) 041 (CIP ), ISBN /,.:...-.F10 CIP (2003) / / 75 / / 6 / ( 010) ( ) / / / mm 1/ 16 / 301

Transcription

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2 ) 041 (CIP ), ISBN /,.:...-.F10 CIP (2003) / / 75 / / 6 / ( 010) ( ) / / / mm 1/ 16 / 301 / / / / / ISBN / F1261 / 26.80,,,,

3 ,,,,,,,,, 20,,,, :,,,,, ;,,,, SAS SPSS T SP, Excel ;,,,,, : ( ), (), ( ), ( ), ( ),,,,,!,,,,!

4 ( 1) ( 1) ( 4) (10) (13) (Delphi poll) (13) (17) (20) (24) (25) (40) (53) (74) (83) (83) (87) (92) ( 111) ( 115) ( 115) ( 116) ( 126) ( 128) ( 128) ( 133) ( 136)

5 2 ( 144) ( 147) ( 150) ( 152) ( 153) ( 155) ( 159) ( 163) X - 11 ( 166) ( 170) ( 170) ( 175) ( 182) ( 188) ( 188) ( 193) ( 197) AR MA ( 202) ( 210) ( 219) ( 223) ( 232) ( 232) ( 237) 1 ( 241) 2 X 2 ( 243) 3 X 2 () ( 245) 4 F ( 247) 5 D.W ( 255) 6 ( r z ) ( 259) ( 260)

6 ( forecasting ),,,,,,,,,,,,,,, ,,,,,,,,,,,,,

7 2 ), (economic forecasting),, 4,,,,,,,,, (),,,,,,,,,,,,,, :,,

8 3 ),,,,,, :,,,,,,, ( ),,,,,,,, ( ),,,,,,,,,,,,, (),, 5 ; 1 5, 1,

9 4,,,,,,,,,,,, :, 1.1 Box - Jenkins 1.1, : () :

10 5 ;,,, ( ) :, ;, (),,,,,, (),, ;, (),,,, ;,,, ( ), : = + = -

11 6 ( ) : 1.,, 2.,, (),,,,,,,,,,,,, ;,, (),,,,

12 7 ),,,,,,, TSP, E-views, SPSS, SAS, Excel, () 1.,, :,,,,,,,,,,,,,,,,,,,,,,, 2.,,

13 8,,,,,,,,,,, 3.,,, 4.,,,,,,, 5.,,,,,, ( ) 1., () (),,,,,,

14 9,, ( ),, ;,,,, 1.2 : 1.2 (),, :,,,,,,,,,,,,,,,,,,,,

15 10,,,,, ;, : 1.,,, ( + ),,, 2., 3. : ;, ;,,,,,,, : (1 ) : (2 ) :,,,,, :

16 11,,,,,,,,,,,,,,,,,,,,,,,,,, ( ),,,,,,,,,,,,,,,,,

17 12 ),,,,,,, (),,,,,

18 ,,,, ;,, :,,,,,, :,,, ( ), :, ; ; :,,,,,,,,,,, (Delphi Poll),,

19 14,,,,,,,,, O. N., T.J., 1964,,,, :,,, 50,,,,,,,, 1964, T.J.O. (1015 ), : ; ; ; ; ;, 50%,,,,,,,, () ( ),,, : ( ),,

20 ( Delphi Poll) 15 20,, ( ),,,,,,,,, (),, (),,,,,,,, (),,,,,,, (),,,,,, 2.1,, B,

21 16,, ( ),, 26, 60, A B C A B A B A B A B ,,,,,,,,, ;

22 17 ;,,,,, : ; ;, : (1 ),, ; (2 ),,, : (1 ) ; (2 ), ; (3 ), (Subjective Probability),,,, : P( Ai ) Ai (1 )0P( Ai )1 (2 ) P(= 1), : (3 )Ai Aj, ij, j = 1, 2, Ai, Aj, : P i = 1 Ai = P ( i = 1 Ai ),,, 1/ 2,

23 18,,,,,, :,, : = :, 2.2 ( ) * ,, 1/ 3, ( )/ 3 = 833.4( ) 950, 750, 50%,

24 )/ 2 = 850( ) 60%, 40%, : = ,,, 8 : % - 1 = - 2 % % = 823.6( ),,, :, 205, ( % ) ( ) 1%,, 99%,,

25 ,,, 199.2, 50%,, ( , )( 193.2, 205.2),, 62.5% (87.5% 25% ),,,,,,,,,,,, ( Leading Indicators ),,,,

26 21 10 M1 18 ( Coincident Indicators ),,,, : M2 10 ( Lagging Indica tors),,,, : 6,,,,, : :, yt xt tth y y th yt = f ( xt - ), yth = f ( xt + h - ), = g(x th - ),,, 2.1

27 22,, t, t ( ) Money supply H ousing Permits Stock market Mortgage debt Residential Investmen t Busines s Loans Capital goods orders Inven tories Busines s invent ory Cr edit outstanding Industr ial construction Unemployed Rate Automobile sales Free r eserves

28 23,,,,,,?, (Diffusion Index ), 1, 0.5, 0, : ( DI t ) = DIt t, 1 6 9,,,, :, 0 < DIt < 50 %, 50%,,,,, 50% < DIt < 100 %,,,, DIt 100 %,, 100% > DIt > 50 %,,,,,,, 50% > DIt > 0,,,,,,, ;,

29 ,,,, ( ), :,,, : 3.1 : (1 ); (2), ; (3 ),, ; (4 )

30 25 ) Y, X, 1. ( ) Y = +X +, Y X ;,,, X,, : 1.Y1 =+X Y2 =+X Y3 =+ X3 + 3, : N.Y N =+ X N + N Y i = +Xi + i, E( i ) = 0 Cov( i, j ) = 2 i = j 0 ij, 50,, : Y = + X +,,, Y =+ X,

31 26.,, n,, : y x 1 y1 x1 : 2 y2 x2 n yn xn a,, b, Y X : y = a + bx + e(, ), a b,, y = a + bx e,, y^ = a + bx y ei = yi - y^i ( i = 1, 2n) : y^1 = a + bx e1 = y1 - y^1 y^2 = a + bx e2 = y2 - y^2 y^3 = a + bx e3 = y3 - y^3 y^ n = a + bx en = yn - y^ n,,, (),, :, a b; a b

32 27,,, y x 1 y1 x1 2 y2 x2 n y n x n y^ = a + bx y, x, a b, yi y^i, n n ( y i = 1 i - y^i ) 2 = i = 1 e2 i n = ( i = 1 yi - a - bx) 2, a b : : b= n n i = 1 xi y i n n i = 1 x2 i a= y - b x b = n i = 1 a = y - b x n n - x i = 1 i i = 1 yi n - ( i = 1 xi ) 2 ( xi - x) ( yi - y) n ( x i = 1 i - x) 2,, a b, : 1.,,, b,, b, 2., : (1 ); (2 ) ; (3 )

33 28 a b, a b,, a b,, a b, a b y, y, a b,, : 2 bn [, n ] ( x i = 1 i - x) 2 an [, ( 1 n + x 2 n ) 2 ] ( x i = 1 i - x) 2 cov( a, b) = - n ( i = 1 xi x 2 - x) 2 : a, b, 2, S y 2 = n i = 1 e2 i / ( n - 2 ), 2, yi y^i, ( ) n b - 2 S y 2 ( xi - x) i = 1 a - ( 1 n + x 2 2 n ) Sy - x) 2 i = 1 ( xi t( n - 2 ) t ( n - 2), a b,: 1. ; 2., E( ei, ej ) = 0 ( ij) ; 3., i N( 0, 2 )

34 29,, ( ) 1., X Y 0, X Y b - ( Sb b ) t, t Sb, H0 : = 0, H1 0 tb = b Sb = b ( x - x) 2 Sy S y 2 = ( y - y^ ) 2 / ( n - 2 ) t tc ( n - 2) t > tc ( n - 2), H0, H1 : 0, 2., y^i = a + bxi y i = a + bx i + ei,,,,, y x,, b 0,,,,,, : H0 : b= 0, F,,, = +, : n n n ( i = 1 yi - y) 2 = ( i = 1 y^i - y) 2 + ( i = 1 yi - y^i ) 2 : n n - 2 : ST = SR + SE,

