Teknik Peramalan: Materi minggu kedelapan

1. 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)

2. General Theoretical ACF and PACF of ARIMA Models ModelACFPACF MA(q): moving average of order qCuts offDies downafter lag q AR(p): autoregressive of order pDies downCuts offafter lag p ARMA(p,q): mixed autoregressive-Dies downDies downmoving average of order (p,q) AR(p) or MA(q)Cuts offCuts offafter lag qafter lag p No order AR or MANo spikeNo spike(White Noise or Random process)

3. Theoretically of ACF and PACF of The First-order Moving Average Model or MA(1) The modelZt =  + at – 1 at-1 , where =   Invertibility condition : –1 < 1 < 1 Theoretically of PACF Theoretically of ACF

4. Theoretically of ACF and PACF of The First-order Moving Average Model or MA(1) … [Graphics illustration] PACF ACF PACF ACF

5. Simulation example of ACF and PACF of The First-order Moving Average Model or MA(1) … [Graphics illustration]

6. Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) The modelZt =  + at – 1 at-1– 2 at-2 , where =   Invertibility condition : 1 + 2< 1 ; 2  1< 1 ; |2|< 1 Theoretically of PACF Theoretically of ACF Dies Down(according to a mixture of damped exponentials and/or damped sine waves)

7. Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (1) PACF ACF PACF ACF

8. Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (2) PACF ACF PACF ACF

9. Simulation example of ACF and PACF of The Second-order Moving Average Model or MA(2) …[Graphics illustration]

10. Theoretically of ACF and PACF of The First-order Autoregressive Model or AR(1) The modelZt =  + 1 Zt-1 + at, where =  (1-1)  Stationarity condition : –1 < 1 < 1 Theoretically of PACF Theoretically of ACF

11. Theoretically of ACF and PACF of The First-order Autoregressive Model or AR(1) … [Graphics illustration] PACF ACF PACF ACF

12. Simulation example of ACF and PACF of The First-order Autoregressive Model or AR(1) … [Graphics illustration]

13. Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) The modelZt =  + 1 Zt-1 + 2 Zt-2 + at, where = (112)  Stationarity condition : 1 + 2< 1 ; 2  1< 1 ; |2|< 1 Theoretically of PACF Theoretically of ACF

14. Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (1) PACF ACF PACF ACF

15. Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (2) PACF ACF PACF ACF

16. Simulation example of ACF and PACF of The Second-order Autoregressive Model or AR(2) …[Graphics illustration]

17. Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) The modelZt =  + 1 Zt-1 + at  1 at-1, where =  (11)  Stationarity and Invertibility condition : |1|< 1 and |1|< 1 Theoretically of PACF Theoretically of ACF Dies Down(in fashion dominated by damped exponentials decay)

18. Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) …[Graphics illustration] … (1) ACF PACF ACF PACF

19. Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) … [Graphics illustration] … (2) PACF ACF PACF ACF

20. Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) …[Graphics illustration] … (3) PACF ACF ACF PACF

21. Simulation example of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1) …[Graphics illustration]