() . 1980. , , .. , , . [7] . : , , , : , , . 12 , .4.1.
4.1 Ѡ
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N () | () | () | |
N () | NN | NA | NM |
() | AN | AA | AM |
() | MN | MA | MM |
D() | DN | DA | DM |
, , . , x 1, x 2,..., xN . xN + 1
(4.4)
ci - .
, xN + 1 , , , .. . , . , . ,
α - 0 < α < 1.
(4.4)
(4.5)
(4.5) (), , . (4.5) :
(4.6)
(4.7)
- N.
(4.6) (4.7) , , .
[8] , μ εt
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Xt = μ + εt.
μ . , μ
β j - .
, μ, . , , , . , , , , () . , [2], , . ARIMA (0,1,1),
(4.8)
εt - 1 (α 1) θ. , α, .
, . (4.8) (4.6) α. ARIMA (0,1,1) 0< α < 2 . , 0< α <1. , α (1; 2), (4.5) , , , .
α . α, 0,1 0,3, , . α, , , . α = 1 , . (4.8), α = 1 a = 0, .
α (0...1) . . . . , a = 0,1 a = 0,9 0,1. a, .
, , , . , t, Lt. (4.6)
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(4.9)
(4.10)
h LN.
4.2. , 12 , 144 . .1.4.
12 . ⍺ = 0,1 .4.5, , 12 , .
.4.5 , ⍺ = 0,1
. -, , . -, . . L t L t = L t- 1 + α *e, e , ( ) . , 0. , .
, ⍺ = 0,9 .4.6.
.4.6 , ⍺ = 0,9
, . , α = 1 , α . α, . ■
, , , Tt, . , γ. (4.9) ,
(4.11)
,
(4.12)
h
(4.13)
(4.11), (4.12) , (4.6).
, , . ⍺ γ, .
4.3. , 4.2, 12 .
.4.7 , ⍺ = γ = 0,1. , , .. . : .
.4.7 , ⍺ = γ = 0,1
0,9, .. ⍺ = γ = 0,9. .4.8.
.4.8 , ⍺ = γ = 0,9
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.4.8 . , , . , , . ■
. Lt, Tt, It , , , t. It , : . , :
mt - (.. ); St - t; ε t - .
xt - It ; - xt / It - . , . - . Lt, Tt It , ⍺, γ, δ. , (0...1).
, LN, TN IN :
(4.14)
(4.15)
(4.16)
s - (s = 4 ; s = 12 ).
, c N,
(4.17)
h = 1, 2, , s.
, c N,
(4.18)
4.4. , 4.2, 4.3 -.
.4.9 , ⍺ = γ = δ = 0,1. , , : . 12 , = 145, , .
.4.9 , ⍺ = γ = δ = 0,1
, ⍺ = γ = δ = 0,9 . 4.10.
.4.10 , ⍺ = γ = δ = 0,9
, ⍺ = γ = δ = 0,1.
" ⍺, γ, δ - . .4.11 4.12.
.4.11
.4.11, a 0,72, . , γ δ 0, .. .
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.4.12 ,
; . ■