Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME...
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Transcript of Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME...
![Page 1: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/1.jpg)
Teknik Peramalan: Materi minggu kedelapan
Model ARIMA Box-Jenkins Identification of STATIONER TIME
SERIES Estimation of ARIMA model Diagnostic Check of ARIMA model Forecasting
Studi Kasus : Model ARIMAX (Analisis Intervensi, Fungsi Transfer dan Neural Networks)
![Page 2: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/2.jpg)
General Theoretical ACF and PACF of ARIMA Models
Model ACF PACF
MA(q): moving average of order q Cuts off Dies down after lag q
AR(p): autoregressive of order p Dies down Cuts off after lag
p
ARMA(p,q): mixed autoregressive- Dies down Dies down moving average of order (p,q)
AR(p) or MA(q) Cuts off Cuts off after lag q after lag p
No order AR or MA No spike No spike (White Noise or Random process)
![Page 3: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/3.jpg)
Theoretically of ACF and PACF of The First-order Moving Average Model or MA(1)
The model Zt = + at – 1 at-1 , where =
Invertibility condition : –1 < 1 < 1
Theoretically of ACF
Theoretically of PACF
![Page 4: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/4.jpg)
Theoretically of ACF and PACF of The First-order Moving Average Model or MA(1) … [Graphics illustration]
ACF
ACF PACF
PACF
![Page 5: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/5.jpg)
Simulation example of ACF and PACF of The First-order Moving Average Model or MA(1) … [Graphics illustration]
![Page 6: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/6.jpg)
Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2)
The model Zt = + at – 1 at-1 – 2 at-2 , where =
Invertibility condition : 1 + 2 < 1 ; 2 1 < 1 ; |2| < 1
Theoretically of ACF
Theoretically of PACF
Dies Down (according to a mixture of damped
exponentials and/or damped sine waves)
![Page 7: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/7.jpg)
Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (1)
ACF PACF
ACF PACF
![Page 8: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/8.jpg)
Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (2)
ACF PACF
ACF PACF
![Page 9: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/9.jpg)
Simulation example of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration]
![Page 10: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/10.jpg)
Theoretically of ACF and PACF of The First-order Autoregressive Model or AR(1)
The model Zt = + 1 Zt-1 + at , where = (1-1)
Stationarity condition : –1 < 1 < 1
Theoretically of ACF
Theoretically of PACF
![Page 11: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/11.jpg)
Theoretically of ACF and PACF of The First-order Autoregressive Model or AR(1) … [Graphics illustration]
ACF PACF
ACF PACF
![Page 12: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/12.jpg)
Simulation example of ACF and PACF of The First-order Autoregressive Model or AR(1) … [Graphics illustration]
![Page 13: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/13.jpg)
Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2)
The model Zt = + 1 Zt-1 + 2 Zt-2 + at, where =
(112)
Stationarity condition : 1 + 2 < 1 ; 2 1 < 1 ; |2| < 1
Theoretically of ACF
Theoretically of PACF
![Page 14: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/14.jpg)
Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (1)
ACF PACF
ACF PACF
![Page 15: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/15.jpg)
Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (2)
ACF PACF
ACF PACF
![Page 16: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/16.jpg)
Simulation example of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration]
![Page 17: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/17.jpg)
Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1)
The model Zt = + 1 Zt-1 + at 1 at-1 , where =
(11)
Stationarity and Invertibility condition : |1| < 1 and |1| < 1 Theoretically of
ACFTheoretically of
PACF
Dies Down (in fashion dominated by damped exponentials decay)
![Page 18: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/18.jpg)
Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) … [Graphics illustration] … (1)
ACF PACF
ACF PACF
![Page 19: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/19.jpg)
Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) … [Graphics illustration] … (2)
ACF PACF
ACF PACF
![Page 20: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/20.jpg)
Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1)
… [Graphics illustration] … (3)
ACF PACF
ACF PACF
![Page 21: Teknik Peramalan: Materi minggu kedelapan Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic.](https://reader036.fdocuments.in/reader036/viewer/2022081420/56649e145503460f94afe5ab/html5/thumbnails/21.jpg)
Simulation example of ACF and PACF of The Mixed
Autoregressive-Moving Average Model or ARMA(1,1) … [Graphics illustration]