Table 2 Testing for Heavy-tailedness

From: On agricultural commodities’ extreme price risk

  \(\hat {\gamma }_{DEH}\) (s.e.) (t-stat) \(\hat {\gamma }_{BVT}\) (s.e.) (t-stat) \(\hat {\gamma }_{FGHN}\) (s.e.) (t-stat)
Panel (a): Right tail of monthly returns in the spot market, 1928-2014
Corn 0.231 (0.13) (1.8) 0.242 (0.10) (2.3) 0.228 (0.12) (1.8)
Cotton 0.268 (0.15) (1.8) 0.268 (0.12) (2.2) 0.262 (0.13) (2.1)
Oats 0.438 (0.11) (4.0) 0.338 (0.11) (3.1) 0.597 (0.20) (3.0)
Soybeans 0.260 (0.20) (1.3) 0.231 (0.15) (1.6) 0.225 (0.15) (1.5)
Wheat 0.165 (0.14) (1.2) 0.088 (0.12) (0.7) 0.194 (0.09) (2.1)
Live cattle -0.016 (0.20) (-0.1) 0.087 (0.17) (0.5) 0.032 (0.12) (0.3)
Oranges 0.320 (0.23) (1.4) 0.350 (0.16) (2.1) 0.248 (0.18) (1.4)
Sugar 0.248 (0.14) (1.7) 0.216 (0.11) (1.9) 0.263 (0.11) (2.3)
Panel (b): Right tail of weekly returns in the futures market, 1979-2012
Corn 0.187 (0.12) (1.5) 0.154 (0.09) (1.7) 0.186 (0.10) (1.9)
Cotton 0.125 (0.12) (1.0) 0.116 (0.10) (1.1) 0.143 (0.09) (1.6)
Oats 0.280 (0.13) (2.1) 0.278 (0.12) (2.4) 0.269 (0.15) (1.8)
Soybeans 0.032 (0.12) (0.3) 0.047 (0.10) (0.5) 0.077 (0.07) (1.1)
Wheat -0.015 (0.13) (-0.1) -0.019 (0.10) (-0.2) 0.055 (0.07) (0.7)
Livecattle -0.108 (0.15) (-0.7) -0.064 (0.10) (-0.7) -0.018 (0.07) (-0.2)
Orange juice 0.307 (0.11) (2.8) 0.297 (0.12) (2.6) 0.320 (0.14) (2.2)
Sugar 0.149 (0.21) (0.7) 0.147 (0.15) (1.0) 0.122 (0.14) (0.9)
  1. Note: The table reports the point estimates and standard errors for parameter γ in the generalized extreme value distribution in Eq. 19. The columns correspond to the generalized Hill estimator of Beirlant et al. (1996) (\(\hat {\gamma }_{BVT}\)), the moment estimator of Dekkers et al. (1989) (\(\hat {\gamma }_{DEH}\)) and the mixed moment estimator of Fraga Alves et al. (2009) (\(\hat {\gamma }_{FGHN}\)). For the monthly returns in the spot market, each tail consists of 50 observations, or approximately 5.4% of the observations. For the weekly returns in the futures markets, each tail consists of 75 observations, or approximately 4.2% of the observations. Heavy-tailedness is not rejected for any of the series (rejection of heavy-tailedness at the 5% significance level requires a t-statistic smaller than − 1.6)