Teknik Forecasting Pendekatan Basis
Teknik
Hasil
Peramalan ekstrapolatif
Ekstrapolasi trend
Analisis rangkaian-waktu Teknik benang-hitam Teknik OLS Pembobotan eksponensial Transformasi data Metode katastrofi
Projeksi
Peramalan Teoretis
Teori
Pemetaan teori Analisis jalur Analisis Input Input-Output Output Pemrograman linier Analisis regresi Estimasi interval Analisis hubungan
Prediksi
Peramalan intuitif
Penilaian subjektif
Delphi konvensional Delphi kebijakan Analisis dampak-silang Penilaian kelayakan
Konjektur
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Asumsi Peramalan Ekstrapolatif 1. Keajegan (persistence): Pola yang terjadi di masa lalu akan tetap terjadi di masa mendatang. Mis: jika konsumsi energi di masa lalu meningkat, ia jika konsumsi energi di masa lalu meningkat, ia akan selalu meningkat di masa depan. 2. Keteraturan (regularity): Variasi di masa lalu akan secara teratur muncul di masa depan Mis: jika secara teratur muncul di masa depan. Mis: jika banjir besar di Jakarta terjadi setiap 16 tahun sekali, pola yg sama akan terjadi lagi. 3. Keandalan (reliability) dan kesahihan (validity) data: Ketepatan ramalan tergantung kepada keandalan dan kesahihan data yg tersedia. Mis: yg data ttg laporan kejahatan seringkali tidak sesuai dg insiden kejahatan yg sesungguhnya, data ttg gaji bukan merupakan ukuran tepat dari pendapatan bukan merupakan ukuran tepat dari pendapatan masyarakat. 2
Klasifikasi Metode Peramalan … Forecasting Method Objective Forecasting Methods Time Series M th d Methods
Subjective (Judgmental) Forecasting Methods
Causal Methods M th d
Analogies
Naïve Methods
Simple Regression
Moving Averages
Multiple Regression
Exponential Smoothing
Neural Networks
Delphi
PERT
Simple Regression
Survey techniques
ARIMA Neural Networks References :
Combination of Time Series – Causal Methods
Intervention Model Transfer Function (ARIMAX) VARIMA (VARIMAX) Neural Networks
Makridakis et al. Hanke and Reitsch Wei, W.W.S. Box, Jenkins and Reinsel
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Ilustrasi M d l Matematis Model M i …
Klasifikasi Metode Peramalan :
Forecasting Method Objective Forecasting o ecast g Methods et ods Time Series Methods Yt= f (Yt-1, Yt-2, … , Yt-k)
Subjective (Judgmental) Forecasting o ecast g Methods et ods
Causal Methods Yt= f (X1t, X2t, … , Xkt)
Examples : ¨ sales l (t) = f ((sales l (t-1), sales l (t-2), …))
Examples : ¨ sales l (t) = f ((price i (t), advert d t(t), …))
Combination of Time Series – Causal Methods Yt= f (Yt-j , j>0 ; Xt-i , i≥0) Examples : ¨ sales(t) = f (sales(t-1), advert(t), advert(t-1), …)
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Klasifikasi Model Time Series : Berdasarkan B t k atau Bentuk t Fungsi F i… TIME SERIES MODELS LINEAR Time Series Models
NONLINEAR Time Series Models ARIMA Box-Jenkins
Models from time series theory ¨ nonlinear autoregressive, etc ...
Intervention Model
Flexible statistical parametric models ¨ neural network model, etc ...
