Transcript PENDEKATAN NEURAL NETWORK UNTUK PEMODELAN TIME …

Analisis Deret Waktu: Materi minggu kedelapan
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Pendahuluan
Naïve Models dan Moving Average Methods
Exponential Smoothing Methods
Regresi dan Trend Analysis
Regresi Berganda dan Time Series Regresi
Metode Dekomposisi
Model ARIMA Box-Jenkins 
Studi Kasus : Model ARIMAX (Analisis Intervensi,
Fungsi Transfer dan Neural Networks)
The Box-Jenkins methodology:
1. Tentative IDENTIFICATION 
 historical data are used to tentatively identify an
appropriate ARIMA model.
2. ESTIMATION 
 historical data are used to estimate the parameters of the
tentatively identified model.
3. DIAGNOSTIC CHECKING
 various diagnostics are used to check the adequacy of the
tentatively identified model,
 if need be, to suggest an improved model, which is then
regarded as a new tentatively identified model.
4. FORECASTING 
 once a final model is obtained, it is used to forecast future
time series values.
Flow Diagram of Box-Jenkins methodology
1. Tentative IDENTIFICATION
NO
2. Parameter ESTIMATION
3. DIAGNOSTIC CHECKING
[ Is the model adequate? ]
 Stationary and nonstationary time series
 ACF dan PACF
(theoritical)
 Testing parameters
 White noise of residual
 Normal Distribution of
residual
YES
4. FORECASTING
 Forecast calculation
General of Time Series Patterns
Time Series Patterns
Stationer
 Nonseasonal
Stationary models
Theoritical ACF and PACF
Trend Effect
 Nonseasonal
Nonstationary models
Seasonal Effect
 Seasonal and
Multiplicative models
Cyclic Effect
 Intervention
models
Stationary and Nonstationary Time Series
Stationer
Nonstationer
The First Differences: Zt = Y2t – Y2t-1
Nonstationer
Differences
Stationer
Sample Autocorrelation Function (ACF)
For the working series Z1, Z2, …, Zn :
ACF for stationary time series
1
cuts off
0
1
8
Lag k
dies down
(exponential)
0
-1
0
8
Lag k
8
Lag k
no oscillation
-1
-1
1
dies down
(exponential)
1
8
oscillation
Lag k
0
-1
dies down
(sinusoidal)
Dying down fairly quickly versus extremely slowly
1
0
Dying down fairly quickly
8
stationary time
series (usually)
Lag k
-1
Dying down extremely slowly
nonstationary time
series (usually)
1
0
-1
8
Lag k
Sample Partial Autocorrelation Function (PACF)
For the working series Z1, Z2, …, Zn : Corr(Zt,Zt-k|Zt-1,…,Zt-k+1)
Calculation of PACF at lag 1, 2 and 3
The sample partial autocorelations at lag 1, 2 and 3
are:
MINITAB output of STATIONARY time series
ACF
PACF
Dying down fairly quickly
Cuts off after lag 2
MINITAB output of NONSTATIONARY time series
ACF
PACF
Dying down extremely slowly
Cuts off after lag 2
Explanation of ACF …
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 t/2 . se(rk)
[MINITAB output]
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 t/2 . se(rk)
General Theoretical ACF and PACF of ARIMA Models
Model
ACF
PACF
MA(q): moving average of order q
Cuts off
after lag q
Dies down
AR(p): autoregressive of order p
Dies down
Cuts off
after lag p
ARMA(p,q): mixed autoregressivemoving average of order (p,q)
Dies down
Dies down
AR(p) or MA(q)
Cuts off
after lag q
Cuts off
after lag p
No order AR or MA
(White Noise or Random process)
No spike
No spike