Teknik Peramalan: Materi minggu kedelapan

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Teknik Peramalan: Materi minggu kedelapan.  Model ARIMA Box-Jenkins  Identification of STATIONER TIME SERIES  Estimation of ARIMA model  Diagnostic Check of ARIMA model  Forecasting

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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)

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)

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

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

PACF

ACF

PACF

ACF

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

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

PACF

ACF

PACF

ACF

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

PACF

ACF

PACF

ACF

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

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

PACF

ACF

PACF

ACF

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

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

PACF

ACF

PACF

ACF

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

PACF

ACF

PACF

ACF

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

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

ACF

PACF

ACF

PACF

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

PACF

ACF

PACF

ACF

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

PACF

ACF

ACF

PACF

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