T Transfer f F Function ti (ARIMAX)
State-dependent, p , time-varying y g parap meter and long-memory models
VARIMA (VARIMAX)
Nonparametric models Models from economic theory
References : Timo Terasvirta, Dag Tjostheim and Clive W.J. Granger, (1994) “Aspects Aspects of Modelling Nonlinear Time Series” Series Handbook of Econometrics, Volume IV, Chapter 48. Edited by R.F. Engle and D.I. McFadden
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POLA O DATA Time Series … e Se es General Time Series General Time Series “PATTERN” PATTERN Stationer Trend (linear or nonlinear) Seasonal (additive or multiplicative) ( p ) Cyclic Calendar Variation Calendar Variation
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General of Time Series Patterns … Time Series Patterns Stationer
9 Nonseasonal Stationaryy models
Trend Effect
9 Nonseasonal Nonstationaryy models
Seasonal Effect
9 Seasonal and p models Multiplicative
Cyclic Effect
9 Intervention models
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Contoh DATA EKONOMI … 1 Time S eries Plot of Inflasi 3
1
Eids holiday effects
2
12
12
12
Inflasi
1
11 12
1
11
11
0
-1 Month Yea Year
Jan 1999
Jan 2000
Jan 2001
Jan 2002
Jan 2003
Jan 2004
Jan 2005
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Contoh DATA EKONOMI … 2
Krisis di Indonesia Pertengahan 1997
Reference : Badan Pusat Statistik (BPS) Indonesia
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Contoh DATA EKONOMI … 3 Krisis di Indonesia Terjadi Mulai Pertengahan 1997
Reference : Dinas Perhubungan Jawa Timur
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Model‐model Time Series Regression g
1. Model Regresi untuk LINEAR TREND Yt = a + b.t + error
Ö t = 1, 2, … (dummy waktu)
2. Model Regresi untuk Data SEASONAL (variasi konstan) Yt = a + b1 D1 + … + bS‐1 DS‐1 + error dengan : : D1, D D2, …, D DS‐1 adalah dummy waktu dalam S 1 adalah dummy waktu dalam satu periode seasonal.
3. Model Regresi untuk Data dengan LINEAR TREND dan SEASONAL ( (variasi konstan) ) Yt = a + b.t + c1 D1 + … + cS‐1 DS‐1 + error  Gabungan model 1 dan 2.
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Problem 4: Hasil Regresi Trend dg MINITAB Problem 4: Hasil Regresi Trend dg MINITAB … (continued)
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Problem 4: Hasil Regresi Trend dg MINITAB Problem 4: Hasil Regresi Trend dg MINITAB …
(continued)
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Problem 5: Regresi Data Seasonal … (Data Electrical Usage) Problem 5: Regresi Data Seasonal (Data Electrical Usage)
Time Series Plot (Data Time Series Plot (Data seasonal) 14
Problem 5: Hasil regresi dengan MINITAB Problem 5: Hasil regresi dengan MINITAB …
MTB > Regress 'Kilowatts' 3 'Kuartal-1'-'Kuartal-3'
The regression equation is Kilowatts = 722 + 281 Kuartal.1 - 97.4 Kuartal.2 - 202 Kuartal.3 Predictor Constant Kuartal.1 Kuartal.2 Kuartal.3 S = 30.84
Coef 721.60 281.20 -97.40 -202.20
SE Coef 13.79 19.51 19.51 19.51
R-Sq = 97.7%
Analysis of Variance Source DF Regression 3 Residual Error 16 Total 19
SS 646802 15220 662022
T 52.32 14.42 -4.99 -10.37
P 0.000 0.000 0.000 0.000
R-Sq(adj) = 97.3%
MS 215601 951
F 226.65
P 0.000
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Problem 6: Regresi Data Trend Linear dan Seasonal Problem 6: Regresi Data Trend Linear dan Seasonal …
Time Series Plot (Data trend dan seasonal) 16
Problem 6: Hasil regresi dengan MINITAB Problem 6: Hasil regresi dengan MINITAB …
Dummy Variable 17
Problem 6: Hasil regresi dengan MINITAB Problem 6: Hasil regresi dengan MINITAB …
MTB > Regress 'Sales' 4 't' 'Kuartal.1'-'Kuartal.3' The regression equation is Sales = 413 + 19.7 t + 130 Kuartal.1 - 108 Kuartal.2 - 228 Kuartal.3 16 cases used d 4 cases contain t i missing i i values l Predictor Constant t K artal 1 Kuartal.1 Kuartal.2 Kuartal.3
Coef 412.81 19.719 130 130.41 41 -108.06 -227.78
S = 35.98
SE Coef 26.99 2.012 26 26.15 15 25.76 25.52
R-Sq = 96.3%
T 15.30 9.80 4 4.99 99 -4.19 -8.92
P 0.000 0.000 0 0.000 000 0.001 0.000
R-Sq(adj) = 95.0%
Analysis of Variance Source Regression Residual Error Total
DF 4 11 15
SS 371967 14243 386211
MS 92992 1295
F 71.82
P 0.000
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Problem 6: Hasil regresi dengan MINITAB Problem 6: Hasil regresi dengan MINITAB …
Forecast
Time Series Plot (Data dan Ramalannya) 19
Perbandingan ketepatan ramalan antar metode Perbandingan ketepatan ramalan antar metode …
K Kasus Sales Video Store S l Vid St
Model
K Kasus Sales Data Kuartalan S l D t K t l
Kriteria kesalahan ramalan MSE
MAD
MAPE
Double M.A.