35 30 ST 2 2 ( n - 1) SR/ 2 2 ( 1) SE/ 2 2 ( n - 2) SR S E, b= 0, F = SR S E/ ( n - 2) = ( y^ - y) 2 / 1 F( 1, n - 2 ) ( y - y^)/ ( n - 2 ),, F F(1, n - 2 ), F > F( 1, n - 2 ),,,, F, 3.1 F SR SE 1 n - 2 S T n - 1 SR SE/ ( n - 2) S R SE/ ( n - 2 ) F : (1 ), ; (2 ) Y X ; (3 ) Y X 3. D.W, : Cov( i, j ) = 0,,,,, t F, D. W, ij : H0 := 0,,

36 31 d n i = 2 ( ei - ei - 1 ) 2 n i = 1 ei 2, n p, Durbin - Wa tson D.W, dl du, d d L du, 3.2 : 3.2 D.W du < d < 4 - du,,, d 2,, 0 < d < dl,, 4 - dl < d < 4,, dl ddu 4 - du d4 - dl, : (1 ); (2 ),, ; (3 ) ; (4 ) ; (5 ) 4. ( S.E. of regression ) S y

37 32 Sy n i = 1 ( yi - y^) 2 n - 2 Sy,, ; Sy 0,,,, ;, Sy, Sy/ y S y/ y 15 %, 5.,, = +,,, R 2, : R 2 =,0R 2 1R 2 n i = 1 ( y^i - y) 2 n = 1 - ( i = 1 yi - y) 2 R 2,, R 2, R 2 n ( y i = 1 i - y^i ) 2 n ( y i = 1 i - y) 2 = 1,, = 0, 1, 0.8,,,,, ( ) 1. ( Mean Error) n ME = ei/ n i = 1 2. ( Mean Absolute Error) n MAE = ei / n i = 1

38 33. ( Sum of Squared Error ) SSE = 4. ( Mean Squared Error) n 2 i = 1 ei 2 MSE = / n n i = 1 ei 5. ( Standard devia tion of Error) SDE = n i = 1 ei 2 / ( n - 1 ),, ;,, ;,,,,,,,,,, ( ), : 1. ( Percentage Error) P Ei = ei/ y100 % 2. ( Mean Percentage Error ) n MP E = P Ei/ n i = 1 3. ( Mean Absolute Percentage Error ) n MA PE = PEi / n i = 1,,, MAP E < 10, x, y (), x,

39 34 y a N (, 1 n + x2 Lx x b N, 2 cov( a, b) = -, Lx x Lx x x L x x 2 ) 2 n 2 = ( xi - x) i = 1, x0,, y^0 = a + bx 0 y^0 N + x0, 1 n + ( x0 - x) 2 Lx x 2 y^0 E( y0 ) = + x0, y^0 y^0,, y0 - y^0 ( ) x0 y^0, 1 - ( ), x0, y0, P( y0 - y^0 ) = 1 - P( y^0 - y0 y^0 + ) = 1 - y^0 -, y^0 + y0 1 -?, x = x0, y0 y^0, y0, y^0 x0, y0 y^0, N (0, 2 ), y0 - y^0, E( y0 - y^0 ) = 0 var ( y0 - y^0 ) = var ( y0 ) + var ( y^0 ) = n + ( x0 - x) 2 Lx x 2

40 35 y - y^0 N 0, ( x0 - x) + n Lx x 2 Sy/ 2 2 ( n - 2 ), S y y0 - y^0, t y0 - y^ n + ( x0 - x) 2 Lx x S y ( n - 2) 2 y0 - y^0 = ^1 + 1 n + ( x0 - x) 2 Lx x t( n - 2 ) ^2 = S y ( n - 2 ) ^ = ^ 2, P y0 - y^0 = P y0 ^1 + 1 n - y^0 t + ( x0 - x) 2 Lx x n ^ ( x0 - x) + n Lx x ^ + ( x0 - x) 2 Lx x = t1 - a 2 ( n - 2) = 1 - : = t1 - a ( n - 2) 2 ^ n + ( x0 - x) 2 Lx x y^0 - t1 - a ( n - 2) 2 ^ n + ( x 0 - x) 2 Lx x, y^0 - t1 - a ( n - 2) 2 ^ n + ( x0 - x) 2 Lx x ^2 = Sy ( n - 2) = y^0 ts y n + ( x0 - x) 2 ( x - x) 2

41 36 Lx x, x0 Lx x x0 x x, Lx x, x = x, x0, : x 3.3 n, n + ( X0 - x) 2 Lx x 1, :, Sy = y^tsy,, Excel, : :, 3.2 :,, 3.4, :,,, 3.5

42

43 38, y x,, 3.6, 3.6 : 3.7

44 39 : (1 ) y^ = (2 ) R 2 = , (3 ) t ta = , tb = %, 21-2 = 19, t, t = ,,, < a < < b< (4 ) F ( ) 3.3 df SS MS F SignificanceF E = 5 %, ( 1, 19 ), F, F (1. 19) = 4. 38, F, (5 ) S y = , S y y = 59.49% > 15%, (6 )D.W d = , = 1%, n = 21 p = 1, D.W, dl = 0.97 du = 1.16,0 < d < dl,,,,, ,, 3.4:

45 Dependent Variable : Y Met hod: Least Squares Sample : Included obse rvations : 15 Variable Coefficient Std. Error t - Statistic P rob. C X R - squared Adjusted R - squared S.E. of regression Sum squared resid Log likelihood Durbin - Watson stat Mean dependen t var S.D. dependent var Akaike info c riterion Sch warz criterion F - statistic Prob( F - statistic) , F d = 1.179, = 1%, n = 15 p = 1, D.W, d1 = 0.81 du = 1.07, du < d < 4 - du, : 2001 x0 = 1100, y^ 0 = % y^0 tsy n 2 ( x0 - x) + ( x - x) 2 = = ( ) , 95 %, ,

46 41,,,,,, ( ) Y, X1, X2, X p,, Y = X1 + 2 X2 + + p X p + j, X Y ; 0, j ( j = 1, 2p),, X,, : 1. Y1 = X X p X 1 p 2.Y2 = X X p X 2 p N. Y N = X N X N2 + + i X N p, : Y i = Xi1 + 2 Xi2 + + p X ip, : + i N (1 )X1, X2, X p,, (2 ) Y, (3 )0, E( i ) = 0 Cov( i, j ) = 2 i = j 0 ij : E( Y ) = X1 + 2 X2 + + p X p va r( Y ) = 2 I

47 42 YN X1 + 2 X2 + + p X, 2 I) Y = X1 + 2 X2 + + p X p ( ),, n,, : y x1 x2 xp 1 y1 x11 x12 x1 p : 2 y2 x21 x22 x2 p n y n x n1 xn2 xnp j, j, b0 : ) bj ( j = 1p), Y X y = b0 + b1 x1 + b2 x2 + + bp x p + e(,, b0 bj 0 j,, y^ = b0 + b1 x1 + b2 x2 + + bp x p e,, y^ = b0 + b1 x1 + b2 x2 + + bp x p y ei = y i - y^i ( i = 1, 2n) (),,, n i = 1 e2 1 = ( yi - b0 - b1 x1 - b2 x2 - bp x p ) 2, 0, : yi = nb0 + b1 xi1 + b2 x i2 + + bp xip x i1 y i = b0 xi1 + b1 x 2 i2 + b2 x i1 xi2 + + bp xi1 xi p x ip y i = b0 xip + b1 x ip x i1 + b2 xip x i2 + + bp x 2 ip

48 43 b0, b1 bp Y = Xb+ e y1 b1 e1 : Y = y2 b= b2 e = e2 yn bp en 1 x11 x1 2 x1 p X = 1 x21 x2 2 x2 p 1 xn1 xn2 xnp A = X X Ab = B, ( X X ) b= ( X Y ) b= A - 1 B = ( X X ) - 1 B = X Y X Y, b : (1 )b0, b1, bp y i ( ) yi, b0, b1, bp, bi, bj N [ j, 2 ( X X ) - 1 ] (2 ), b0, b1, bp 0, 1, p, 2 ( X X ) - 1 2, ^2, bj t, n - p - 1, : t = bj - j Sb, Sb bj (3 ) b 2 A - 1, Cov( bj, bk ) = 2 Cjk ( j, k = 1, 2p) C= A - 1, A, : 1.,,

