中央大学理工学部情報工学科

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1 04D F

2

3 AR MA ARMA ARIMA

4

5 NYMEX 100 [11] [11]

6 [7][15 7] Y X Y + X + u = 1 2 u u 1 2 X Y X u u u = Y + X ) ( = 1,2,, ) ( 1 2 n n u S = u 2 = { Y ( X )}

7 S S S Y X ^ 1 ^2 1 2 ^ 1 ^2 1 2 ^ 1 ^2 0 ) ( 2 0 ) ( = = = = X X Y S X Y S = + = + Y X X X Y X n ) ( ) ( ) ( _ X _ Y X Y _ ^ 2 _ ^ 1 2 _ ^ 2 ) ( ) )( ( X Y X X Y Y X X = = ^ 1 ^2 Y ^ Y ), 1,2, ( ^ n Y Y e = =

8 X Y Y _ ( 2 Y Y ) X _ ^ _ 2 ( e 2 2 Y ) = ( Y Y) + Y X 2 ( Y ) = ^ 2 2 ( Y Y ) e ^ Y _ Y X R 2 = 1 ( Y e 2 _ Y ) 2 = ^ _ ( Y Y ) ( Y _ 2 Y ) R ARAuto RegressveMAMovng AverageARMAAuto Regressve Movng Average,ARIMAAuto Regressve Integrated Movng Average AR AR p x( = a x( t m) + u( m= 1 m p a m u(p 4

9 AR ARpp p AR a p z 2 p 1 a z a z a p z = p AR MA MA q x( = u( b u( t m) m= 1 m q u( q MA MAqq b m x = u( b u( t 1) b u( t 2) bqu( t ) ( 1 2 q MA 1 AR q MA b q z 2 q 1 b z b z b q z = 1 AR ARMA ARMA AR MA 5

10 x( = p m= 1 a m x( t m) + u( q n= 1 b u( t n) n pq AR MA a b u( ARMApq a MA b AR m n ARMA AR MA m n ARIMA ARMA ARIMA ARIMA ARMA AR MA p x( = am x( t m) + u( b m= 1 n= 1 u( t n) x( = x( x( t s), u ( = u( u( t s) q n ARMA p q AR MA b n u(s ARIMApsq a m ARIMA ARIMA

11 AR 1 12 SpSsSq ARIMA ARIMApsqSpSsSq N X ( x, x2,, ) ( 1 k = k 1 =, 2,, ) f ( x, ) X f ( x, ) N () = f (, ) = 1 x x n L N () = log f (, ) l = 1 x 7

12 ) ( ) ( ) ( ), ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( s t u t u t u s t r t r t r n t u b t u m t r a t r t r t x t y q n n p m m = = + = + + = = = r(p q AR MA s u(arima m a n b 8

13 SPSS 15.0J [9] 9

14

15 [1012] ARIMA ARIMA ARIMA ARIMA ARIMA

16 ARIMA SPSS15.0J ARIMA () ARIMA ARIMA ARIMA ARIMA ARIMA y( x( ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) + u( * ( u( t 1) u( t 13)) r( u( x(

17 [10] 13

18 y( x( L ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) * ( r( t 2) r( t 14)) + u( r( u(

19 3.2.1 x( L L

20 [10]

21 y( x( L ARIMA y( = * x( + R( R( = r( r( t 12) = 0.591* ( r( t 1) r( t 13)) + u( r( u( x( L

22 3.3.2 [10]

23 3.4.1 y( x( km ARIMA y( = * x( + R( R( = r( r( t 12) = u( ( 0.346) * ( u( t 1) u( t 13)) ( 0.280) * ( u( t 2) u( t 14)) r( u( x( km

24 [46]3.2 20

25 y( x( L ARIMA y ( y( t 12) = u( * ( u( t 12) u( t 24)) u(

26 [46]

27 y( x( L ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) + u( * ( u( t 1) u( t 13)) r( u(

28 3.6.1 x( L

29 1 [8]

30 y( x( 1 1 L ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 12) r( t 24)) + u( ( 0.425) * ( u( t 1) u( t 13)) r( u( x( L

31 [8]

32 y( x( 1 1 ARIMA y( = * x( + R( R( = r( r( t 12) = 0.658*( r( t 12) r( t 24)) + u( ( 0.426) * ( u( t 1) u( t 13)) r( u( x(

33 [1012] 29

34 y( x( ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) + u( ( 0.998) * ( u( t 1) u( t 13)) r( u( x(

35

36 3.9 [1012]

37 y( x( ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) + u( * ( u( t 1) u( t 13)) r( u( x(

38 [10]

39 y( x( L ARIMA y( = * x( + R( R( = r( r( t 12) = * ( r( t 1) r( t 13)) + u( * ( u( t 1) u( t 13)) r( u( x( L

40

41 %

42 3 [3] X > 1 X < 1 X = 1 X 4.1.1D P X d D / D = d P / P DMnDD PMnPP d logy /dy = 1/ Y d logy = dy / Y

43 X d D / D d log D = = d P / P d log P log D = + X log P

44 4.2.1 X km X 4.3.1T D 40

45 T X = D

46 42

47

48 [1]SPSS 2006 [2] 2006 [3]2006 [4] 2001 [5]2006 [6] [7]1991 [8] < [9] < [10] < [11] < [12] < 44

49

50 1

51

52

53 2

54

55

56 3 1

57

58

59 4 1

60

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62 5

63

64

さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+

さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+ 5 5. 5.. a a n n A m n a m a n = a m+n (a m ) n = a mn 3 (ab) n = a n b n a n n 0 3 3 0 = 3 +0 = 3, 3 3 = 3 +( ) = 3 0 3 0 3 3 0 = 3 3 =, 3 = 30 3 = 3 0 a 0 a`n a 0 n a 0 = a`n = a n a` = a 83 84 5 5.

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36 36 37 38 P r R P 39 (1+r ) P =R+P g P r g P = R r g r g == == 40 41 42 τ R P = r g+τ 43 τ (1+r ) P τ ( P P ) = R+P τ ( P P ) n P P r P P g P 44 R τ P P = (1 τ )(r g) (1 τ )P R τ 45 R R σ u R= R +u u~ (0,σ

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