metode peramalan deret waktu stk 352
TRANSCRIPT
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Metode Peramalan Deret Waktu β STK 352
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Pendugaan parameter dilakukan setelah menentukan model tentatif, berdasarkan data pengamatan π1, π2, β¦ , ππ.
Metode yang bisa digunakan:
Metode momen
Metode kuadrat terkecil
Metode kemungkinan maksimum
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Method of Moments (MM)
Methods of Moment estimation is a general method where equations for
estimating parameters are found by equating population moments with the
corresponding sample moments:
etc.
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Trivial MM estimates are estimates
of the population mean ( ) and the
population variance ( 2).
The benefit of the method is that the
equations render possibilities to
estimate other parameters.
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Model: ππ‘ = πππ‘β1 + ππ‘
π = π1
ππ = ππ untuk π = 1,2, β¦ π1 = π π1 = π
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ππ‘ = π1ππ‘β1 + π2ππ‘β2 + β― + ππππ‘βπ + ππ‘
πΆππ£(ππ‘, ππ‘βπ) = π1πΆππ£ ππ‘β1, ππ‘βπ + π2πΆππ£ ππ‘β2, ππ‘βπ + β―
+πππΆππ£(ππ‘βπ, ππ‘βπ) + πΆππ£(ππ‘ , ππ‘βπ)
πΎπ = π1πΎπβ1 + π2πΎπβ2 + β― + πππΎπβπ
ππ = π1ππβ1 + π2ππβ2 + β― + ππππβπ
dibagi πΎ0
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ππ = π1ππβ1 + π2ππβ2 + β― + ππππβπ untuk π β₯ 1
Jika π = 1,2, β¦ dengan π0 = 1 dan ππ = πβπ , diperoleh
persamaan umum Yule-Walker:
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Persamaan yule-walker:
ππ = π1ππβ1 + π2ππβ2 + β― + ππππβπ
Sehingga:
π1 = π1+π1π2 π1 = π1+π1 π2
π2 = π1π1+π2 π2 = π1π1+ π2
dan
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Model: ππ‘ = ππ‘ β πππ‘β1
π1 = βπ
1 + π2 π1 = β π
1 + π2
Jika π1 < 0.5 maka:
π = β1
2π1Β±
1
4π12 β 1 =
β1 Β± 1 β 4π12
2π1
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Menduga πΎ0 = πππ ππ‘ menggunakan ragam contoh:
π 2 =1
π β 1
π‘=1
π
ππ‘ β π 2
Untuk model AR(p):
ππ2 = 1 β π1π1 β π2π2 β β― β ππππ π 2
Untuk kasus khusus AR(1)
ππ2 = 1 β ππ1 π 2 = 1 β π1
2 π 2
dengan π = π1
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Untuk kasus MA(q):
ππ2 =
π 2
1 + π12 + π2
2 + β― + ππ2
Untuk kasus ARMA(1,1):
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Misalkan terdapat data deret waktu sbb:
Jika untuk data tersebut menggunakan model AR(1): ππ‘ = πΌ + πππ‘β1 + ππ‘
Tentukan penduga parameternya, yaitu πΌ dan π denganmetode momen!
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If the process mean is different than zero
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we expect the plot to suggest a rectangular scatter around a zero horizontal level with no trends whatsoever
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Increased variation
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Very large magnitudes
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quantile-quantile plots are an effective tool for assessing normality
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Outliers
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To check on the independence of the noise terms in the model, we consider the sample autocorrelation function of the residuals, denoted ππ.
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H0: sisaan saling bebas
H1: sisaan tidak saling bebas
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Lakukan prosedur uji
Ljung-Box berdasarkan
informasi di atas !
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AIC
BIC
MAPE
MSE
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1. Cryer JD, Chan KS. 2008. Time Series Analysis with Application with R. New York: Springer.
2. Pustaka lain yang relevan.