teknik peramalan: materi minggu kedelapan model arima box-jenkins identification of stationer time...
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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
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)
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
Theoretically of ACF and PACF of The First-order Moving Average Model or MA(1) … [Graphics illustration]
ACF
ACF PACF
PACF
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 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)
Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (1)
ACF PACF
ACF PACF
Theoretically of ACF and PACF of The Second-order Moving Average Model or MA(2) … [Graphics illustration] … (2)
ACF PACF
ACF PACF
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 model Zt = + 1 Zt-1 + at , where = (1-1)
Stationarity condition : –1 < 1 < 1
Theoretically of ACF
Theoretically of PACF
Theoretically of ACF and PACF of The First-order Autoregressive Model or AR(1) … [Graphics illustration]
ACF PACF
ACF PACF
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 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
Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (1)
ACF PACF
ACF PACF
Theoretically of ACF and PACF of The Second-order Autoregressive Model or AR(2) … [Graphics illustration] … (2)
ACF PACF
ACF PACF
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 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)
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)
ACF PACF
ACF PACF
Theoretically of ACF and PACF of The Mixed Autoregressive-Moving Average Model or ARMA(1,1)
… [Graphics illustration] … (3)
ACF PACF
ACF PACF
Simulation example of ACF and PACF of The Mixed
Autoregressive-Moving Average Model or ARMA(1,1) … [Graphics illustration]