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1 NO GDP %9 7.6%2 1.%
2 1 2 GDP %9 7.6%2 1 1.%7 11.5% GDP GDP 1 5 2GDP UFJ UFJ GDP 7 4GDP 4 11/7-9 1/1-12 9/ UFJ 2 1 2/7-9 2/1-3 5/7-9 7/ UFJ 2
3 GDP GDP GDP GDP GDP GDP UFJ 3
4 2 GDP N N 2 N var(g JPN )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(1) i=1 i=1 j=1,j i var(g JPN ) GDP %G JPN var(g i ) i GDP G i cov(g i,g j ) i j 2 w i w j i j GDP % w i (1) (1) %
5 2GDP (1) UFJ 1 GDP % 1,81 1, % 1, % % % % % , UFJ , UFJ 5
6 GDP GDP UFJ 3198 GDP
7 GDP IT GDP /7-9 9GDP 9/ /1-3 3/ /1-12 8/1-3 2/ UFJ UFJ GDP 51 D.C.(2) var(g US )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(2) i=1 i=1 j=1,j i var(g US ) GDP %G US var(g i ) i GDP G i cov(g i,g j ) i j w i w j i j GDP % , % 2 1, % % 28.9% %67.2% 11 7
8 3GDP (2) UFJ , UFJ , UFJ GDP (3) %8 92.6% %88.2% var(g EUR )=w i2 *var(g i )+w i *w j *cov(g i,g j ) -----(3) i=1 i=1 j=1,j i var(g EUR ) GDP %G EUR var(g i ) i GDP G i cov(g i,g j ) i j w i w j i j GDP % 8
9 3 2 12GDP GDP 11/7-9 9/ /1-12 2/ 8/ / UFJ UFJ 4GDP (3) UFJ GDP % 87.9% %88.5% % 85.8% %86.5% 15 1%
10 1 14 GDP 1 15 GDP UFJ UFJ (4) (5)2 %1% X Y 1 1% 2 2% 3 97% 1 3% 2 96% 3 1%4% =1%+2%+1% 2% 3% 5%22% 32% 46% 96% =2%+3%+46% (4) min(x i /X,AX i /AX) X i GDP i %X i /X i AX i /AX (5) min(x i /X,Y i /Y) X i GDP X i /X i Y i Y i /Y GDP % 2.7% % %4 15% 1
11 5 16GDP 5 17GDP 4 3 1/ / UFJ UFJ 5Southeast Far West Mideast D.C.Great Lakes 9 11
12 GDP GDPG JPN GDPw i GDPG i G JPN = w i * G i i=1 = w 1 *G 1 +w 2 *G 2 +w 47 *G E(G JPN ) = w i * E(G i ) i=1 = w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 ) GDPvar(G JPN ) var(g JPN ) = E{G JPN -E(G JPN )} 2 = EG JPN2-2G JPN *E(G JPN )+E(G JPN ) 2 = E{w 1 *G 1 +w 2 *G 2 +w 47 *G 47 } 2-2*(w 1 *G 1 +w 2 *G 2 +w 47 *G 47 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} + {w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} 2 = E(w 1 *G 1 ) 2 +(w 2 *G 2 ) 2 +(w 47 *G 47 ) 2 + (w 1 *G 1 )*{(w 2 *G 2 ) +(w 47 *G 47 )}+(w 2 *G 2 )*{(w 1 *G 1 )+(w 3 *G 3 ) +(w 47 *G 47 )} + (w 47 *G 47 )*{(w 1 *G 1 )+(w 2 *G 2 ) +(w 46 *G 46 )} - 2*[(w 1 *G 1 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )}+(w 2 *G 2 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )} + (w 47 *G 47 )*{w 1 *E(G 1 )+w 2 *E(G 2 ) +w 47 *E(G 47 )}] + {w 1 *E(G 1 )} 2 +{w 2 *E(G 2 )} 2 +{w 47 *E(G 47 )} 2 + {w 1 *E(G 1 )}*[{w 2 *E(G 2 )} +{w 47 *E(G 47 )}]+{w 2 *E(G 2 )}*[{w 1 *E(G 1 )}+{w 3 *E(G 3 )} +{w 47 *E(G 47 )}]} + {w 47 *E(G 47 )}*[{w 1 *E(G 1 )}+{w 2 *E(G 2 )} +{w 46 *E(G 46 )}] = w 12 *E{G 1 -E(G 1 )} 2 +w 22 *E{G 2 -E(G 2 )} 2 +w 472 *E{G 47 -E(G 47 )} 2 + w 1 *w 2 *E{G 1 -E(G 1 )}{G 2 -E(G 2 )}+w 1 *w 3 *E{G 1 -E(G 1 )}{G 3 -E(G 3 )} +w 1 *w 47 *E{G 1 -E(G 1 )}{G 47 -E(G 47 )} + w 2 *w 1 *E{G 2 -E(G 2 )}{G 1 -E(G 1 )}+w 2 *w 3 *E{G 2 -E(G 2 )}{G 3 -E(G 3 )} +w 2 *w 47 *E{G 2 -E(G 2 )}{G 47 -E(G 47 )} + + w 47 *w 1 *E{G 47 -E(G 47 )}{G 1 -E(G 1 )}+w 47 *w 2 *E{G 47 -E(G 47 )}{G 2 -E(G 2 )} +w 47 *w 46 *E{G 47 -E(G 47 )}{G 46 -E(G 46 )} 47 = w i2 *var(g i ) i= w i *w j *cov(g i,g j ) i=1 j=1,ji cov(g i,g j )G i G j cov(g i,g j )=E{G i -E(G i )}*{G j -E(G j )} H yasuhiro_ishimaru@mufg.jp UFJ
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