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2C. ARMA(P, Q) ARIMA(P, D, Q)

1. MA(Q) AR(P), - - , "" ""
, (, ), \' = (.
. . ,?_X,?O,?L, ,?) "" ( ) = ().
(. ID), H = (˄) ARMA-,
HN = + ?, (1)

= (A0 + ˄_ + +APHN-P) + (ժ- +2-2 + + BQSN_Q). (2)
- : (7 = 1. (1) (2) ,
HN {A.IHN-1 H APHN-P)
= + [ + ժ-L + H^N-2 + BQ?N-Q] (3)

A(L)HN = A0 + 0(1) , (4)

A(L) = 1 -AXL-...~ APLP (5)

0(L) = L + B1L + --- + BQLQ. (6)
, , Q = ,
A(L)HN = WN,
WN = + , .. ()-. (. (5) 2.) , , (3)
" = + ! (7)
.. ()-. (. (4) 2.) (4) ,
HN=P+^\\EN, (8)


, , (9)
1 (AI 1-)
( AI + + 1).
( L2) (3). (8) ( . 5 2) , "" A(L), . . ARMA(P, <7)-.
(37) 2 ( , AJ 1), ( L2) H = (H).
( U(AX)
|| 1 U(AX) , \\ U()
()(1-1)2
LIM .
-5- ^ 1.
" EAI(M)N(AI - AI)2
|AI| < 1 ("" ) AI : U(A\\)
- DA AJ , < 1. N DAIAI
:
SUP SUPLPAI {/(){9) [SI((0)) - AX] < } - ()| 0,
LAIL^L :
SUP SUP|PAI{/(){) [(()) - AX] < ) - ()\\-> 0. \'
^
2.
ARMA(P, Q) ARIMA(P, D, Q)
1. MA(Q) AR(P), - , "" - "".
, (?1,&,(&),), = (. . . , ?_1, ?0) ?1> , ?) " " ( ) ? = (?).
(. ID), H (HN) ARMA-,
HN + ?, (1)

MN ( + AIHN HAPH-P)+ (ܲ-1 +2?-2 B-BQ?N-Q). (2)
: <7 = 1. (1) (2) ,
HN (AI^N-I APHN-P)
= 0 + [ + >_ 4- 62-2 + Ī-] (3)

A(L)HN =0 + 0(1), (4)

A(L) = 1 A\\L ... APLP (5)

0(L) = L + B1L+--- + BQLQ. (6)
, , Q = ,
A(L)HN = Ȅ,
W = + .. ()-. (. (5) 2.) , = 0, (3)
= +/?(?) (7)
. . (<7)-. (. (4) 2.) (4) ,
HN=N+^SN, (8)
A(L)

_ 22 (Q\\
1-(1 + ...+) W
( -I HAP 1).
( 2) (3). (8) ( .
5 2) , "" A(L), . . ARMA(P, <7)-.
(37) 2 ( , AI-L 1), ( L2) H (HN).
(8) ,
= Z җ ()
1 - (AI + )
(. (42) 2.)
(3) , R(K) = COV(/I, /+) > Q
R(K)=AIR{K-L) + --- + APR(K-P) (11)
- , AR(P). (. (43) 2B.)
< Q R(&) , (11), ϗ _FC.
2. ARMA( 1,1), (1) ( 1):
HN A\\HN-I = AQ + + &I?N_I. (12)
|| <1 ("").
A(L) = 1 -AIL, J3(L) = L + BXL (13)
(8)
0 L + &I L
HN = : ^
1 1 A\\L
A0
+ (AX + ܲ) 2 + (14)
, R(K) = COV(FTN,/I+FC) :
R(JFC) =AIR(FC-L), >2,
R(L) = EIR(0) + FTI, (15)
R(0) = AJR(L) + (1 +AI6X +

100 200 300 400 500 600 700 800 900 1000
. 20. H = (HN), ARMA(1,1)- CHN = + AXHNI + 6_ + = 1, AI = 0.5, B\\ = 0.1, 0.1; - = 0 0 ^ N 1000

R(0) = D HN =
1 4- 2ܲ + BJ L-A\\
(16)
.. . R(FC) _ (L + OIFTI)(OI FC-I
PW ~ R(0) ~ 1 + 2AIH + BJ 1 \'
, |AI| < 1 , A RMA (1,1) ( (P,Q)) .
3.
ARMA(P, Q) , , . , = [), = X-I AT*XN D "" < - (<).

. 21. = (), ARIMA(0,1,1)- = + \\ϗ + &? -. / = 1, \\ = 1, & = 0.1; = 0
: , = () ARIMA(P, D, )-, * - (ADA;N) - ARMA(P, Q)-.
:
ADARIMA(P,D,Q) = ARMA(P,Q).
, - ARIMA(0,1,1). , -- HN, (HN) ( 1), ..
= (B0 + B\\L)EN.
( "") S, S = -1, , ,
S=L + L + L2 + --- = {1-L)~\\ ,
= {SH)N, / = + (BO + B\\L)EN = + &? + ?>I?N-I-
, = () "" H = (HN), ( 1),
ARIMA = AR + I + MA,
I - "INTEGRATED" (. . 18 21.)
, [53]. ., , [351].
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: . .. . 1. . .: ,1998. 512 . (, .2). 1998

2C. ARMA(P, Q) ARIMA(P, D, Q):

  1. 2C. ARMA(P, Q) ARIMA(P, D, Q)
- - , - , , - - - - - - -
- - - - - - - - () - - - - - - - - - , - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -