Teknik Forecasting. Pendekatan Basis Teknik Hasil Peramalan ekstrapolatif

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1 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-Output Pemrograman linier Analisis regresi Estimasi interval Analisis hubungan Prediksi Peramalan intuitif Penilaian subjektif Delphi konvensional Delphi kebijakan Analisis dampak-silang Penilaian kelayakan Konjektur 1

2 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 akan selalu meningkat di masa depan. 2. Keteraturan (regularity): Variasi di masa lalu akan secarateratur muncul di masadepan. 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: data ttg laporan kejahatan seringkali tidak sesuai dg insiden kejahatan yg sesungguhnya, data ttg gaji bukan merupakan ukuran tepat dari pendapatan masyarakat. 2

3 Klasifikasi Metode Peramalan Forecasting Method Objective Forecasting Methods Subjective (Judgmental) Forecasting Methods Time Series Methods Causal Methods Analogies Naïve Methods Moving Averages Exponential Smoothing Simple Regression ARIMA Neural Networks Simple Regression Multiple Regression Neural Networks Delphi PERT Survey techniques Combination of Time Series Causal Methods Intervention Model Transfer Function (ARIMAX) VARIMA (VARIMAX) Neural Networks References : Makridakis et al. Hanke and Reitsch Wei, W.W.S. Box, Jenkins and Reinsel 3

4 Klasifikasi Metode Peramalan : Model lmatematis Ilustrasi Forecasting Method Objective Subjective (Judgmental) Forecasting oecast Methods Forecasting oecast Methods Time Series Methods Y t = f (Y t-1, Y t-2,, Y t-k ) Causal Methods Y t = f (X1 t, X2 t,, Xk t ) Examples : sales (t) = f( (sales (t-1), sales (t-2), ) Examples : sales (t) = f( (price (t), advert (t), ) Combination of Time Series Causal Methods Y t = f (Y t-j, j>0 ; X t-i, i 0) Examples : sales (t) = f (sales (t-1), advert (t), advert (t-1), ) 4

5 Klasifikasi Model Time Series : Berdasarkan Bentuk atau Fungsi TIME SERIES MODELS LINEAR Time Series Models NONLINEAR Time Series Models ARIMA Box-Jenkins Intervention Model Transfer Function (ARIMAX) Models from time series theory nonlinear autoregressive, etc... Flexible statistical parametric models neural network model, etc... State-dependent, time-varying para- 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 of Modelling Nonlinear Time Series Handbook of Econometrics, Volume IV, Chapter 48. Edited by R.F. Engle and D.I. McFadden 5

6 POLA DATA Time Series es GeneralTime Series PATTERN Stationer Trend (linear or nonlinear) Seasonal (additive or multiplicative) Cyclic Calendar Variation 6

7 General of Time Series Patterns Time Series Patterns Stationer Trend Effect Seasonal Effect Cyclic Effect Nonseasonal Stationary models Nonseasonal Nonstationary models Seasonal and Multiplicative models Intervention models 7

8 Contoh DATA EKONOMI 1 Time Series Plot of Inflasi 3 1 Eids holiday effects Inflasi Month Jan Jan Jan Jan Jan Jan Jan Year

9 Contoh DATA EKONOMI 2 Krisis di Indonesia Pertengahan 1997 Reference : Badan Pusat Statistik (BPS) Indonesia 9

10 Contoh DATA EKONOMI 3 Krisis di Indonesia Terjadi Mulai Pertengahan 1997 Reference : Dinas Perhubungan Jawa Timur 10

11 Model model Time Series Regression 1. Model Regresi untuk LINEAR TREND Y t = a + b.t + error t = 1, 2, (dummy waktu) 2. Model Regresi untuk Data SEASONAL (variasi konstan) Y t = a + b 1 D b S 1 D S 1 + error dengan : D 1, D 2,, D S 1 adalah dummy waktu dalam satu periode seasonal. 3. Model Regresi untuk Data dengan LINEAR TREND dan SEASONAL (variasi konstan) Y t = a + b.t + c 1 D c S 1 D S 1 + error Gabungan model 1 dan 2. 11

