Эконометрика: учебно-методический комплекс 978-5-374-00053-5

Citation preview

М

ы

«

М

ы

ы Е

э

ы ы

. . хи я . . хи в . . и и

к У

ик -

кв 2008 1

» ,

К 519.2 К 22.172 936

М

я

В.С., А . – .:

М.

., С

.

В.П. . 2008. – 144 .

:

-

,

-

061700 «

ISBN 978-5-374-00053-5

»

© © © ©

.

. ., 2008 .Ю., 2008 . ., 2008 , 2008

2

и .......................................................................................................

5

................................................................................................................................

6

..................................................................................................

7

...................................................................................... .................................................................................... ............................................................................ ............................................................................ ............................... ........................................................ ....................................................................................................... ............................................................................

7 8 10 10 11 11 12 15

......................................................................................................

16

......................................................................................... ...................................................................... ...................................................... ........................................................................................................ .......................................................................... ....................................................................................................... ............................................................................

16 18 19 20 20 22 25

1. К 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8.

,

2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7.

.К

3. 3.1. 3.2. 3.3. 3.4. 3.5. 3.6.

........................................

27

............................................................................ ( ) .......................................... ...................................................................................... .................................................................................... .................................................................................................................. ............................................................................

27 29 32 33 33 37

............................................................................................

38

4. 5.

..............................................

41

.......................................................................................................

45

..................................................................................................................................

47

6.

...............................................................................

48

7.

.......................................................................................................................

49

Ы ................................................

65

.................................

66

2.

.........................................................

66

3.

............................................................

67

...................................................................................

67

............................................................................................... ................................................................................................... .К ......................................

67 69 70

5.1.

1. Ц

4.

,

,

1. К 2. 3.

3

4. 5.

5. 6.

......................................................................................... ................................................

72 73

..............................................................................

75

...............................................................................

76

7.1. ................................................................................................................................ 7.2. .................................................................................................................... 7.3. INTERNET.............................................................................................................

76 76 77

..........................................................................................................................

79

7.

1. Ц

85

................................................................................................................................

86

.................................

87

2.

.............................................................................................................

88

3.

...............................................................................

89

4.

,

..................................................................................

4.1. К 4.2. 4.3. 4.4.

5. К 6.

8.

Ы

,

...................................................................................

90

...................................................................................................... ......................................................................................................... ................................................................................... .К ............................................

90 94 97 99

.......................................................................................................

106

.............................................................................................................

107

1....................................................................................................................................... 2....................................................................................................................................... 3....................................................................................................................................... 4....................................................................................................................................... 5....................................................................................................................................... 6....................................................................................................................................... 7....................................................................................................................................... 8....................................................................................................................................... 9....................................................................................................................................... 10.....................................................................................................................................

107 108 110 111 112 113 115 116 117 118

.......................................................................................................................

120

1 ...............................................................................................................................

120

...........................................................................................

123

................................................................................................

141

4

У

5

, -

.

, ?

-

, . – ,

, ,

-

,

. ,

. , ,

-

, .

,

,

, . . . -

,

,

,

,

, . . -

.

6

Ы

1. 1.1. ,

.

.

, –

-

x. . , . , . .

, +1,

-1

-

+1, . –

0,

,

. ( 0

)

,

;

-

1. .

( ),

), .

( :

 x11 ⋅ ⋅ ⋅ ⋅ x1 j ⋅ ⋅ ⋅ ⋅ x1k     ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅   X=  xi1 ⋅ ⋅ ⋅ ⋅ xij ⋅ ⋅ ⋅ ⋅ xik   ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅    x ⋅ ⋅ ⋅ ⋅x ⋅ ⋅ ⋅ ⋅x  nj nk   n1 (n x k), ik(j=1, 2, ..., k).

i-

(

X k-

,

) n

k-

-

. , ( x ), (k×k):  x1   s1       x2   s2  1    .   . x =   , s =   , R=  r21  .   .  r    .   k1  .    s  x   k  k

s

(R)

r12 1 rk 2

. . r1k   . . r2 k  . . . 1 

7

: -

Ы

(

)

R (rjl = rlj) n 2 1 1 x = ∑ xij , s j = xij − x j , ∑ n i =1 n 1 n ∑ xij − x j xil − xl n r jl = i =1 , s j sl

(

)(

)

i-

xij –

j-

:

(1.1)

(1.2) ; ril –

-

,

xj

rjl

xl.

