<<
>>

2. MA(Q)

1. ( ) "" = (), (.
. 17) , - - .
( "2-") , = () , Ū = 0, 2 <
Ū = 0 (1)
N ^ . ( 0, 1, 2,... .)
, - .
(-) , = () () , , , = () , ~ 2), . 2 = 1. ( , = () - ; , ; . 2D, . III.)

. 17. HN ê = 0.1Ȫ ~<(0,1)


-1
(5)
HN = 4 + Ϊ + -1)
,
(6) (7)
EHN = N, DHN = BL + B\\, COV(/IN,/IN+1) = B0BI, COV(HN,HN+K) = 0, > 1.
, H (HN) (HN /+), HN HN+K > 2 .
, , FRO&I > 0, HN /+ .
BOBI < 0, . ( 3, . IV, .)
(6) (7) , H - (HN) - , . (, , , - () - Ū = 0, DE^ = 1 (5) .) , H = (HN) ( ) . , = () , H = (HN) , , , . H = (HN) , . .
LAW(/IIJ,..., HIN) = LAW(/IIL+JFC,..., HIN+K)
> 1, I\\,..., FC.

FE=I
(8)
- .
"" HN - , HN "" /.
4. (HI,..., H) - , HK FC = 1,..., N
- 2 = \\HN /|2 -: > 00
(9)
2 0 ? R(FC) -> ,
= 1
R(FC) COV(HN,HN+K) H = (HN) - - .
, , , = HN - 0.
FE=L 4 FE=L \' FC=L
, , (9) ,
FC=L 4=1 FC#/ 7
= | EE )->)
/=1 FC=0
J > 0 (<5) , I > (6)
1 \'-1
7 R(*)
1-
I
JFC=0
<6.
> (6)
1-1
N(S) 1-1
^EER(FC) = ^EER(FC) + ^ ERW
= FE=O = FE=O =()- FC=O
N 1 1-1
E 4ER(*)
1
N(S) 1-
N\'
=(5)+ FE=O
EER
I=L JFC=0
N(*) -
EERNJ
(=1 FE=0
(($) < , |R(0)| < CONST,
1 " \'
LIME
N
SSS,
FC=L
(5 > 0 <=.
, ( 1) "- " , HN ( L2) /, , , . ( "", "", " " ., , [439; .
V].)
"" - , HI,H,2,... , "" , , , , , ..
5. , COV(HN,HM) CORR(/IN, HM)
COV(/IN,/IM)
(10)
RR{HN,HM) =
VDHNDHM
- , | CORR(/IN, /IM)| ^ 1.
COV(/IN, HN+K) . R(FC)
()
R(FC)
R(0)\'
P(K) \' CORR(HN,HN+K) -
(7), (1)
\'1, JB = 0,
P(K) = ITVT? FC = 1\'
(12)
+ I , FC > .
, \\ = >/&, ,
(13)
² ()
(1) =
1 + 02 1 - (1/01>2 \'
, , (\\ L/#I) (1).
6. MA(Q):
HN=N + 0(L)EN, (3(L) = B0 + B1L + --- + BQLQ.
,
EHN = P.,
D/I = + BL + +

QK
Y, BJBK+J, K = L,...,Q,
(14)
R(FC) = I ?
> Q.
I 0,
(14) , MA(Q) ( {) - H = (HN), HN > Q, .
. , , , " - H ()" , .
1,^2! , , , ,

FE=I


=1
.
( FC)
71

, (, , (12) (14)) , - (, , , ܳ (12) (14)) .
, , .
7. MA(Q) (), . . ,

HN = - + BJ?N- (15)
J=
, (15) . ,

5>*<, (16)
J=0
(15) .


EHN = /, DHN = (17)
J=


R ( = 53*+-> FC>- (18)
3=
- (15) H = {HN) , HN " ~ (BJ), = ()"
, "" ( ) H - (HN) (15) (16). , , "" "" ( "" , (15)); . 2D , , , [439; . VI, 5].
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: . .. . 1. . .: ,1998. 512 . (, .2). 1998

2. MA(Q):

  1. .
  2. Id. -
  3. 2. MA(Q)
  4. 2C. ARMA(P, Q) ARIMA(P, D, Q)
  5. 2.
  6. 1.8.1.
- - , - , , - - - - - - -
- - - - - - - - () - - - - - - - - - , - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -