.


:




:

































 

 

 

 


 

:

1) , .. p q, RMA (, q);

2) , ..

1 ,..., p θ1,..., θ q

Xt = 1 Xt -1 + + p Xt -p + at + θ1 t 1 ++ θ q t q,

;

3) , .. .

 

 

. , , , , ρ k kk. ρ k kk . , . , , , , , . RMA (, q) R () MA (q), .

 

:

();

(Hirotugu Akaike).

. AR (p). , , τ . AR (p) , τ , t t τ. "" t t τ.

(.1.4), , t t + k , t + k k t + k - 1, t + k - 2,..., t.

Xt 1; - Xt 2; - Xt 3 ..

, 2 Xt - 2 AR (1), Xt = 1,1 Xt - 1 + a 1 t. 3 Xt - 3 AR (2) .. AR (p) , j > p. p, , AR (p) :

;

k > p.

, , AR (p) .

, AR (p). . , [Brockwell, .173 ]

AIC = (-2)* T -1 ln Q + 2* T -1 l,

Q - ; l - ; T - .

AR (p) AIC

- at.

AIC (l) l = 0,1,..., P, P - , p, AIC (l).

 

 

-. - , .. Xt (q), ρ q ≠ 0, ρ l = 0 l > q. - .

AR (p) MA (q) . , { Xt } MA (q), q. , { Xt } AR (p).

ARMA (p, q) AR (p) MA (q), ARMA (p, q) τ > q , . τ > q ARMA (p, q) AR (p), .. .

, : , AR (p) τ > , ARMA (p, q) τ > MA (q). , , ARMA (p, q) .

[ 2 ,.1, .196] , , q, (q ) . , (p q).

q. , q ARMA (p, q). , .

. , Statistica , . , , . , ( 2), .

1. (p): - ; - 1, .

2. (p): ; 1, 2, .

3. (q): 1, . .

4. (q): 1, 2, . .

5. (p) (q): 1; - 1.



<== | ==>
|
:


: 2018-10-15; !; : 190 |


:

:

, , .
==> ...

1015 - | 777 -


© 2015-2024 lektsii.org - -

: 0.012 .