66.6963
6.68889
0.9557
Holt’s H lt’ Method
28.7083
4.4236
0.6382
Regresi Trend
21.6829
3.73048
0.5382
Holt’s Method : Alpha (level): 0.202284 (level): 0 202284 Gamma (trend): 0.234940
Kriteria kesalahan ramalan
Model
MSE
MAD
MAPE
Winter’s Method
4372.69
52.29
9.67
Regresi Trend & Seasonal
890.215
23.2969
4.3122
Winter’s Method : Alpha (level): 0.4 Gamma (trend): 0.1 Delta (seasonal): 0.3 20
Contoh • Tahun 2000: Penjualan mobil = Rp. 300 M Indeks harga mobil = 135 • Tahun 2001: Penjualan mobil = Rp. 350 M Indeks harga mobil = 155 Pertanyaan: • Berapa peningkatan nominal ? Berapa peningkatan nominal ? • Berapa peningkatan riilnya ?
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Perhitungan g • Peningktan Nominal Peningktan Nominal • Rp. 350 M – p Rp. 300 p M = Rp. 50 M
• Peningktan Riil g Penjualan tahun 2000 (Rp. 300M) (100/135) = Rp. 222,222 M Penjualan tahun 2001 ( (Rp. 350M) (100/155) )( / ) = Rp. 225,806 M Peningkatan: 225,806M – 222,222 M = Rp. 3,584 M Rp. 3,584 M 22
Mr. Aringanu akan menganalisis laju pertumbuhan penjualan toko yang menjual 70% mebeler dan 30% alat rumah tangga.
Tahun Penj IH Mebel IH ART 1983 42.1 111.6 105.3 1984 47.2 47 2 117 2 108.5 117.2 108 5 1985 48.4 124.2 109.8 1986 50.6 128.3 114.1 1987 55.2 136.1 117.6 1988 57.9 139.8 122.4 1989 59.8 145.7 128.3 1990 60.7 156.2 131.2
IH Penj Penj. Riil 109.7 38.4 114 6 114.6 41 2 41.2 119.9 40.4 124.0 40.8 130.6 42.3 134.6 43.0 140.5 42.6 148.7 40.8 23
Trend Tahun Pertama Tahun Dasar
Thn X Th Penjj (Y) X^2 P XY 1990 0 108 0 0 1991 1 119 1 119 1992 2 110 4 220 1993 3 122 9 366 1994 4 130 16 520 JMH 10 589 30 1225
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Trend Titik Tengah sbg tahun Dasar k h b h Thn X Penj (Y) X^2 XY 1990 -2 2 108 4 -216 216 1991 -1 119 1 -119 1992 0 110 0 0 1993 1 122 1 122 1994 2 130 4 260 JMH 0 589 10 47
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Trend Eksponensial k l Thn X Penj (Y) Log Y X log Y 1990 -2 108 2.0334 -4.0668 1991 -1 119 2.0755 -2.0755 1992 0 110 2.0414 0 1993 1 122 2.0864 2.0864 1994 2 130 2.1139 2 1139 4.2279 4 2279 JMH 0 589 10.351 0.1719 26
Trend Kuadratik Trend Kuadratik Thn X 1981 -55 1982 -3 983 -1 1983 1984 1 1985 3 1986 5 Jlh 0
Y 2 5 8 15 26 37 93
X^2 X^3 25 -125 125 9 -27 1 -1 1 1 9 27 25 125 70 0
X^4 625 81 1 1 81 625 1414
XY -10 10 -15 -88 15 78 185 245
X^2Y 50 45 8 15 234 925 1277 27
Naïve Model Naïve Model
³ The recent periods are the best predictors of the future. 1. The simplest model for stationary data is
Yˆt +1 = Yt 2. The simplest model for trend data is
Yˆt +1 = Yt + (Yt − Yt −1 ) or Yt ˆ Yt +1 = Yt Yt −1 3. The simplest model for seasonal data is
Yˆt +1 = Y(t +1) − s
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Average Methods Average Methods
1. Simple Averages ³ obtained by finding the mean for all the relevant values and g p then using this mean to forecast the next period. n
Yt ˆ Yt +1 = ∑ t =1 n
for stationary data
2. Moving Averages ³ obtained by finding the mean for a specified set of values and then using this mean to forecast the next period using this mean to forecast the next period.
