:
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) :
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;
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). , .
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. , Statistica , . , , . , ( 2), .
1. (p): - ; - 1, .
2. (p): ; 1, 2, .
3. (q): 1, . .
4. (q): 1, 2, . .
5. (p) (q): 1; - 1.