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Table 1 Mean of the absolute percentage errors (MAPE) for e 0 and \( {e}_0^{\dagger } \) over the forecast years by country and method

From: Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

Country and Measure Method
Lee-Carter Lee-Carter, Rotated (Li et al.) Bohk and Rau
Validation 1 (ref. years: 1965–1990; forecast years: 1991–2009)
 Italy
   e 0 0.003 0.003 0.005
   \( {e}_0^{\dagger } \) 0.019 0.015 0.014
 Japan
   e 0 0.002 0.003 0.002
   \( {e}_0^{\dagger } \) 0.087 0.080 0.034
 Denmark
   e 0 0.008 0.007 0.006
   \( {e}_0^{\dagger } \) 0.065 0.054 0.009
Validation 2 (ref. years: 1960–1985; forecast years: 1986–2009)
 Italy
   e 0 0.010 0.010 0.002
   \( {e}_0^{\dagger } \) 0.029 0.021 0.018
 Japan
   e 0 0.002 0.002 0.004
   \( {e}_0^{\dagger } \) 0.092 0.076 0.014
 Denmark
   e 0 0.005 0.004 0.017
   \( {e}_0^{\dagger } \) 0.094 0.077 0.021
Validation 3 (ref. years: 1955–1980; forecast years: 1981–2009)
 Italy    
   e 0 0.014 0.014 0.002
   \( {e}_0^{\dagger } \) 0.027 0.019 0.012
 Japan    
   e 0 0.009 0.009 0.003
   \( {e}_0^{\dagger } \) 0.118 0.092 0.022
 Denmark    
   e 0 0.007 0.008 0.029
   \( {e}_0^{\dagger } \) 0.048 0.033 0.023
Validation 4 (ref. years: 1950–1975; forecast years: 1976–2009)
 Italy
   e 0 0.018 0.018 0.008
   \( {e}_0^{\dagger } \) 0.032 0.023 0.053
 Japan
   e 0 0.018 0.018 0.012
   \( {e}_0^{\dagger } \) 0.131 0.094 0.032
 Denmark
   e 0 0.015 0.014 0.035
   \( {e}_0^{\dagger } \) 0.020 0.018 0.043
  1. Note: MAPEs are shown for four validating settings that all forecast mortality until 2009, but they use different historical periods.