49 44 bj xi, bj, 2., : (1 ) ; (2 ); (3 ) ( ),, bj, 0,,,,, bj 0,,,, t H0 : j = 0, H1 : j 0 bj, t = bj Sb bj, t Cj j = S ( n - p - 1) ( j = 1, 2p), Cj j C = A - 1 j S, t tc ( n - p - 1) t > tc ( n - p - 1 ), H0, H1 : 0,, t F, F, : H0 F = ( bj - j ) 2 Cjj ( S ( n - p - 1) ) F(1, n - p - 1 ), F = b 2 j Cjj S ( n - p - 1 )

50 45 : ; ;, ( ),,, : H0 b1 = b2 = b3 = = bp = 0 F F( p, n - p - 1 ) = ( y^i - y) 2 / p ( yi - y^i ) 2 / n - p - 1 F( p, n - p - 1 ) > F F( p, n - p - 1 ) F,,,, : (1 ); (2 ) (), : R 2, R 2 R 2 = ( y^i - y) 2 = 1 - ( yi - y^i ) 2 ( yi - y) 2 ( yi - y) 2 1,,, ( y^i - y) 2, ( y^i - y) 2,, R 2 R 2,, : R 2 = 1 - ( yi - y^i ) 2 / n - p - 1 ( yi - y) 2 / n - 1,,,,, R 2 R 2,, R 2 R 2

51 46 R 2 R = 1 - (1 - R 2 ) n - 1 n - p - 1,, F R 2 : F( p, n - p - 1) = R 2 n - p R 2 p y F y x j ( j = 1, 2p), ( ) (D.W ),D.W, Sy = n ( y - y^) 2 i = 1 n - p - 1,,,,,,,,,, () 1.,,, y x 1 b1 ( 1 ), y x2 b2 ( 1 ), y x 1, x2 b1 ( 2 ), b2 ( 2 ), x1 x2,, b1 ( 1 ) b1 ( 2 ), b2 ( 1 ) b2 ( 2 ), x1 x2, x2 x1,, x1 x2, x1 x2, r12 0, b1 ry1 r1 2, x2 x1,, x1 x2,,,

52 47 2., R 2, R 2 y, ( yi - y) 2 y,, ( y^i - y) 2, ( yi - y^) 2, R 2, S( x1 ) y x1, S( x2 ) y x2, S( x1 x2 ) y x1, x2, S( x1 x2 ) x2, x1, S( x1 x2 ) = S( x2 ) - S( x1 ) x1 x2,, S( x1 x2 ) = S( x1 ) S( x1 ) y x1, x1 x1 x2, x1 x2, x1 S( x2 ), S( x1 x2 ) < S( x1 ),,, y ( ), (1 ) F, t ; (2 ), ; (3 ); (4 ),, r > 0.7, (),, ; ;,,,,

53 48,, : ( ),,,,, () AIC AIC ( An information criterion ), 1973 ( Akaike) ARMA, AR, MA AIC AIC = nlog ^2 + 2 p ^2 2, S p, n, p ^2 = 1 ^ ^ ( Y - X ) ( Y - X ) n ^ = ( X X ) - 1 X Y AIC,, AIC, AIC () Cp ( Mallows), Cp Cp Cp = S^2 + 2 p ^2 = S ( n - p - 1 ), p, p ( S p - 1SS ) Cp,, Cp, Cp,,,,

54 49,, : 3.5 :2000 Excel :, : 3.8

55 50 3.9, M ultiple R R Square Adjusted R Square df SS MS F Significance F E E E Coefficients ts t a t P - v alu e Lo wer95 % Upper 95 % 95.0 % 95.0% In t erce pt X Variabl e E X Variabl e E X Variabl e X Variabl e

56 51, (1 ) y^ = x x x x4 (2 ) R 2 = R 2 = , (3 ) t tb 0 = , tb 1 = , tb 2 = , tb 3 = , tb 4 = %, = 12, t, t0.025 = ,, b3, b4 (4 ) F ( ), = 5%, ( 1, 15 ), F, F0.05 (1, 15) = 4.54, F, (5 ) S y = , Sy y = 1.953% < 15%, (6 )D.W d = , = 1%, n = 17 p = 4, D.W, dl = 0.68 du = 1. 77, dl < d < du,,,,, F,,, x 1 x1 x2 x3 x4 1 x x x ,,,,, X4,,, 3.9

57 52.9 Dependent Variable : Y Met hod: Least Squares Sample : Included obse rvations : 17 Variable Coefficient Std. Error t - Statistic P rob. C X X X R - squared Mean dependent var Adjusted R - squared S.D. dependent var S.E. of regression Akaike info criter ion Sum squared resid Schwarz criterion Log likelihood F - statistic Durbin - Watson stat Prob( F - statistic) b3, D.W x3,, Dependent Variable : Y Met hod: Least Squares Sample : Included obse rvations : 17 Variable Coefficient Std. Error t - Statistic Prob. C X X X R - squared Mean dependent var Adjusted R - squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F - statistic Durbin - Watson stat Prob( F - statistic)

58 53 D W, x4 x3, x4,, : 3.11 Dependent Variable : Y Met hod: Least Squares Sample : Included obse rvations : 17 Variable Coefficient Std. Error t - Statistic Prob. C X X R - squared Mean dependent var Adjusted R - squared S.D. dependent var S.E. of regression Akaike info c riterion Sum squared resid Schwarz criterion Log likelihood F - statistic Durbin - Watson stat P rob( F - statistic) ,,,, y^ = x x2, x1, x2,,,, ( ),,,, y, y

59 54 1. :, ( 2 n ),,,,,,,,,,, ;, 3.,,,,,,,,,,,,,, ;, 4. (2 ) ( 3 ),,,, ( ),,,,,,,,,,,

60 55,,, :??,,,, F ;,,,,,,, : l, bj l S= bj L jy j = 1 = S- S, L jy l x j, : : V j : V j = b2 j C jj S= S- S = S- S = S- S Cj j ( A) Cij j : V ( l) j = ( l) b( j ) 2 C ( j j l) (1 ),, k, V ( l) k V ( l) l) k = min j V( j, F= ( n - l - 1) V k ( l) S ( l) FFa 2,, (2 ),,

61 56 ( l + 1 ) V k k, l + 1 ) = max j V( j ( l + 1 ) V k, F= ( n - ( l + 1 ) - 1 ) V k ( l + 1 ) S ( l + 1 ) = ( n - l - 2) V k ( l + 1 ) ( S ( l) - V k ( l + 1 ) ) FF 1,, ( ) y^ = b0 + b1 x1 + b2 x2 + + bp x p y^ - y = b1 ( x1 - x1 ) + b2 ( x2 - x2 ) + + bp ( x p - xp ) : x i = xi - xi S x i Sx i = n 1 n - 1 ( x i = 1 i - xi ) 2 y^ - y S y = b1 x1 - x1 S y + b2 x2 - x2 S y + + bp x p - xp S y = b1 x1 - x1 Sx 1 S x 1 Sy + b2 x2 - x2 S x 2 S x 2 Sy + + bp x p S x p - x p S x p S y b j = bj S x j S y = bj L j j L0 0, Lj j = ( x j - x j ) 2, L0 0 = ( yi - y) 2 : y^ - y S y x 1 = b1 - x1 Sx 1 x2 + b 2 - x2 Sx b p x p - xp S x p y^ = b 1 x 1 + b 2 x b p x p n ( x i1 i = 1 n n - x 1 ) 2 b i1 i = 1 - x 1 ) ( x ip - x p ) b p = i1 i = 1 - x 1 ) ( y i - y) ( x ip - x p ) ( x i1 - x 1 ) b ( x ip - x p ) 2 = ( x ip - x p ) ( y i - y)

62 57 L 1 L00 L 11 b 1 + L 12 L00 L00 b L L 1 p b 22 L p = L 10 pp Lp1 L 00 b 1 + Lp2 L 11 L 00 b Lpp L 22 L 00 b p = Lp0 L pp k ( k = 1,2, p) L00, Lj j ( j = 1,2p) L 11 L 11 b 1 + L 11 L 11 L 12 b L 22 L 11 L 1 p b p = L pp L 10 L 00 L 11 Lpp Lp1 L11 b 1 + Lpp L p2 L22 b L pp Lpp = r10 r11 b 1 + r1 2 b Vip b p L pp b p = r21 b 1 + r2 2 b r2 pb p = r2 0 rp1 b 1 + rp2 b rpp b p = rp0 RX = r1 1 r1 2 r1 p r2 1 r2 2 r2 p rp1 rp1 rpp b= Rx b= Ry b 1 b 2 b p b= R - 1 x R y : RY = r10 r20 L00 L p0 rp0 Lpp b j = bj L jj L00 bj = b j Sij Cij : Cij = r ( - 1 ) i j : L ii L j j L00 L jj, S= L0 0, S= L0 0 S S ( ), V = L00 V, R = R, S = L00 S t, ti = t i, Ry x i = R y x i,,

63 58 ), r11 r12 r1 p r1 y r21 r22 r2 p r2 y R ( 0 ) =, rp1 rp2 rpp rpy ry1 ry2 ryp ry y,, R m = r ( m) i j m, m + 1 k, m + 1, : r ( m + 1 ) i j = ( m) rkj ( m) rkk i = k, jk rij ( m) - rik ( m) rkj ( m) rkk ( m) ik, jk 1 rkk ( m) i = k, j = k - rik ( m ) rkk ( m) ik, j = k m : ( m ) r11 ( m) r12 ( m) r1 p ( m) r1 y r21 ( m ) r22 ( m) r2 p ( m) r2 y ( m) R ( m) = ryi ( m) : rp1 ( m) rp2 ( m) rpp ( m ) rpy ( m) ry1 ( m) ry2 ( m ) ryp ( m) ry y ( m ) x1, x2 x1, ( l < p), : (1 ) ( m) ( m) (2 )xi, ryi = - riy, = riy ( m), ( m) (3 ) ry y (4) R ( m) k1, k2 k1 k1, k2 k1 ( ),R 0, Cij = r ( ij - 1) Sii Sjj (5 ) : m + 1, xk m) V k ( m + 1 ) = r( k y r ( kk m) 2

64 59 y( / ) : x1 3CaOAl2 O3 ( % ) ; x2 3CaO SiO2 ( % ) ; x3 4CaO Al2 O3 Fe2 O3 ( % ) ;x2 4CaOSiO2 ( % ) x 1 x 2 x 3 x 4 y y x1, x2, x3, x4 ( ) 1. 0 r11 ( 0 ) r12 ( 0 ) r1 p ( 0 ) r1 y ( 0 ) R ( 0 ) = ( 0 ) r21 ( 0 ) r22 ( 0 ) r2 p ( 0 ) r2 y rp1 ( 0 ) rp2 ( 0 ) rpp ( 0 ) rpy ( 0 ) ( 0 ) ( 0 ) ( 0 ) ( 0 ) ry1 ry2 ryp ryy = , F

65 60 F,, F ( ) ; F,,,,, n m, ( n - m - 1), = 0.10, 4 2-3, f1 f2 = 10, F F( 1, 10 ) = 3.28 ( ) : = 1 ( 1 ), (1 )( ), (, ) : V j ( 1 ) = ( rjy ( 0 ) ) 2 rjj ( 0 ) = U = blx y, F, ( 1 ) V1 = ( r1 y ) 2 r11 V2 ( 1 ) = ( r2 y ) 2 ( 1 ) V3 x4, : x4 ( 1 ) F4 r22 = ; V4 = ( 1 ) Fj = ( ) 2 = = ( ) 2 = ( 1 ) = ( n - 2 ) V j 1 - V j = * ( 1 ) ( 1 ) = > 3.28 (2 ), 1 R ( 1 ) R ( 1 ) = = ( rij ( 1 ) )

66 61 x : R ( 0 ) x4, x : 3.13 F = / 1 = / 11 : (1 ), 1 R ( 1 ), V1 Fj ( 2 ) = = ( 2 ) ( 2 ) V j ( 2 ) V 1 ( 2 ) V2 = ( rjy = ( 1 ) ) 2 ( 1 ) rjj (0.5291) = V3, F, ( n - ( l + 1) - 1) Vj ( ) V 1 S ( l + 1 ) ( 2 ) ( 2 ) = S- V1 ( l + 1 ) = * ( 2 ) (13-3 ) x1, x1 = = > 3.28 (2 ) x1 2 : R ( 2) = (3 ) R ( 2 ) :

67 62 x, x4 : b4 ( 2 ) ( 2 ) b1 = = : 3.14 F x1, x4 x1, x4 F, F,, V4 F4 ( 2 ) x4 : F (2 ) = ( r4 y ( 2 ) ) 2 ( 2 ) = ( ) 2 r = ( n - l - 1) V k ( l) ( l) = S = > 3.28 = ( ) (1 ), 2 R ( 2 ), V2 ( 3 ) ( 3 ) V j V2 ( 3 ) = ( 3 ) V3, F, Fj ( 3 ) = = = ( rj y ( 2 ) ) 2 ( 2 ) rj j ( ) = ( n - ( l - 1) - 1) Vj S ( l + 1 ) ( l + 1 ) ( ) = * = > 3.28

68 x, x2 (2 ) x2 3 : R ( 3 ) = (3 ) R ( 3 ) : x1, x4, x2 : b ( 3 ) 4 = ( 3 ) b1 = b2 ( 3 ) = : F x1, x4, x2 x2 F, F,,, x1, x4 ( 3 ) V4 ( 3 ) F4 ) 2 = ( ( 2 ) r4 y ( 2 ) = r4 4 ( 3 ) ( 3 ) = S = ( n ) V4 = < 3.28 F ( ) x2, x4, x4 : (1 ) F x4 (2 )x4,,

69 R 4 ) = (3 )R ( 4 ) : x1, x4 : b1 ( 4 ) ( 4 ) b2 = = : 3.16 F x1, x2 F, F1 ( 4 ) = > 3.28 F2 ( 4 ) = > 3.28 :, ( 5 ) V 3 ) 2 = ( ( 4 ) r3 y ( 4 ) = r33 V 4 ( 5 ) = x4, x4,, ( ) 1. 4 x3, x , R ( 4 ) =

70 65 x, x2 x1, x2, C ( 2 ) = x1, x2 2. bj = b j L00 L jj L0 0 = , L11 = , L22 = b 1 = b 2 = b1 = b2 = b0 = y - b1 x1 - b2 x2 = : y = x x F s = R 2 = n ( y i = 1 i - y^i ) = x1, x2, y x 3, x4 : r3 y 12 2 = ( r3 y ( 4 ) 2 r4 y 12 ) 2 r33 ( 4 ) ry y ( 4 ) = = ( r4 y ( 4 ) r44 ( 4 ) ry y ) 2 ( 4 ) = SPSS : : SPSS, :

71 66.10 : (1 ) Analyze Regression Linear (Dependent), ( Independent),

72 67 2 ) Statistics, 3.12 (3 ) Continue Plots, 3.13 (4 ) Continue Save,

73 68.14 (5 ) Continue Option s 3.15

74 69, : 3.18 ( Descriptive Statistics) Mean Std. Deviation N Y X X X X ( Correlations ) Y X1 X2 X3 X4 Pea rson Corr elation Y X X X X Sig. ( 1 - tailed) Y X X X X

75 ( Variables Entered/ Removed) Varia bles Va riables Model E ntered Removed M e thod 1 X4 Stepwise (Criteria: F-to-enter > = 3.840, F-to-remove < = 2.710). 2 X1 Stepwise (Criteria: F-to-enter > = 3.840, F-to-remove < = 2.710). 3 X2 Stepwise (Criteria: F-to-enter > = 3.840, F-to-remove < = 2.710). 4 X4 Stepwise (Criteria: F-to-enter > = 3.840, F-to-remove < = 2.710). a Dependen t Variable: Y 3.21 ( Model Summary) R Adju st ed Std. E rror of Mod el R R Square Squ are R Square the Es tima te Cha nge Ch a ng e St atistics F df1 df2 Ch a ng e Dur bin Sig. F -Wa tson Ch ang e a b c d e Predictors : ( Constant), X4 Predictors : ( Constant), X4, X1 Predictors : ( Constant), X4, X1, X2 Predictors : ( Constant), X1, X2 Dependent Variable : Y 3.22 ( ANOVA ) Model Sum of Squares df Mean Squa re F Sig. 1 Regression R esidual To tal Regression R esidual To tal Regression R esidual To tal Regression R esidual To tal a b c d e Predictors : ( Constant), X4 Predictors : ( Constant), X4, X1 Predictors : ( Constant), X4, X1, X2 Predictors : ( Constant), X1, X2 Dependent Variable : Y