12 Problem 4: Hasil Regresi Trend dg MINITAB (continued) 12

13 Problem 4: Hasil Regresi Trend dg MINITAB (continued) 13

14 Problem 5: Regresi Data Seasonal (Data Electrical Usage) Time Series Plot (Data seasonal) 14

15 Problem 5: Hasil regresi dengan MINITAB MTB > Regress 'Kilowatts' 3 'Kuartal-1'-'Kuartal-3' The regression equation is Kilowatts = Kuartal Kuartal Kuartal.3 Predictor Coef SE Coef T P Constant Kuartal Kuartal Kuartal S = R-Sq = 97.7% R-Sq(adj) = 97.3% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

16 Problem 6: Regresi Data TrendLinear dan Seasonal Time Series Plot (Data trend dan seasonal) 16

17 Problem 6: Hasil regresi dengan MINITAB Dummy Variable 17

18 Problem 6: Hasil regresi dengan MINITAB MTB > Regress 'Sales' 4 't' 'Kuartal.1'-'Kuartal.3' The regression equation is Sales = t Kuartal Kuartal Kuartal.3 16 cases used 4 cases contain missing i values Predictor Coef SE Coef T P Constant t Kuartal Kuartal Kuartal S = R-Sq = 96.3% R-Sq(adj) = 95.0% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

19 Problem 6: Hasil regresi dengan MINITAB Forecast Time Series Plot (Data dan Ramalannya) 19

20 Perbandingan ketepatan ramalan antar metode Kasus Sl Sales Video Store Kasus Sl Sales Data Dt Kuartalan Model Double M.A. Holt s Method Regresi Trend Kriteria kesalahan ramalan MSE MAD MAPE Model Winter s Method Regresi Trend & Seasonal Kriteria kesalahan ramalan MSE MAD MAPE Holt s Method : Alpha (level): Gamma (trend): Winter s Method : Alpha (level): 0.4 Gamma (trend): 0.1 Delta (seasonal):

21 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 peningkatannominal nominal? Berapa peningkatan riilnya? 21

22 Perhitungan Peningktan Nominal Peningktan Riil Penjualan tahun 2000 Rp. 350 M Rp. 300 (Rp. 300M) (100/135) M = Rp. 222,222 M = Rp. 50 M Penjualan tahun 2001 (Rp. 350M) (100/155) = Rp. 225,806 M Peningkatan: 225,806M 222,222 M = Rp. 3,584 M 22

23 Mr. Aringanu akan menganalisis laju pertumbuhan penjualan toko yang menjual 70% mebeler dan 30% alat rumah tangga. Tahun Penj IH Mebel IH ART IH Penj. Riil

24 Trend Tahun Pertama Tahun Dasar Thn X Penj (Y) X^2 XY JMH

25 Trend Titik Tengah sbg tahun Dasar Thn X Penj (Y) X^2 XY JMH

26 Trend Eksponensial Thn X Penj (Y) Log Y X log Y JMH

27 Trend Kuadratik Thn X Y X^2 X^3 X^4 XY X^2Y Jlh

28 Naïve Model The recent periods are the best predictors of the future. 1. The simplest model for stationary data is Y ˆ = t+1 Y t 2. The simplest model for trend data is Yˆ t Yˆ + 1 = Yt + ( Yt Yt 1) t+ 1 = Y t Y Y t t 1 3. The simplest model for seasonal data is Yˆ t+ 1 = Y( t + 1) s or 28

29 Average Methods 1. Simple Averages obtained by finding the mean for all the relevant values and then using this mean to forecast the next period. Yˆ + = n t 1 t= 1 2. Moving Averages Y t n for stationary data obtained by finding the mean for a specified set of values and then using this mean to forecast the next period. M t = Y ( Y + