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Table 9 97.5%-VaR backtesting analysis for 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 45 1.28 2.69 (0.10) 0.16 (0.68) 40 1.14 0.70 (0.40) 0.01 (0.89) 23 0.65 4.79 (0.03) 0.76 (0.38)
Chile 35 49 1.40 5.11 (0.02) 0.04 (0.82) 43 1.22 1.75 (0.18) 0.32 (0.57) 23 0.65 4.79 (0.03) 0.73 (0.39)
Colombia 27 33 1.00 1.06 (0.30) 0.85 (0.35) 32 1.16 0.71 (0.39) 0.99 (0.32) 30 1.09 0.22 (0.63) 1.30 (0.25)
Mexico 35 50 1.42 5.83 (0.01) 0.43 (0.51) 46 1.31 3.23 (0.07) 0.20 (0.65) 32 0.91 0.27 (0.60) 0.09 (0.76)
Peru 35 41 1.17 1.00 (0.31) 0.03 (0.84) 40 1.14 0.70 (0.40) 0.01 (0.89) 37 1.05 0.11 (0.73) 2.01 (0.15)
Czech 35 44 1.25 2.19 (0.14) 3.59 (0.06) 41 1.17 1.00 (0.31) 4.43 (0.03) 33 0.94 0.11 (0.73) 1.42 (0.23)
Egypt 30 39 1.30 2.53 (0.11) 10.44 (0.00) 36 1.20 1.15 (0.28) 8.40 (0.00) 21 0.70 3.08 (0.08) 3.77 (0.05)
Greece 35 37 1.05 0.11 (0.73) 0.87 (0.35) 35 1.00 0.00 (1.00) 0.01 (0.89) 34 0.97 0.02 (0.86) 0.03 (0.85)
Hungary 35 39 1.11 0.45 (0.50) 0.00 (0.93) 36 1.02 0.02 (0.86) 1.90 (0.17) 38 1.08 0.25 (0.61) 2.12 (0.14)
Poland 35 46 1.31 3.23 (0.07) 1.23 (0.27) 44 1.25 2.19 (0.14) 1.53 (0.21) 32 0.91 0.27 (0.60) 1.59 (0.21)
Qatar 35 43 1.22 1.75 (0.18) 6.62 (0.01) 36 1.02 0.02 (0.86) 3.15 (0.07) 34 0.97 0.02 (0.86) 1.27 (0.26)
Russia 35 46 1.31 3.23 (0.07) 3.12 (0.07) 42 1.20 1.35 (0.24) 2.60 (0.11) 33 0.94 0.11 (0.73) 1.59 (0.21)
South Africa 35 41 1.17 1.00 (0.32) 0.03 (0.84) 35 1.00 0.00 (1.00) 0.01 (0.89) 23 0.65 4.79 (0.03) 0.76 (0.38)
Turkey 35 36 1.02 0.02 (0.86) 6.11 (0.01) 35 1.00 0.00 (1.00) 6.50 (0.01) 32 0.91 0.27 (0.60) 4.26 (0.04)
China 22 32 1.42 3.64 (0.05) 0.57 (0.44) 25 1.11 0.27 (0.60) 0.12 (0.72) 12 0.53 6.03 (0.01) 0.32 (0.57)
India 35 45 1.28 2.69 (0.10) 0.20 (0.65) 42 1.20 1.35 (0.24) 0.39 (0.53) 39 1.11 0.45 (0.50) 0.00 (0.93)
Indonesia 35 48 1.37 4.44 (0.03) 0.97 (0.32) 41 1.17 1.00 (0.32) 0.47 (0.49) 23 0.65 4.79 (0.03) 3.65 (0.05)
Korea 32 50 1.53 8.32 (0.00) 1.88 (0.17) 42 1.298 2.61 (0.11) 0.28 (0.59) 21 0.64 4.76 (0.03) 0.88 (0.35)
Malaysia 32 37 1.13 0.61 (0.43) 0.00 (0.95) 39 1.20 1.25 (0.26) 0.02 (0.87) 35 1.07 0.19 (0.66) 0.96 (0.33)
Philippines 35 45 1.28 2.69 (0.10) 5.89 (0.15) 43 1.22 1.75 (0.18) 6.62 (0.01) 30 0.85 0.76 (0.38) 8.71 (0.00)
Taiwan 35 57 1.62 11.95 (0.00) 0.05 (0.82) 53 1.51 8.22 (0.00) 0.00 (0.99) 25 0.71 3.24 (0.07) 0.90 (0.34)
Thailand 35 37 1.05 0.11 (0.73) 0.00 (0.98) 35 1.00 0.00 (1.00) 0.01 (0.89) 31 0.88 0.48 (0.48) 0.13 (0.72)
  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