76 71.23 (Coefficients ) Model Unstanda rdized Coefficie nts Std. B E rror Standardized Coefficie nts Be ta t Sig. 95 % Confide nce Int erval for B Lower U pper Bound Bound Correla tion s Zero- order Partial Part 1 ( C) X ( C) X X ( C) X X X ( C) X X a Depe ndent Variable : Y 3.24 ( Ex clude d Varia bles ) Model Beta In t Sig. Partial Correlation Collinearity Statistics Tolera nce 1 X X E - 02 X X E - 02 X X E X X E - 02 a b c d e P redictors in the Model: (Constant), X4 P redictors in the Model: (Constant), X4, X1 Predictors in the Model : (Constant), X4, X1, X2 Predictors in the Model : (Constant), X1, X2 Dependent Va ria ble : Y

77 Coefficient Correlations Model X4 X1 X2 a 1 Correlations X Covariances X E Correlations X X Correlations X E E - 03 X E E - 02 X Correlations X X X E E E - 02 Correlations X E E E - 04 X E E E Correlations X X Correlations X E E - 03 X E E - 03 Dependent Va riable : Y 3.26 ( Residuals Sta tistics ) Minim um Maximu m Mean Std. Deviation N P redicted Value Std. P redicted Value Standard Error of Predicted Value Adjusted Predicted Value Residual E St d. Residual Stud. R esidual Deleted Residual E Stud. Deleted Residual Mahal. Dista nce Cook s Dista nce Cen ter ed Lever age Value a Dependent Va riable : Y

78

79 ,,, ( ),

80 75,,,,,, :, ( ), : 1. y = b0 + b1 x + b2 x bk x k + e y = b0 + b1 x1 + b2 x bk x k k + e y = ab x e y = ae bx e 3.23

81 76. y = ax b e y = a + b x + e 1 y = a + b x + e y = a + bln x + e 3.26

82 77. y = a + bsin x + e ( ), : 1. y = b0 + b1 [ e x p( b2 x) ] + e y = L + ab x y = L + ae bx 3.27 y = L , ^ y = Le - ae - bx y = La bx 3.28,y = L/ e, x = lna/ b, 3.28

83 78., ^ y = L 1 + ae - bx, y = L/ 2, x = ln a/ b, 3.29 S, S, ( ),,, : y = b0 + b1 x + b2 x bk x k + e X1 = x, X2 = x 2, Xk = x k y = b0 + b1 X1 + b2 X2 + + bk X k + e y = a+ b x + e X = 1 x, y = a + b X + e

84 79 y a + bln x + e X = ln x, y = a + b X + e y = a + bsin x + e X = sin x, y = a + b X + e,,,, ( ), y = ae bx e ln y = ln a + bx + lne Y = ln y, A = ln a, B = b, E = ln e Y = A + Bx + E,, y = ax b e ln y = ln a + bln x + ln e Y = ln y, A = ln a, B = b, X = ln x, E = lne Y = A + B X + E,, - ae - bx y = Le : y L = e- ae - bx ln y L = - aebx ln L y = aebx ln( ln L y ) = ln a - bx

85 80 L y L y > 1, ln L y > 0, Y = ln( ln L y ), A = ln a, Y = A - bx, L,,, y = L 1 + ae - bx : L y - 1 = ae- bx ln( L y - 1) = ln a - bx Y = ln( L y - 1), A = ln a, Y = A - bx, L,,,,,, y,,,,,,,,,,, ( x) ( y),

86 81.28 :,, y^ = a+ b x + e, X = 1 x y = a + b X + e 3.30 :, Excel,,, 3.31

87 82.31 a= , b= , y^ = x 28.5, 29 30,, : % % %

88 ( ) Y t, {Y t, t = t0, t1 }Y t, t = 1, 2,, ,,, Warren Persons (),,,,,,,,,,, ( T) ( S) ( C) ( I)

89 84. (T ),,,,,, 2. (S ), 5, 3. (C ),,,, , 4. (I ),,,,, ( ),, : 1.,,,,,,,,

90 85.,,,,,, , 3.,, 4., ( ),,, 5.,,,,,,,, t, t, t,, ( ),

91 86,,,, : Y t = f( T1, S1, C1, I1 ), : : Y t = T1 St Ct It : Y t = Tt + St + Ct + It Y t Y t = Tt St + Ct It,, ;, ;,,,, ( ),,,,,,, Box - Jenkins 4.1, Box - Jenkins 4.1

92 87,,,,, : n : y1, y2, y3 yn - 1, yn t, t + 1 : Ft + 1 = y = i = 1 t, y t, Ft + 1 t + 1 : t yi et + 1 = yt Ft + 1 t + 2, : Ft + 2 t + 1 yi = y = i = 1 t + 1 et + 2 = yt Ft + 2, : ;, Ft + 1 = y = i = 1 t t yi

93 88 t + 1 yi Ft 2 = y = i = 1 t + 1 = y1 + y2 + + yi + y i + 1 t + 1 = t Ft yt + 1 t + 1 Ft + 3 = t + 1 t + 2 Ft t + 2 yt + 2 = t t + 1 Ft t + 1 yt + 1,,,,,,,,,, t,, : t + 1 t t + 2 Ft + 1 = Ft + 2 = y1 + y2 + + yt t y2 + y3 + + yt + 1 t, = 1 t t i = 1 yi = 1 t + 1 t i = 2 yi, Excel, : : : C5 = AVERAGE( B2: B4 ), : C5, C14,, 4.2

94 ,,,,,, :, t, 12, 4,

95 90 t + 1 Ft 2 = 1 t i = 2 yi = 1 t ( y1 + y2 + yt + yt y1 ) = Ft t ( yt y1 ),, ( ),,,,,,, : Ft + 1 =, i, wi Ft + 1 t i = 1 i y i t i i = 1 t = i = 1 wi y i t, w1 w2 wt, wi = 1 i = 1 Excel,, : :, 0 = 1.5, 1 = 1, 2 = 0.5 : D5 : = ( B B31 + B20.5)/ 3, : D5, D14, : 4.2

96 91.3,,,,,,, : ( t ), ;, ;,,,,,, 4.3

97 92 4.3,,,,,,,,,, Ft + 1 = Ft + 1 n ( y t - yt - n ) n, t Ft y t - n, Ft + 1 = Ft + 1 ( yt - Ft ) n Ft + 1 = 1 n y t n Ft = 1, 0 < < 1, n Ft + 1 =yt + (1 - ) Ft, Ft t Ft + 1 t + 1, t + 1 : St + 1 =yt + (1 - ) St

98 93, : St = y t + ( 1 - a) St - 1, 0.2, 0.5, 0.7, ( ) y t = 0.2 = 0.5 = : = 0.2 S1 = = S2 = = : 4.4

99 94 0.2,,= 0.7,,, (1 - ) n S t - n + 1 St = yt - 1 St =yt + (1 - ) St - 1 =yt + ( 1 - ) St - 1 St - 1 =yt (1 - ) St (1 - ) yt ( 1 - ) 2 yt ( 1 - ) n y t - n + 1 +,, t,, 4.4 = 0.3 = 0.2 = ,,,, ;,, : ( ),

100 , 0.30,,,,,,,, SSE MSE MAE ( ), n, (1 - ) n,,, ;,, ;,,, :,,,, 8 3,,,,,, ( ),,, (), : St + 1 = St + ( yt - St ) St + 1 = St + ( et ) = +,,,, ( 4.5 ),

101 96, : S ( 1 ) t = Yt + (1 - ) S ( 1 ) t - 1 S ( 2 ) t = S ( 2 ) t + ( 1 - ) S ( 2 ) t ,,,,,,, : : at bt Ft + m = at + bt m t ; t ; m at bt, () ( Brown ) 1. (1 ), : S ( t 1 ) = Yt + (1 - ) S ( t 1 - ) 1 S ( t 2 ) = S ( t 1 ) + ( 1 - ) S ( t 2 - ) 1,,,, 1 - bt, bt t

102 97,, (2 ), : t bt Ft + m t t m,, 2. = t + bt m at = S ( 1 ) t + S ( 1 ) t - S ( 2 ) t = 2 S ( 1 ) t - S ( 2 ) t bt = 1 - ( S( t 1 ) - S ( 2 ) t ) ( )

103 98 Excel : : S ( 1 ) 0 = S ( 2 ) 0 = 143,= 0.2 0, D2, E2 143 D3 : = 0.2 * C * D2, D2 6, : E3 E26, : F3 F26, : G3 G2 6, b : = 0.2 * D * E2, : = 2 * D3 - E3, : = 0.2 * (D3 - E3 )/ 0.8, : 1 ( m = 1 ), H4 H27, 225 : = F3 + G3, 2, Ft + m = at + bt m m = 2, F26 = a24 + b24 2 = = ( ) m = 3, F27 = a24 + b24 3 = = ( ), : 4.7

104 ( ) ( H OLT ) 1., ( ) : St =yt + (1 - ) ( St bt - 1 ) bt - 1 St - 1,, St, yt ( ) bt = ( St - St - 1 ) + ( 1 - ) bt - 1, St,,, : : St bt Ft + m = St + bt m t ; t ; m - St - 1,, 2., :

105 100 b0 b0 = ( ) + ( ) + ( ) 3 S0 = 143, b0 = , = = 0.2,= 0.3 D2 143, E D3 : = 0.2 * C * (D2 + E2), : E3 : = 0.3 * (D3 - D2) * E2, : D3, E3, E26, : 1 ( m = 1 ), F3 : = D2 + E2, H27, 225 2, Ft + m = at + bt m : m = 2, F26 = a24 + b24 2 = = ( ) m = 3, F27 = a24 + b24 3 = = ( ), : 4.8

106 ( H OLT ),,,,, bt 0,,,,, h, b h = 1 - (1 - b ) 2,= 1 - b,, 2(1 - b ), 2 - b, ( H OLT )

107 102.8 : ( ) 1.,, S ( 1 ) t = Yt + (1 - ) S ( 1 ) t - 1 S ( t 2 ) = S ( t 1 ) S ( 3 ) t = S ( 2 ) t + ( 1 - ) S ( t 2 - ) 1 + ( 1 - ) S ( 3 ) t - 1,, Ft + m = at + bt m ct m2, at = 3 S ( t 1 ) - 3 S ( t 2 ) + S ( t 3 ) bt = ct = 2 (1 - ) S ( 1 ) t ) 2 [ ( ( S ( 1 ) (1 - ) 2 t - 2 S ( 2 ) t + S ( 3 ) t ) - (10-8 ) S ( 2 ) t + (4-3 ) S ( 3 ) t ],,,

108 103. : 4.9 ( ) Excel, : : S ( 1 ) 0 = S ( 2 ) 0 = S ( 3 ) 0 = 3.4,= 0.250, D2, E2, F2 3.4D3 : = 0.25 * C * D2, D26, : E3 E26, : F3 F26, : G3 G2 6, a : H3 : = 0.25 * D * E2, : = 0.25 * E * F2, : = 3 * D3-3 * E3 + F3, :

109 * ( ( 6-5 * 0.25 ) * D3-2 * (5-4 * 0.25 ) * E3 + ( 4-3 * 0.25) * F3 )/ (2 * 0.75 * 0.75 ), H26, b : I3 : = 0.25 * 0.25 * ( D3-2 * E3 + F3 )/ (2 * 0.75 * 0.75 ), I2 6, c : 1 ( m = 1 ), J4 : = G3 + H3 + I3, J27, 225 2, Ft + m = at + bt m ct m2, : m = 2, F2 6 = a2 4 + b c24 22 = = ( ), : 4.10 :

110 ( ) ( ) 1., St = y t b1 It - L + ( 1 - ) ( St bt - 1 ) = ( St - St - 1 ) + ( 1 - ) bt - 1 It = y t S t + ( 1 - ) It - L L, I,, Ft + m = ( St + bt m) It - L + m : ( St ), ( bt ) ( It ) 2. : 4.11 ( )

111 ,, :,,,,,,, : :, S0 = , b0 = 2.335, : I - 3 = 1.37, I - 2 = 0.81, I - 1 = 0.851, I0 = = 0.2,= 0.2,= 0.3, : D6 : = 0.2 * ( C6/ F2) * ( D5 + E5), E6 : = 0.2 * (D6 - D5) * E5, F6 : = 0.3 * ( C6/ D6) * F2, D7 : = 0.2 * ( C7/ F3) * ( D6 + E6), E7 : = 0.2 * (D7 - D6) * E6, F7 : = 0.3 * ( C7/ D7) * F3, D8 : = 0.2 * ( C8/ F4) * ( D7 + E7), E8 : = 0.2 * (D8 - D7) * E7, F8 : = 0.3 * ( C8/ D8) * F4, D9 : = 0.2 * ( C9/ F5) * ( D8 + E8), E9 : = 0.2 * (D9 - D8) * E8, F9 : = 0.3 * ( C9/ D9) * F5, : D6, E6, F6, D9, E9, F9, F33, : 1 ( m = 1), G6 : = ( D5 + E5) * F2, G7 : = ( D6 + E6) * F3, G8 : = ( D7 + E7) * F4, G9 : = ( D8 + E8) * F5, G6G9 G34, 229 2, Ft + m = ( St + bt m) It - L + m : m = 2, F30 = ( S28 + 2b28 )I26 = ( )0.78

112 ( ) m = 3, F31 = ( S28 + 3b28 )I27 = ( )0.80 = ( ), : 4.12 ( )

113 ) ( ), St = ( yt - It - L ) + ( 1 - ) ( St bt - 1 ) bt = ( St - St - 1 ) + ( 1 - ) bt - 1 It = ( yt - St ) + (1 - ) It - L L, I,, 2. Ft + m = ( St + bt m ) + It - L + m, : :, S0 = , b0 = 2.335, : I - 3 = , I - 2 = , I- 1 = , I0 = = 0.2,= 0.2,= 0.3, : D6 : = 0.2 * ( C6 - F2 ) * (D5 + E5 ), E6 : = 0.2 * (D6 - D5) * E5, F6 : = 0.3 * ( C6 - D6 ) * F2, D7 : = 0.2 * ( C7 - F3 ) * (D6 + E6 ), E7 : = 0.2 * (D7 - D6) * E6, F7 : = 0.3 * ( C7 - D7 ) * F3, D8 : = 0.2 * ( C8 - F4 ) * (D7 + E7 ), E8 : = 0.2 * (D8 - D7) * E7, F8 : = 0.3 * ( C8 - D8 ) * F4, D9 : = 0.2 * ( C9 - F5 ) * (D8 + E8 ), E9 : = 0.2 * (D9 - D8) * E8, F9 : = 0.3 * ( C9 - D9 ) * F5, : D6, E6, F6, D9, E9, F9, F33, X : 1 ( m = 1),

114 109 G : = ( D5 + E5) + F2, G7 : = ( D6 + E6) + F3, G8 : = ( D7 + E7) + F4, G9 : = ( D8 + E8) + F5, G6G9 G34, 229 2, Ft + m = ( St + bt m) + It - L + m : m = 2, F30 = ( S28 + 2b28 + I2 6 = ( ) = ( ) m = 3 F31 = ( S b28 ) + I27 = ( ) = ( ), 4.13, ( ) 4.12, 4.13

