Mot So Vi Du Mo Hinh ARIMA

V d 1Table 9-3 trong Hanke & Wichern cha Transportation Index trong 65 ngy.

Chui thi gian cha dng, khng c yu t ma v

Ly sai phn cp 1

Chui thi gian dng

ACF gim v 0 sau tr 1 gi m hnh MA(1)PACF gim v 0 sau tr 1 gi m hnh AR(1)C ACF v PACF u khng gim theo hm m, do vy cn th c hai m hnh

Chy hi quy: d_indexes c AR(1)

Chy hi quy: d_indexes c MA(1)

ARIMA(0,1,1) tt hn do c AIC nh hn.

V d 2Table 7-3 trong Makridakis cha s liu v s ngi truy cp internet server mi 1 pht trong 100 pht.

Chui thi gian cha dng, khng c yu t ma v

Ly sai phn cp 1

Chui thi gian dng vi =10%

ACF gim gim theo hm mPACF gim v 0 sau tr 3 gi m hnh AR(3)

Chy hi quy: d_users c AR(1) AR(2) AR(3)

Cc phn d nhiu trng

V d 3Table 7-4 trong Makridakis cha s liu v bn hng ca my in v my nh ch t 1/1963 n 12/1972

Chui thi gian cha dng, c yu t ma v

Ly sai phn ma vds_sales = d(sales, 0, 12)

Ly sai phn ma v v cp 1 ds_sales = d(sales, 0, 12)

Chui thi gian dng

ARIMA(p,1,q)(P,1,Q)12PACF gim gim theo hm mACF cao 1 v 12 gi q=1 v Q=1M hnh ARIMA(0,1,1)(0,1,1)12

Chy hi quy: ds1_sales MA(1) SMA(12)

Cc phn d nhiu trng

V d 4Table 7-5 trong Makridakis cha s liu v bn hng ca cc thit b gy nhim mi trng 1/1986 n 10/1996

Ly sai cp 1dl_polution = d(l_polution, 1)

Chui thi gian cha dng, c yu t ma v

PACF cao tr 1 v 2 gi AR(2)PACF cao tr 12 gi SAR(1)M hnh ARIMA(2,1,0)(1,0,0)12

Chy hi quy: d1_polution AR(1) AR2 SAR(12)

Cc phn d nhiu trng