. , . X1 r12 / 3, 4..., k =-

Rjl – Rjl =(-1)

j+l

,

X2 R12

(k-2)-

:

R11 R22

,

(1.3) rjl

×

jl,

Mjl –

,

j-

R. ,

l-

R

. (k-1)-

) X1

r 1 / 2,3,...,k =r 1 = 1 −

-

(

-

: R R11

,

R –

(1.4) R.

1.2.

x f ( x, y ) = Q2 ( x, y) =

−1

2 (1−

[( 2

)

1

2 σx σ y 1 −

2

exp{Q2 ( x, y )} ,

y,

-

(1.5)

y − µy 2 x − µx 2 x − µx y − µ y ) −2 ) ], ⋅ +( σx σy σx σy

:

M ( x) = µ , D( x) = σ , x x 2

M ( y) = µ , D( y) = σ 2 , y y

M[

x − µx y − µ y ]= , ⋅ σx σy 2

≠ 1.

,

, : 8

Ы

M ( y / x) − My = yx ( x − Mx) – M ( y / x) − Mx = xy ( y − My ) –

yx

=

σ

xy

=

σ

y

–

y

x;

x – σ y

x

y.

σ

x;

x

y;

x

ρ2 , . .

, ,

. К

, y (M(y/x)),

y

βyx

(β>0)

x

(β F (α, k – 1, n – k), α, ν 1 = k – 1, ν 2 = n – k. 1.6.

(1.8) , . . X2,...,X ,

X1 F

F–

,

К

1 1+ r Z = ln r 2 1− r

ρ

. 1.

ρo .

,

α,

[0, t1− / n − 3 ] .

, ,

2. r2, ..., rk –

Ho:ρ =ρo

α.

-

r

, |Z −Z r

|

-

o

. .

, n1, n2, ..., nk.

: -

k

r1 , -

Ho:ρ1=ρ2= ...=ρk=ρ. ( zri − z ρ ) 2 i =1 1 / ( n − 3) i Σ k

χ2

.

k

11

zρ

-

Ы

Σzi ni , Σni

zr =

,

( zri − zr ) 2 Σ i =1 1 / ( n − 3) i k

χ2 ν=k−1

α

χ2

.

ν=k−1

( z − z )2 ri r , . < Σ i =1 1 /( n − 3) i k

α.

.

Ho r,

ρ

zr . 1.7.

n=8 (X2)

1 .

(X1),

-

(X3).

. X1 ( 2(

. .

) )

30 20 20

3

20 30 25

40 50 20

35 70 15

45 80 10

25 20 30

50 90 10

30 25 20

: 1.

ρ 13/ 2

2.

ρ 23/1

,

α = 0.05

-

.

γ = 0.95

3. α =0.05

ρ 13/ 2 .

ρ 12/ 3 , ρ 1 / 23

. :

(x j )

1.

j =1, 2, 3, (S j ), : 30 + 20 + 40 + 35 + 45 + 25 + 50 + 30 x1 = = 34.375 8 x 2 = 48 .125 x3 = 18 .75

S1=9,49

12

r 12 , r 13

.

.

r 23

Ы

S 2 = 26,68 .

S3 = 6,48 r12 =

x1 x2 − x1 x 2 1875 − 34.375 × 48,125 220.70 = = = 0.871, S1 S 2 9.49 × 26,68 9.49 × 26.68

1 n 1 ∑ xi1 xi 2 = (30 × 20 + 20 × 30 + 40 × 50 + ... + 30 × 25) = 1875 . n i =1 8 : 0.871 −0.874  1  34.38  9.49        1 .  ; S=  26.68  ; R=  0.871 X =  4812 −0.879 .      6.48  1   18.75  −0.874 −0.879   x1 x2 =

2. r 12 / 3 = −

R12 , R11 × R22

R12 – R11

r 12

R22

R12 = (− 1) × 3

R11 = (− 1) × 2

R22 = (− 1) × 4

r12 / 3 =

R,

0.871 − 0.879 = −0.103 − 0.874 1

1-

2-

− 0.879 1 = 0.227 − 0.879 1

− 0.874 1 = 0.236 − 0.874 1

0.103 = 0.445 0.227 × 0.236 : r13/2=-0.462

r 23/1 =-0.494.

ν = n−l−2 = 5) = 0.754, l– ). l = 1. r