115 ,,

116 111.,,,,,,,,,, :,,,,,,,,, ( ),,,,,,,,,,,,,,,

117 112,,,,, (, ) ; : A ( ) B ( ) C( ) A1 B1 C1 A2 B2 C2 A3 B3 C3 : 4.15 A - 1 A - 2 A - 3 B - 1 B - 2 B - 3 :,

118 113 C 1 C - 2 C - 3 : 4.16 A1 A2 A3 B1 B1 S t + 1 = y t + ( 1 - ) S t F t + 1 = S t + 1 S t = ( y t - I t - L ) + ( I - ) S t - 1 F t + m = S t + I t - m + L I t = ( y t - S t ) + ( 1 - ) I t - L S t =( y t / I t - L ) + ( 1 - ) S t - 1 F t + m = S t I t - m+ L I t =( y t / S t ) + ( 1 - ) I t - L S (1 ) t =Y t + ( 1 - ) S ( t 1 - ) 1 S ( t 2 ) =S ( t 1 ) + ( 1 - ) S ( t 2 - ) 1 S t =y t + (1 - ) ( S t b t - 1 ) a t = S (1) t + ( S ( t 1) - S (2) t ) = 2 S (1 t ) - S ( t 2) b t = 1 - ( S( t 1 ) - S ( t 2 ) F t + m = a t + b t m F t + m = S t + b t m b t = ( S t - S t- 1 ) + (1 - ) b t - 1 C1 S (1 ) t =Y t + ( 1 - ) S ( t 1 - ) 1 S ( t 2 ) =S ( t 1 ) S ( t 3 ) =S ( t 2 ) + ( 1 - ) S ( t 2 - ) 1 + ( 1 - ) S ( t 3 - ) 1 a t = 3 S ( t 1) - 3 S ( t 2 ) + S ( t 3) b t = 2( 1 - ) 2 [(6-5 ) S (1) t - (10-8 )S (2) t + (4-3 ) S (3) t ] c t = 2 (1 - ) 2 ( S( t 1 ) - 2 S ( t 2 ) + S ( t 3 ) ) F t + m = a t + b t m c t m 2

119 114 B B3 S t = (y t - I t- L ) + (1 - )(S t b t- 1 ) b t = ( S t - S t- 1 ) + (1 - ) b t - 1 F t + m = ( S t + b t m ) + I t - L + m I t = ( y t - S t ) + ( 1 - ) I t - L S t = y t + (1 - ) ( S I t b t - 1 ) t- L b t = ( S t - S t- 1 ) + (1 - ) b t - 1 F t + m = ( S t + b t m ) I t - L + m I t = y t S t + ( 1 - ) I t - L

120 ( self - adaptive filtering) -,,,,,,, y1, y2 yt, y^t + 1 = w1 yt + w2 yt wn y t - n + 1 y^t + 1 n = i = 1 wi y t - i + 1 t + 1, W i, n yt - i + 1 t - i + 1,,,,, yt + 1 t + 1, yt + 1 = y^t et + 1 = w1 yt + w2 yt wn y t - n et + 1 et + 1 et + 1 = yt y^ t + 1,,,,

121 116 et + 1 ( ),, : w i = wi - ke 2 t + 1, W i, W i, e 2 t + 1 e 2 t + 1 ; k,,,, B.Widrow k : k n 1 i = 1 y2 i n, n ( ) ma x wi et + 1 = y t y^t + 1 = y t w1 yt - w2 yt wn y t - n - 1 e 2 t + 1 = ( yt w1 yt - w2 y t wn y t - n - 1 ) 2 : e 2 t + 1 = e2 t + 1 wi w i = wi et + 1 = 2 et + 1 wi = 2 et + 1 ( - yt - i + 1 ) = - 2 et + 1 yt - i + 1 w i = wi + 2 ket + 1 yt - i ke 2 t + 1 ( i = 1, 2n), n yt - i + 1 t - i + 1 ( ),, :

122 117 :, n 4 : k k n 1 i = 1 y2 i max = = :, W i = 1 n = 1 4 = 0.25, n = 4, t t = 4 y^t + 1 = y^5 = w1 y4 + w2 y3 + w3 y2 + w4 y1 = = 5 et + 1 = e5 = y5 - y^ 5 = 10-5 = 5 W i = wt, + 2 ket + 1 y t - i + 1 : w 1 = = w 2 = = w 3 = = w 4 = = :,,,, : t = 5, y^t + 1 = y^6 = w1 y5 + w2 y4 + w3 y3 + w4 y2 = = 8.28 et + 1 = e6 = y6 - y^6 = = 3.72 w i = wi + 2 ket + 1 yt - i + 1 : w 1 = = w 2 = = w 3 = = w 4 = = 0.291, t = 6, t = 7, t = 8,, t = 10, y1 1, e11 wi,,, t = 4, ( ),

123 118, : w1, w2, w3, w4 11, 12 : 11 y^1 1 = w1 y1 0 + w2 y9 + w3 y8 + w4 y7 12 y^1 2 = w1 y^1 1 + w2 y10 + w3 y9 + w4 y8, Excel, : :, 4,, : K6 : = G6 * C6 + H6 * D6 + I6 * E6 + J6 * F6, : L6 : = B6 - K6, : G7 : = G6 + 2 * * L6 * B5, w1 H7 : = H6 + 2 * * L6 * B4, w2 I7 : = I6 + 2 * * L6 * B3, w3 J7 : = J6 + 2 * * L6 * B2, w4 K6, L6, L7,

124 : G7, H7, I7, J7, K7, L7, L11, : word,, G6 J6 (, ),, 5.5,, :

125 ,,,,, : ( ) ( n),, 4 8, 12 n,,, n 2 6 n, n (),,, wi = 1 n r1, r2 Yule - Walker

126 121 n, w1 = ( ) k r1 ( 1 - r2 ) 1 - r 2 1, w2 = r2 - r r 2 1, k, n,,,, k, k 1 n : 5.8 ( ) Excel, : :, 1 3, wi = 1/ 3

127 122 k = : J5 : = G5 * D5 + H5 * E5 + I5 * F5, : K5 : = C5 - J5, L5 : = K5 * K5, : G6 : = G5 + 2 * * K5 * C5, w1 H6 : = H5 + 2 * * K5 * C4, w2 I6 : = I5 + 2 * * K5 * C3, w3 J5, K5, L5, L6, : G6, H6, I6, J6, K6, L6, L25, L / 21 = : 5.9

128 word,, G5 I5 (, ),, 5.10: , :

129 ,,, 18, :

130 : : w1 = , w2 = , w3 = : y25 = = 20.33( ) y26 = = 21.33( )

131 126 (1 ),, (2 ),,,,,,,,,,,,,,,,, n wi = 1,, i = 1,,,,, 1,,, ( Weight ed Sum) ( ),,,,,,,,,

132 127, ;, 1, ( ) ARMA AR MA : y^t + 1 = 1 yt + 2 yt n y t - n + 1 n : y^t + 1 = w1 yt + w2 yt wn y t - n + 1,, ARMA,, 1973,,,,,,

133 ,,,,, t, y, y^ = F( t), t, (trend projection ) t,,, : y^ = F( t), n n Q = ( y - y^) 2 i = 1 n 2 = [ y - F( t) ] i = 1 (),, : Q = 0 ( i = 1,2p) i p

134 129 :,,, t, y, : ( ) yt ^ = a+ bt 6.1 () yt ^ = b0 + b1 t + b2 t 2 6.2

135 130 ) ^ yt = at b 6.3 ( 1) ( b > 0 ) 6.4 (2 ) ( a < 0) () yt ^ = b0 + b1 t + b2 t 2 + b3 t () yt ^ = a+ blnt

136 131.6 ( ) yt ^ = a+ b 1 t 1 ^ = a + b1 t yt 6.7 () yt ^ = ae bt 6.8

137 132 ) ^ yt = L + ae bt ( a< 0, b< 0 ) yt ^ = L + ab t ( a< 0, 0 < b < 1) 6.9 () yt ^ = La bt - ae - bt yt ^ = Le 6.10 () yt ^ = 1 L + ab t ( )

138 133 yt = L 1 + ae - bt 6.11, t,,, : ( ) t, :

139 134.12,,,,,,,,,,, : 6.2,, 6.2 ( t) yt = a + bt ( yt - yt - 1 ) a + b a + 2 b a + 3 b a + 4 b - b b b t - 1 t a + ( t - 1) b a + tb b b 6.3,,

