p q AR - MA - , d - . , (ARMA), ARFIMA, . , .
d .
. . 50- , . , - . . , . R S. (R / S -). Yr
(3.45)
Y ,
(3.46)
(3.46) ; xm - . Yn ,
, Y , Y , . Rn .
Rn, , , n. n = T , . , T
R = T . (3.47)
n. (3.47) . , , (3.47) , .
(3.47),
(3.48)
; H .
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R / S , (). R Sn , , .
(3.48)
(3.49)
log log n . (3.49) . .3.38. , 1000 , .3.38. - log (R / S) n log t. ( log (R / S) n Fractan).
)
)
.3.38. () log (R / S) n ()
H d (3.30), H = 0,64 d =0,14.
R / S - : , . , R / S - , , , .
d . , , m ,
- .
, n, .. { x 1,..., xn } k , m , n = k m,
(3.50)
- j ,
(3.51)
(3.50) d, ,
, d = 0 , (3.50), -1. , , (2 d 1).
.
1. m 2 n /2 n m j (3.51).
2. ,
- .
3. lg sm 2 lg m.
4. m 2 d 1. , - 1.
.3.39 d = 0,4 n =1000 . k = 20 m = 50 (3.50), .
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. 3.39
, , .. d. , d . , , , . ( , ) . (semiparametric), [12]. (-) , . .
d . d [15]. : d. [15] , , d .
d. (3.33), ut Su (f), ..
(1 B) d Xt = ut.
Xt S (f)
(3.52)
, Xt . , I (fj , T) - . (3.52) fj , T
d ( - GPH ), :
- ;
- ;
- , ();
(- d) - ;
- , .
ln[ Su (fj , T) / Su (0)] , , .
- GPH ࠠ
ln{ I (fj,T)} = α + β ln[4sin2(fj,T)] + vj,
vj - .
, d < 0 , - . , - , d .
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