Transcript PENDEKATAN NEURAL NETWORK UNTUK PEMODELAN TIME SERIES

Analisis Deret Waktu: Materi minggu kesebelas
 Model ARIMA Box-Jenkins SEASONAL
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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)
General Theoretical ACF and PACF of ARIMA Seasonal Models
with L (length of seasonal period).
Model
ACF
MA(Q)
Has spike at lag L, 2L, …, QL
and cuts off after lag QL
Dies down at the seasonal
level
AR(P)
Dies down at the seasonal
level
Has spike at lag L, 2L, …, PL
and cuts off after lag PL
Has spike at lag L, 2L, …, QL
and cuts off after lag QL
Has spike at lag L, 2L, …, PL
and cuts off after lag PL
ARMA(P,Q)
Dies down fairly quickly at
the seasonal level
Dies down fairly quickly at
the seasonal level
No seasonal
operator
Has no spikes (contain small
ACF)
Has no spikes (contain small
PACF)
AR(P) or MA(Q)
PACF
Theoretically of ACF and PACF of The First-order
Seasonal L=12 Moving Average Model or MA(1)12
The model
Zt =  + at – 1 at-12
, where  = 
 Invertibility condition : –1 < 1 < 1
Theoretically of ACF
Theoretically of PACF
Dies Down at the seasonal level
(according to a damped
exponentials waves)
Simulation example of ACF and PACF of The First-order Seasonal
L=12 Moving Average Model or MA(1)12 …
[Graphics illustration]
Has spike only at lag 12 (cuts off)
12
Dies down at seasonal lags
Theoretically of ACF and PACF of The First-order Autoregressive Seasonal L=12 Model or AR(1)12
The model
Zt =  + 1 Zt-12 + at , where  =  (1-1)
 Stationarity condition : –1 < 1 < 1
Theoretically of ACF
Theoretically of PACF
Simulation example of ACF and PACF of The First-order Autoregressive Seasonal L=12 Model or AR(1)12 …[Graphics illustration]
Has spike only at lag
12 (cuts off)
Dies down at seasonal lags
12
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| < 1 and |1| < 1
Theoretically of ACF
Theoretically of PACF
Dies Down at the
nonseasonal and
seasonal level
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
Theoretically of ACF and PACF of The Multiplicative Autoregressive 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| < 1 and |1| < 1
Theoretically of ACF
Dies Down at the nonseasonal
and seasonal level
Theoretically of PACF
Cuts off at the lag 1
[nonseasonal] and lag 12
[seasonal] level
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)