140 yt b0 b1 b2 ( yt - yt - 1 ) ( t) = + t + t 2 1 b 0 + b 1 + b 2-2 b b 1 + 4b 2 b b 2 3 b b 1 + 9b 2 b b 2 4 b0 + 4 b1 + 16b2 b1 + 7 b2 t - 1 b 0 + ( t - 1 ) b 1 + ( t - 1 ) 2 b 2 b 1 + ( 2t - 3) b 2 t b0 + b1 t + b2 t 2 b 1 + ( 2t - 1) b 2 [ ( y t - y t - 1 ) - ( yt yt - 2 ) ] b 2 2 b2 2 b 2 2 b2 6.4,, 6.4 ( t) y t = b 0 + b 1 t + b 2 t 2 + b 3 t 3 1 b 0 + b 1 + b 2 + b b b b 2 + 8b b b b b 3 2 b b 3-4 b 0 + 4b b b 3 2 b b 3 6 b3 t - 1 b0 + ( t - 1) b1 + ( t - 1) 2 b2 + ( t - 1) 3 b3 2 b 2 + 6( t - 1 ) b 3 6 b 3 t b0 + b1 t+ b2 t 2 + b3 t 3 2 b 2 + 6tb 3 6 b3 6.5,, 6.5 ( t) y t = ae bt ( y 1 / y t - 1 ) t - 1 t ae b ae 2b ae 3b ae 4b ae ( t - 1) b ae tb - e b e b e b e b e b

141 136.6,, 6.6 ( t) yt = a + bc t ( y t - y t - 1 ) y t - y t t - 1 t y t = a + bc yt = a + bc 2 y t = a + bc 3 y t = a + bc 4 yt = a + bc ( t - 1) y t = a + bc t - bc( c - 1 ) bc 2 ( c - 1) bc 3 ( c - 1) bc t - 2 ( c - 1) bc t - 1 ( c - 1) - - c c c c yt yt ,, 6.7 ( t) y t = La bt lg y t = lg L + b t lg a lg y t - lg y t - 1 lg yt - lg yt - 1 lg y t lg y t t - 1 t La b La b2 La b3 La b4 La bt - 1 La bt lg L + blga lg L + b 2 lga lg L + b 3 lga lg L + b 4 lga lg L + b t - 1 lg a lg L + b t lg a - b( b - 1) lga b 2 ( b - 1) lga b 3 ( b - 1) lga b t - 1 ( b - 1)lg a b t ( b - 1) lga - - b b b b, : ;,

142 137,,,, t 6.1, y^t = ae bt ln y^ t = ln a + bt, ln y, t ln yt, ln a b Excel : : ln yt D2 : = LN ( C2 ), D : t ln y t, : 6.13

143 138 : M ultiple R R Square Adjusted R Square df SS MS F Significance F E Coefficie nts t Sta t P - value Lower 95 % Upper 95 % 95.0 % 95.0 % Int ercept E XVariable E : ln a = , b= :

144 139 y t = t e t y^ t = :, ln yt E, F2 : = EXP ( E2 ),, F13, yt F14 : = * ( )^( * 13 ), 2003 y^2 003 = : ,,, :

145 y = a + bx y = a + b/ x y = L + ab x y = L + ax b y = 1/ (1/ L + ab x ) y = a + bx y = a + b( 1/ x) lg( y - L) = lg a + lgbx lg( y - L) = lg a + blg x lg (1/ y - 1/ L) = lg a + lgbx ( ),, (), () 1. y^t = L + ae bt ( a< 0, b< 0 ),,,, y0, y1, yn - 1,, y3 ( n - 1 ) 3 n,, yi, yn - 1 y3 n - 1 y0 = L + ae 0 y1 = L + ae b = L + ae ( n - 1 ) b = L + ae ( 3 n - 1 ) b, n,, n y = yi = nl + a( e0 + i = 0 e b + + e ( n - 1 ) b ) = nl + a enb - 1 e b - 1

146 2 n - 1 y = y i = nl + aenb i = n e nb - 1 ( e 0 + e b + e ( n - 1 ) b ) = nl + ae nb e b n y = y i = 2 n i = nl + nb ae2 ( e 0 + e b + e ( n - 1 ) b 2 nb enb - 1 ) = nl + ae e b - 1 nb ( e nb - 1) 2 ae 3 y - 2 y 2 y - 1 y = ( e b - 1 ) a ( ebn - 1) 2 ( e b - 1 ) 2 y - 1 y = a ( enb - 1 ) 2 ( e b - 1 ) a = (2 y - 1 y) ( eb - 1 ) ( e nb - 1 ) 2 b= ln n 3 y - 2 y 2 y - 1 y L = 1-1 (1 y - aenb n e b - 1 ) = 1 n [ 1 y3 y - (2 y) 2 1 y + 3 y - 22 y ], 3,,,,,, y^t = L + ab t ( a< 0, 0 < b < 1) 2. a = ( 2 y - 1 y) b - 1 ( b n - 1) 2 b= n 3 y - 2 y 2 y - 1 y L = 1 n [ 1 y - a( bn - 1 b - 1 ) ] y^t = La b t 141

147 142 ln yt = ln L + ( ln a) b t, 3. ln a = (2 ln y - 1 ln y) b - 1 ( b n - 1) 2 b= n 3 ln y - 2 ln y 2 ln y - 1 ln y ln L = 1 n [1 ln y - ln a( bn - 1 b - 1 ) ] ^ y t = 1 L + ab t 1 ^ = L + abt yt, a = (2 b= n L ^ yt = 1 + ae - bt 1 ^ = 1 L + a L e - bt yt : 1 b c = e- ( 1 - e - nb ) 1 - e - b 1 y y ) b - 1 ( b n - 1 ) 2 1 y y 1 y y L = 1 n [1 1 y - a( bn - 1 b - 1 ) ] 1 y, 1 2 y, 1 3 y

148 143 1 y = 1 ( n + ac) ( t = 1, t = 0 ) L y = 1 L ( n + ace- nb ), 1 y = 1 L ( n + ace- 2 nb ) 1 y y = ac L ( 1 - e- nb ) 1 y y = ac L e - nb (1 - e - nb ) 2 e - nb = 1 1 y y 1 y y b = 1 n [ln(1 1 y y ) - ln (2 1 y y ) ] 1 a = L (1 c y y ) y y y L = n y y y 1 1 y 3 y - 1 (2 y ) 2 :, 6.14 : : I10 = P OWE R ( ( E14 - E8 )/ ( E8 - E2), 1/ 6 ), b; I9 = ( E8 - E2 ) * ( ( I10-1)/ ( I10^6-1)^2 ), a; I9 = 1/ 6 * ( E2 - I9 * ( ( I10^6 ) - 1 )/ (I10-1) ), L : y^t = t : F 2 : 1/ ( * ( )^ B2 ), F21, , 6.14

149 ,,, ;,,,,,, ( ) 1.,,, 6.15,,,

150 145 A B C yt = ae bt yt = b0 + b1 t + b2 t 2 y^ t = b0 + b1 t + b2 t 2 + b3 t 3, y^t t = e y^t = t t 2 y^t = t t t ,, B C,

151 ,, : 6.16 A B C E E , C,,, ( ),,, : ;, :

152 147,, ;,,,,, ;,,,,,,,,,,,,, 6.17, 6.17,,, A B C,, y^t t = e yt = t t 2 y^t = t t t 3

153 ( ) ( y) ( ) ( y)

154 149,,,, 6.18,,,,,,, A B C

155 150, 6.19: 6.19 ( ) ( ) ,,,,,,,,, :

156 F t + m = a t + b t m ^t, t y = a + bt, t, m F t + m = a t + b t m c t m 2 ^t y = b0 + b1 t + b2 t 2, t, t, m,,,,,,,,

157 ,,,,,,,, (),, 12, 4, ;, ;,,,, :, ( S ) ; (T ) ;,, (C ),, ( I ) : Y = TCI S, ; X - 11 X - 11

158 153 y^t = yf i y ; f i, 35 ( ) , 7.1 : (), : 7.1

159 154 ( ) :,, B13 : = AVERAGE( B2: B12),, M13 N2 : = A VE RAGE ( A2: M2 ),, N13, 112 (),, %,,, 1200, : f i = ( ) ( ) B14 : = B13/ ,, M14 B15 : = B14 * 1200/ ,, M15 7.2

160 155.2 : 7.2 ( ) , : y^i = ( ) f i B16 : = * B15/ 100,, M y^t = ( a + bt) f i : ( a + bt) ; f i,

161 : 7.4 ( ) 7.3,,,, 7.3 : (), (1 ), Ft = a + bt,,, 12 ; EXCEL :

162 157.5 Coefficie nts t St a t P - value Lower 95 % U pper 95 % 95.0 % 95.0 % Intercept E XVariable E M ultiple R R Square Adjusted R Square df SS MS F Significance F E : Ft = t, (2 ), ; E2 : = C2/ D2,, E61