Teknik Peramalan: Materi minggu kesebelas

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Teknik Peramalan Materi minggu kesebelas

• ? Model ARIMA Box-Jenkins SEASONAL
• ? Identification of SEASONAL TIME SERIES
  ? Estimation of ARIMA seasonal model
  ? Diagnostic
  Check of ARIMA seasonal model
  ? Forecasting
• ? Studi Kasus Model ARIMAX (Analisis
  Intervensi, Fungsi Transfer dan Neural Networks)

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General Theoretical ACF and PACF of ARIMA
Seasonal Models with L (length of seasonal
period).
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Theoretically of ACF and PACF of The First-order
Seasonal L12 Moving Average Model or MA(1)12
The model
Zt ? at ?1
at-12 , where ? ? ? Invertibility
condition 1 lt ?1 lt 1
Theoretically of PACF
Theoretically of ACF
Dies Down at the seasonal level (according to a
damped exponentials waves)
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Simulation example of ACF and PACF of The
First-order Seasonal L12 Moving Average Model or
MA(1)12 Graphics illustration
Has spike only at lag 12 (cuts off)
Dies down at seasonal lags
12
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Theoretically of ACF and PACF of The First-order
Auto-regressive Seasonal L12 Model or AR(1)12
The model
Zt ? ?1 Zt-12
at , where ? ? (1-?1) ? Stationarity
condition 1 lt ?1 lt 1
Theoretically of PACF
Theoretically of ACF
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Simulation example of ACF and PACF of The
First-order Autore-gressive Seasonal L12 Model
or AR(1)12 Graphics illustration
Has spike only at lag 12 (cuts off)
Dies down at seasonal lags
12
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Theoretically of ACF and PACF of The
Multiplicative Moving Average Model or
ARIMA(0,0,1)(0,0,1)12 or MA(1)(1)12
The model
Zt ? at
?1 at-1 ? ?1 at-12 ?1.?1 at-13 , where ?
? ? Stationarity condition ?1 lt 1 and ?1 lt
1
Theoretically of ACF
Theoretically of PACF
Dies Down at the nonseasonal and seasonal level
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Simulation example of ACF and PACF of The
Multiplicative Moving Average Model or MA(1)(1)12
Graphics
illustration
Has spike only at lag 1 (cuts off)
Has spike only at lag 12 (cuts off)
Dies down at non seasonal lags
Dies down at seasonal lags
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Theoretically of ACF and PACF of The
Multiplicative Autore-gressive Model or
ARIMA(1,0,0)(1,0,0)12 or AR(1)(1)12
The model
Zt ?
?1 Zt-1 ?1 Zt-12 ? ?1.?1 Zt-13 at ?
Stationarity condition ?1 lt 1 and ?1 lt 1
Theoretically of ACF
Theoretically of PACF
Cuts off at the lag 1 nonseasonal and lag 12
seasonal level
Dies Down at the nonseasonal and seasonal level
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Simulation example of ACF and PACF of The
Multiplicative Moving Average Model or AR(1)(1)12
Graphics
illustration
Dies down at non seasonal lags
Dies down at seasonal lags
Has spike only at lag 1 (cuts off)
Has spike only at lag 12 (cuts off)