0.04) 0.62 (0.43) 26 0.74 2.60 (0.10) 0.44 (0.51)
Poland 35 34 0.97 0.02 (0.86) 1.69 (0.19) 35 1.00 0.00 (1.00) 1.79 (0.18) 38 1.08 0.25 (0.61) 2.12 (0.14)
Qatar 35 49 1.40 5.11 (0.02) 0.04 (0.82) 54 1.54 9.09 (0.00) 0.00 (0.95) 62 1.77 17.43 (0.00) 3.23 (0.07)
Russia 35 42 1.20 1.35 (0.24) 1.87 (0.17) 35 1.00 0.00 (1.00) 1.13 (0.28) 22 0.62 5.69 (0.01) 0.70 (0.40)
South Africa 35 43 1.22 1.75 (0.18) 0.32 (0.57) 37 1.05 0.11 (0.73) 0.87 (0.35) 32 0.91 0.27 (0.60) 1.59 (0.21)
Turkey 35 30 0.85 0.76 (0.38) 1.95 (0.16) 27 0.77 2.03 (0.15) 2.59 (0.11) 29 0.82 1.11 (0.29) 2.15 (0.14)
China 22 38 1.68 9.10 (0.00) 0.28 (0.59) 37 1.64 8.04 (0.00) 0.22 (0.64) 56 2.35 30.89 (0.00) 0.00 (0.94)
India 35 43 1.22 1.75 (0.18) 0.32 (0.57) 36 1.02 0.02 (0.86) 0.99 (0.32) 24 0.68 3.97 (0.04) 0.62 (0.43)
Indonesia 35 44 1.25 2.19 (0.14) 0.25 (0.61) 46 1.31 3.23 (0.07) 1.23 (0.27) 43 1.22 1.75 (0.18) 0.09 (0.76)
Korea 32 40 1.23 1.65 (0.20) 0.43 (0.51) 36 1.10 0.37 (0.54) 0.00 (0.99) 14 0.43 13.68 (0.00) 0.30 (0.58)
Malaysia 32 28 0.86 0.66 (0.41) 2.14 (0.14) 28 0.86 0.66 (0.41) 2.14 (0.14) 32 1.00 0.00 (0.92) 1.39 (0.24)
Philippines 35 38 1.08 0.25 (0.61) 0.76 (0.38) 38 1.08 0.25 (0.061) 0.76 (0.38) 47 1.34 3.81 (0.05) 0.11 (0.74)
Taiwan 35 41 1.17 1.00 (0.31) 0.03 (0.84) 39 1.11 0.45 (0.50) 0.00 (0.93) 42 1.20 1.35 (0.24) 0.39 (0.53)
Thailand 35 39 1.11 0.45 (0.50) 2.23 (0.13) 37 1.05 0.11 (0.73) 2.01 (0.15) 34 0.97 0.02 (0.86) 1.69 (0.19)
  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