Table 2 MCS procedure using the T_max,M test applied to the RMSFE in the validation set from 1996 to 2005 for forecasting the Japanese female and male national and sub-national mortality for ages between 60 and 100+. From the 17 models, below is the selected superior set of the model(s)

Japan

1

1

Hokkaido

1, 8, 9, 10, 11, 12, 13, 14, 15, 16

16

Aomori

7

16

Iwate

3, 5, 7, 8, 13, 14, 15, 17

13

Miyagi

2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

1, 3, 5, 8, 13, 14, 15, 16, 17

Akita

7

14

Yamagata

13, 14, 16

5, 7

Fukushima

3

13

Ibaraki

1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 17

16

Tochigi

2, 7, 14, 15

8, 17

Gunma

8

2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Saitama

8

14

Chiba

3, 8, 9, 10, 11, 15

16

Tokyo

8

13, 15, 16

Kanagawa

8

14

Niigata

3, 5, 7, 8, 14, 15

3, 5, 7, 8, 13, 17

Toyama

3, 5, 7, 8

13, 17

Ishikawa

2, 3, 4, 5, 7, 8, 13, 14, 15, 17

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Fukui

3

3, 4, 5, 7, 8, 13, 14, 15, 16, 17

Yamanashi

7

5, 13, 14, 15, 16, 17

Nagano

8

14

Gifu

13

3, 5, 7, 13, 14, 15, 16, 17

Shizuoka

1, 8, 10

13, 14, 15, 16

Aichi

1, 3, 8, 9, 10, 11, 12, 14

13, 14, 15, 17

Mie

9

8

Shiga

8

13

Kyoto

8, 13, 14, 15, 17

14

Osaka

8

17

Hyogo

8

13, 14, 15, 16, 17

Nara

3, 5, 7, 8, 13, 14

13, 14, 15, 16, 17

Wakayama

8

17

Tottori

7

3, 5, 8, 13, 14, 15, 16, 17

Shimane

13, 15

1, 3, 5, 7, 8, 13, 14, 15, 16, 17

Okayama

10

1, 3, 8, 13, 14, 15, 16

Hiroshima

10

15

Yamaguchi

8, 15

14

Tokushima

7

7

Kagawa

14

3, 5, 7, 8, 13, 14, 15, 16, 17

Ehime

7

3, 8, 13, 14, 15, 16, 17

Kochi

14

17

Fukuoka

1

13

Saga

3, 5, 7, 8, 9, 10, 11, 12, 15

5, 7, 14

Nagasaki

1, 8, 10, 11, 13, 14, 15, 16, 17

17

Kumamoto

15

14

Oita

13, 14

5, 7, 13, 14, 15, 16

Miyazaki

2, 3, 5, 8, 13, 14, 15, 17

16

Kagoshima

1, 3, 8, 9, 10, 11, 12, 13, 14, 15

3, 13, 14

Okinawa

9, 10, 11, 12, 13, 14, 15, 17

13, 14, 15, 16, 17