Post on 11-Apr-2019
25/02/2015
1
Analisis Deret Waktu
Pertemuan 2
FMA, PKS. Dept. Statistika IPB
Jenis Data
• Cross sectionBeberapa pengamatan diamati bersama‐sama pada periode waktu tertentup p g p pHarga saham semua perusahaan yang tercatat di BEJ pada hari Rabu 27 Februari 2008
• Time SeriesSatu pengamatan diamati selama sekian periode secara teraturHarga saham P.T. TELKOM di BEJ dari 2 Januari 2008 hingga 27 Februari 2008
• Longitudinal/panelBeberapa pengamatan diamati bersama‐sama selama kurun waktu tertentu p p g(gabungan cross section dan time series)Harga saham P.T. TELKOM, P.T. INDOSAT, dan P.T. Mobile8 di BEJ dari 2 Januari 2008 hingga 27 Februari 2008
FMA, PKS. Dept. Statistika IPB
25/02/2015
2
Pola Data Time Series
5
6
7
8
9
30
35
40
45
50
0
1
2
3
4
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
14
16
18
20
25
Konstan Trend
FMA, PKS. Dept. Statistika IPB
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 360
5
10
15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Seasonal Cyclic
Metode Forecasting
Metode forecasting dapat dibedakan menjadi dua kelompok:dua kelompok:•Smoothing
Moving average, Single Exponential Smoothing, Double Exponential Smoothing, Metode Winter
•Modeling/ARIMA, ARCH/GARCH
FMA, PKS. Dept. Statistika IPB
25/02/2015
4
Sekilas Tentang Smoothing
• Prinsip dasar: pengenalan pola data dengan h l k i i l k lmenghaluskan variasi lokal.
• Prinsip penghalusan umumnya berupa rata‐rata.
• Beberapa metode penghalusan hanya cocok untuk pola data tertentuuntuk pola data tertentu.
FMA, PKS. Dept. Statistika IPB
Metode Yang Dibahas
• Single Moving Average• Double Moving Average• Single Exponential Smoothing• Double Exponential Smoothing• Metode Winter untuk musiman aditif• Metode Winter untuk musiman multiplikatif
FMA, PKS. Dept. Statistika IPB
25/02/2015
5
Ilustrasi
• All these methods will be illustrated with the following example: Suppose that a hospital would like to forecast the number of patients arrival from the following historical p gdata:Week Patients Arrival
1 4002 3803 4114 415
• Note: Although week 4 data is given, some methods require that forecast for period 4 is first computed before computing forecast for period 5.
web4.uwindsor.ca/users/b/.../73.../Lecture_5_Forecasting_f04_331.ppt
Time Series MethodsSimple Moving Average
450
A moving average of order N is simply the arithmetic average of the most recent Nobservations For 3 week moving averages N=3;450 —
430 —
410 —
390 —
ent a
rriva
ls
observations. For 3-week moving averages N=3; for 6-week moving averages N=6; etc.
Week
370 —
Pat
i
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
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450 Patient
Time Series MethodsSimple Moving Average
450 —
430 —
410 —
390 —
ent a
rriva
ls
PatientWeek Arrivals
1 4002 3803 411
Given 3-week data, one-step-ahead forecast for week 4 or two step ahead forecast for370 —
Pat
i
Week
| | | | | |0 5 10 15 20 25 30
for week 4 or two-step-ahead forecast for week 5 is simply the arithmetic average of the first 3-week data
450 Patient
Time Series MethodsSimple Moving Average
4f kforecast ahead-step-One
450 —
430 —
410 —
390 —
ent a
rriva
ls
at e tWeek Arrivals
1 4002 3803 411
=4F4for week 370 —
Pat
i
Week
| | | | | |0 5 10 15 20 25 30
25/02/2015
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450
Time Series MethodsSimple Moving Average
Patient450 —
430 —
410 —
390 —
ent a
rriva
ls
PatientWeek Arrivals
1 4002 3803 411
5f kforecast ahead-step-Two
370 —
Pat
i
| | | | | |0 5 10 15 20 25 30
Week
5for week
=5F
450 Patient
Time Series MethodsSimple Moving Average
One-step-ahead forecast for week 5 is computed from the arithmetic average of weeks 2, 3 and 4 data450 —
430 —
410 —
390 —
ent a
rriva
ls
at e tWeek Arrivals
2 3803 4114 415
5f kforecast ahead-step-One
data
370 —
Pat
i
Week
| | | | | |0 5 10 15 20 25 30
5for week
=5F
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450 3 k MA
Time Series MethodsSimple Moving Average
450 —
430 —
410 —
390 —
ent a
rriva
ls
3-week MAforecast
370 —
Pat
i
Week
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
450 3 k MA 6-week MA
Time Series MethodsSimple Moving Average
450 —
430 —
410 —
390 —
ent a
rriva
ls
3-week MAforecast
6-week MAforecast
Week
370 —
Pat
i
| | | | | |0 5 10 15 20 25 30
Actual patientarrivals
25/02/2015
9
FMA, PKS. Dept. Statistika IPB
Single Moving Average
Ide: data pada suatu periode dipengaruhi oleh data beberapa periode sebelumnyabeberapa periode sebelumnyaCocok untuk pola data konstan/stasionerPrinsip dasar:
Data smoothing pada periode ke‐tmerupakan rata‐rata darim buah data dari data periode ke‐t hingga ke‐(t‐m+1) 1 t
t iS X= ∑Data smoothing pada periode ke‐t berperan sebagai nilaiforecasting pada periode ke‐t+1
Ft = St‐1 dan Fn,h = Sn
1t i
i t mm = − +∑
FMA, PKS. Dept. Statistika IPB
25/02/2015
10
Ilustrasi MA dengan m=3Periode (t) Data (Xt) Smoothing (St) Forecasting (Ft)
1 5 - -2 7 - -2 7 - -3 6 6 -4 4 5.6 65 5 5 5.66 6 5 57 8 6.3 58 7 7 6 38 7 7 6.39 8 7.6 710 7 7.3 7.611 7.312 7.3
Pengaruh Pemilihan Nilai m
8.00
9.00
2.00
3.00
4.00
5.00
6.00
7.00
SemulaMA (m=3)MA (m=6)
FMA, PKS. Dept. Statistika IPB
0.00
1.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Waktu
MA dengan m yang lebih besar menghasilkan pola data yang lebih halus.
