, :
1. , , ( ).
2. , . , .
3. , .
.
AR (1)
0=0; ( ) σ2=0,2; =0,8.
Xt = 0,8 Xt - 1 + at.
100 .2.9. .2.10 , ( ), , .2.9, AR (1).
.2.9. AR (1)
.2.3, 0,84, =0,8.
.2.10. () ()
2.3 AR (1)
. .2.11., ( ), . ( ).
.2.12 AR (1) ࠠ
Xt = - 0,8 Xt - 1 + at,
.
)
)
.2.11 () ()
, AR (1)
ρ(1) = γ(1) / γ(0) = .
, ( 1) , . , , , . .2.9 2.12 , , .
.2.12. AR (1) = - 0,8
.2.13.
|
|
.2.13 () () AR (1)
, , : ρ1(1)~ 1=0,841; ρ2(1)~ 1= - 0,839 ( . 2.3 2.4).
2.4 AR (1)
AR (2)
Xt = 1 Xt - 1 + 2 Xt - 2 + at.
: 1 = 2 = 0,25; at .
.2.15 , - .2.16.
.2.16 AR (2)
, , , , AR (2).
)
)
.2.16. () () AR (2)
.2.5 AR(2), .
2.5 AR (2)
, AR (2).
, .
MA (1)
Xt = at - θ at -1. : θ = 0,8; at . .2.17.
.2.17. (1)
. 2.18, (1).
)
)
.2.18 () () (1)
.2.6 θ (1), , .
2.6 (1)
, , .. θ = - 0,8. (.2.19), (.2.20) (.2.7) .
.2.19. (1)
)
)
.2.20. () () (1)
2.7 (1)
, (1).
.
(2)
Xt = at + 1,0 at -1 - 0,5 at -2. : θ1 = 1,0; θ2 = -0,5; at . .2.21, (2) - .2.8.
.2.21. (2)
|
|
.2.8, θ1 =1,15 θ2 =-0,60 , . .
2.8 (2)
, .
ARMA ( 1,1 )
Xt = 0,5 Xt - 1 + at - 0,5 a t - 1. 100 .2.22.
.2.22. ARMA ( 1,1 )
.2.23, .
)
)
.2.23 - () ()
[8 ] . , .2.9 .
2.9
ARMA(1,1); | 1 | 1 |
ARMA(1,1); | 1 | 1 |
ARMA(p,q) | q | p |
.2.10 , ARMA (1,1).
2.10
.2.10, .