(Y + Yt −1 + K + Yt − n +1 ) M t = Yˆt +1 = t n
for stationary data
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Average Methods … Average Methods … (continued)
3. Double Moving Averages ³ one set of moving averages is computed, and then a second set computed as a moving average of the first set.
is
(Y + Yt −1 + K + Yt − n +1 ) M t = Yˆt +1 = t n ( M t + M t −1 + K + M t − n +1 ) (ii) M t′ = (ii). n (i).
(iii). at = 2M t − M t′ (iv).
bt =
2 ( M t − M t′ ) n −1
Yˆt + p = at + bt p
f for a linear trend data li t dd t 30
MINITAB implementation MINITAB implementation
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MINITAB implementation … MINITAB implementation … (continued)
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Moving Averages Result … Moving Averages Result … (continued)
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Moving Averages VS Double Moving Averages Moving Averages Double Moving Averages Results Results
MA or Moving Averages
DMA or Double Moving Averages
MSE.MA = 132.67, MSE.DMA = 63.7 34
Exponential Smoothing Methods Exponential Smoothing Methods 9 Single Exponential Smoothing Ö for stationary data
Yˆt +1 = αYt + (1 − α )Yˆt 9 Exponential Smoothing Adjusted for Trend : Holt’s Method 1. The exponentially smoothed series : At = α = α Yt + (1−α) (A + (1−α) (At‐1+ T + Tt‐1) 2. The trend estimate : Tt = β (At − At‐1) + (1 − β) Tt‐1 3. Forecast p periods into the future :
Yˆt + p = At + pTt 35
Exponential Smoothing Adjusted for Trend and Seasonal Variation : Winter’s Method Variation : Winter’s Method
1. The exponentially smoothed series : Y At = α t + (1 − α ) ( At −1 + Tt −1) St − L 2. The trend estimate : Tt = β ( At − At −1) + (1 − β )Tt −1
3. The seasonality estimate :
Three p parameters models
Y St = γ t + (1 − γ ) St −1 At 4. Forecast p periods into the future : Yˆt + p = ( At − pTt ) St − L + p 36
SES: MINITAB implementation SES: MINITAB implementation
SES dengan alpha 0,1
SES dengan alpha 0,6
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SES: MINITAB implementation SES: MINITAB implementation …
( (continued) i d)
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SES: MINITAB implementation SES: MINITAB implementation …
( (continued) i d)
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DES (Holt’ss Methods): MINITAB implementation … DES (Holt Methods): MINITAB implementation
( (continued) i d)
DES dengan alpha 0,3 dan beta 0,1 40
DES: MINITAB implementation DES: MINITAB implementation …
( (continued) i d)
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Winter’ss Methods: MINITAB implementation Winter Methods: MINITAB implementation
Winter’s Methods dengan alpha 0,4; beta 0,1 dan gamma 0,3 42
Winter’ss Methods: MINITAB implementation Winter Methods: MINITAB implementation …
( (continued) i d)
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