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Example: Weekly Department Store Sales
• The weekly sales figures (in millions of dollars)
d i h f ll i
Period (t) Sales (y)1 5,32 4,43 5,44 5,85 5,6presented in the following
table are used by a major department store to determine the need for temporary sales personnel.
5 5,66 4,87 5,68 5,69 5,410 6,511 5,112 5,813 514 6,215 5,616 6,717 5,218 5,519 5,820 5,121 5,822 6,723 5,224 625 5,8
Example: Weekly Department Store Sales
Weekly Sales
8
2
3
4
5
6
7
8
Sale
s
Sales (y)
0
1
2
0 5 10 15 20 25 30
Weeks
25/02/2015
12
Example: Weekly Department Store Sales
• Use a three-week moving average (k=3) for th d t t t l t f t f ththe department store sales to forecast for the week 24 and 26.
• The forecast error is
9.53
8.57.62.53
)(ˆ 21222324 =
++=
++=
yyyy
1.9.56ˆ242424 =−=−= yye
Example: Weekly Department Store Sales
• The forecast for the week 26 is
7.53
2.568.53
ˆ 23242526 =
++=
++=
yyyy
25/02/2015
13
Latihan: Weekly Department Store Sales
Period (t) Sales (y) forecast1 5.3• RMSE = 0.632 4.43 5.44 5.8 5.0333335 5.6 5.26 4.8 5.67 5.6 5.48 5.6 5.3333339 5.4 5.33333310 6.5 5.53333311 5.1 5.83333312 5.8 5.66666713 5 5.814 6.2 5.315 5.6 5.66666716 6.7 5.6
RMSE 0.63Weekly Sales Forecasts
3
4
5
6
7
8
Sale
s Sales (y)
forecast
17 5.2 6.16666718 5.5 5.83333319 5.8 5.820 5.1 5.521 5.8 5.46666722 6.7 5.56666723 5.2 5.86666724 6 5.925 5.8 5.966667
5.666667
0
1
2
3
0 5 10 15 20 25 30
Weeks
faculty.wiu.edu/F-Dehkordi/DS-533/.../Moving-average-methods.ppt
Double Moving Average
• Mirip dengan single moving average• Mirip dengan single moving average• Cocok untuk data yang berpola tren• Proses penghalusan dengan rata‐rata dilakukan dua kali– Tahap I: 1 t
S X= ∑p
– Tahap II:
1,1
t ii t m
S Xm = − +
= ∑
2, 1,1
1 t
t ii t m
S Sm = − +
= ∑
FMA, PKS. Dept. Statistika IPB
25/02/2015
14
Double Moving Average (lanjutan)
• Forecasting dilakukan dengan formula• Forecasting dilakukan dengan formula
dengan
2, , ( )t t h t tF A B h+ = +
1, 2,2t t tA S S= −
FMA, PKS. Dept. Statistika IPB
( )1, 2,2
1t t tB S Sm
= −−
Ilustrasi DMA dengan m=3t Xt S1,t S2,t At Bt F2,t
1 12.50
2 11.80
3 12.85 12.38
4 13.95 12.87
5 13.30 13.37 12.87 13.87 0.50
6 13.95 13.73 13.32 14.14 0.41 14.37
7 15.00 14.08 13.73 14.43 0.35 14.55
8 16.20 15.05 14.29 15.81 0.76 14.788 16.20 15.05 14.29 15.81 0.76 14.78
9 16.10 15.77 14.97 16.57 0.80 16.57
10 17.37
11 18.17
12 18.97FMA, PKS. Dept. Statistika IPB