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Table 4 99%− 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 33 44 1.33 3.35 (0.07) 1.19 (0.27) 29 0.88 0.51 (0.47) 0.51 (0.47) 22 0.67 4.20 (0.04) 0.30 (0.59)
Chile 33 45 1.36 3.96 (0.05) 2.04 (0.15) 37 1.12 0.47 (0.49) 3.26 (0.07) 28 0.85 0.81 (0.37) 5.23 (0.02)
Colombia 26 64 2.46 39.86 (0.00) 2.80 (0.09) 38 1.46 4.90 (0.03) 0.30 (0.59) 29 1.12 0.34 (0.56) 0.94 (0.33)
Mexico 33 56 1.70 13.39 (0.00) 0.92 (0.34) 39 1.18 1.04 (0.31) 0.49 (0.49) 31 0.94 0.12 (0.72) 0.59 (0.44)
Peru 33 52 1.58 9.40 (0.00) 1.31 (0.25) 37 1.12 0.47 (0.49) 3.35 (0.07) 36 1.09 0.27 (0.60) 3.54 (0.06)
Czech 33 58 1.76 15.61 (0.00) 2.08 (0.15) 49 1.48 6.82 (0.01) 1.48 (0.22) 34 1.03 0.03 (0.86) 0.71 (0.40)
Egypt 31 59 1.90 20.20 (0.00) 11.21 (0.00) 46 1.48 6.38 (0.01) 8.01 (0.00) 32 1.03 0.03 (0.86) 4.04 (0.04)
Greece 33 40 1.21 1.40 (0.23) 0.98 (0.32) 30 0.91 0.28 (0.59) 0.55 (0.46) 24 0.73 2.74 (0.10) 0.35 (0.55)
Hungary 33 40 1.21 1.40 (0.23) 0.98 (0.32) 33 1.00 0.00 (1.00) 0.67 (0.41) 36 1.09 0.27 (0.60) 0.79 (0.37)
Poland 33 45 1.36 3.96 (0.05) 2.04 (0.15) 37 1.12 0.47 (0.49) 3.26 (0.07) 38 1.15 0.73 (0.39) 3.09 (0.08)
Qatar 33 61 1.85 19.19 (0.00) 0.57 (0.45) 43 1.30 2.79 (0.09) 1.14 (0.29) 46 1.39 4.61 (0.03) 1.30 (0.25)
Russia 33 55 1.67 12.34 (0.00) 0.01 (0.93) 44 1.33 3.35 (0.07) 1.19 (0.27) 31 0.94 0.12 (0.72) 0.59 (0.44)
South Africa 33 45 1.36 3.96 (0.05) 1.24 (0.26) 38 1.15 0.73 (0.39) 0.89 (0.35) 10 0.30 2.28 (0.74) 0.06 (0.80)
Turkey 33 46 1.39 4.61 (0.03) 1.91 (0.17) 33 1.00 0.00 (1.00) 4.04 (0.04) 25 0.76 2.14 (0.14) 0.38 (0.54)
China 27 47 1.74 12.26 (0.00) 0.04 (0.84) 48 1.04 0.04 (0.85) 0.59 (0.44) 34 1.26 1.69 (0.19) 0.57 (0.45)
India 33 44 1.33 3.35 (0.07) 0.25 (0.62) 35 1.06 0.12 (0.73) 0.75 (0.39) 28 0.85 0.81 (0.37) 1.39 (0.24)
Indonesia 33 53 1.61 10.34 (0.00) 3.44 (0.06) 38 1.15 0.73 (0.39) 0.54 (0.46) 26 0.79 1.62 (0.20) 0.41 (0.52)
Korea 30 41 1.37 3.66 (0.06) 1.14 (0.29) 27 0.90 2.15 (0.08) 0.51 (0.47) 12 0.40 14.12 (0.00) 0.10 (0.76)
Malaysia 33 50 1.52 7.64 (0.01) 3.98 (0.05) 45 1.36 3.96 (0.05) 2.04 (0.15) 36 1.09 0.27 (0.60) 0.68 (0.41)
Philippines 33 49 1.48 6.82 (0.01) 7.55 (0.01) 36 1.09 0.27 (0.60) 3.44 (0.06) 35 1.06 0.12 (0.73) 3.63 (0.06)
Taiwan 33 58 1.76 15.61 (0.00) 0.77 (0.38) 47 1.42 5.30 (0.02) 0.15 (0.70) 35 1.06 0.12 (0.73) 0.75 (0.39)
Thailand 33 44 1.33 3.35 (0.07) 1.19 (0.27) 29 0.88 0.51 (0.47) 0.51 (0.47) 24 0.73 2.74 (0.10) 0.35 (0.55)
  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