Table 1.

Mean of the absolute percentage errors (MAPE) for e ₀ and $e_0^{†}$ over the forecast years by country and method

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
$e_0^{†}$	0.019	0.015	0.014
Japan
e 0	0.002	0.003	0.002
$e_0^{†}$	0.087	0.080	0.034
Denmark
e 0	0.008	0.007	0.006
$e_0^{†}$	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
$e_0^{†}$	0.029	0.021	0.018
Japan
e 0	0.002	0.002	0.004
$e_0^{†}$	0.092	0.076	0.014
Denmark
e 0	0.005	0.004	0.017
$e_0^{†}$	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
$e_0^{†}$	0.027	0.019	0.012
Japan
e 0	0.009	0.009	0.003
$e_0^{†}$	0.118	0.092	0.022
Denmark
e 0	0.007	0.008	0.029
$e_0^{†}$	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
$e_0^{†}$	0.032	0.023	0.053
Japan
e 0	0.018	0.018	0.012
$e_0^{†}$	0.131	0.094	0.032
Denmark
e 0	0.015	0.014	0.035
$e_0^{†}$	0.020	0.018	0.043

Note: MAPEs are shown for four validating settings that all forecast mortality until 2009, but they use different historical periods.