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)

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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)

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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 lt ?1 lt 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 model
Zt ? at ?1
at-1 ?2 at-2 , where ? ? ?
Invertibility condition ?1 ?2 lt 1 ?2 ? ?1
lt 1 ?2 lt 1
Theoretically of PACF
Theoretically of ACF
Dies Down (according to a mixture of damped
exponentials and/or damped sine waves)
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Theoretically of ACF and PACF of The Second-order
Moving Average Model or MA(2) Graphics
illustration (1)
PACF
ACF
PACF
ACF
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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 model
Zt ? ?1 Zt-1
at , where ? ? (1-?1) ? Stationarity
condition 1 lt ?1 lt 1
Theoretically of PACF
Theoretically of ACF
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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 model
Zt ? ?1 Zt-1
?2 Zt-2 at, where ? ?(1??1??2) ?
Stationarity condition ?1 ?2 lt 1 ?2 ? ?1
lt 1 ?2 lt 1
Theoretically of PACF
Theoretically of ACF
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Theoretically of ACF and PACF of The Second-order
Autoregressive Model or AR(2) Graphics
illustration (1)
PACF
ACF
PACF
ACF
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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 model
Zt ? ?1 Zt-1
at ? ?1 at-1 , where ? ? (1??1) ?
Stationarity and Invertibility condition ?1
lt 1 and ?1 lt 1
Theoretically of PACF
Theoretically of ACF
Dies Down (in fashion dominated by damped
exponentials decay)
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Theoretically of ACF and PACF of The Mixed
Autoregressive-Moving Average Model or ARMA(1,1)
Graphics illustration (1)
ACF
PACF
ACF
PACF
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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
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Simulation example of ACF and PACF of The Mixed
Autoregressive-Moving Average Model or ARMA(1,1)
Graphics illustration