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Model ARIMA Box-Jenkins. Pertemuan 11. Metodologi Box-Jenkins:. . 1. Identifikasi model untuk sementara  data lampau digunakan untuk mengidentifikasi model ARIMA yang sesuai. 2. Penaksiran parameter pada model sementara

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metodologi box jenkins
Metodologi Box-Jenkins:

1. Identifikasi model untuk sementara

 data lampau digunakan untuk mengidentifikasi model ARIMA yang sesuai.

2. Penaksiran parameter pada model sementara

 data lampau digunakan untuk mengestimasi parameter dari model sementara.

3. Pemeriksaan diagnosa, apakah model memadai?

 berbagai diagnosa digunakan untuk memeriksa kecukupan model sementara.

jika memenuhi, maka model bisa digunakan untuk meramalkan. Bila tidak, maka ditetapkan model sementara yang baru.

4. Meramalkan

 model sementara yang sudah sesuai dapat digunakan untuk meramalkan nilai yang akan datang.

diagram metodologi box jenkins
Diagram Metodologi Box-Jenkins

 Stationary dannon- stationary ACF dan PACF

1. Identifikasi model sementara

2. Estimasi parameter

Tdk

 Testing parameter

 Tingkat residu  Distribusi Normal dari residual

3. Pemeriksaaan diagnosa

[ apakah modelmemadai? ]

Ya

4. Meramalkan

 Perhitungan peramalan

pola umum data time series
Pola umum data time series

 Nonseasonal Stationary models

 Nonseasonal Nonstationary models

 Intervention models

 Seasonal and Multiplicative models

ACF dan PACF

perbedaan pertama z t y2 t y2 t 1
Perbedaan pertama: Zt = Y2t – Y2t-1

Nonstationer

Differences

Stationer

sample autocorrelation function acf
Sample Autocorrelation Function (ACF)

For the working series Z1, Z2, …, Zn :

acf for stationary time series

1

1

0

8

8

Lag k

0

Lag k

-1

-1

1

1

0

0

8

8

Lag k

Lag k

-1

-1

ACF for stationary time series

dies down (exponential)

cuts off

no oscillation

dies down (sinusoidal)

dies down (exponential)

oscillation

dying down fairly quickly versus extremely slowly

1

1

Lag k

0

0

8

-1

-1

Lag k

8

Dying down fairly quickly versus extremely slowly

Dying down fairly quickly

stationary time series (usually)

Dying down extremely slowly

nonstationary time series (usually)

sample partial autocorrelation function pacf
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
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
MINITAB output of STATIONARY time series

ACF

PACF

Dying down fairly quickly

Cuts off after lag 2

minitab output of nonstationary time series
MINITAB output of NONSTATIONARY time series

ACF

PACF

Cuts off after lag 2

Dying down extremely slowly

explanation of acf minitab output
Explanation of ACF … [MINITAB output]

+

+

 t/2 . se(rk)

 t/2 . se(rk)

general theoretical acf and pacf of arima models
General Theoretical ACF and PACF of ARIMA Models

ModelACFPACF

MA(q): moving average of order qCuts offDies downafter lag q

AR(p): autoregressive of order pDies downCuts offafter lag p

ARMA(p,q): mixed autoregressive-Dies downDies downmoving average of order (p,q)

AR(p) or MA(q)Cuts offCuts offafter lag qafter lag p

No order AR or MANo spikeNo spike(White Noise or Random process)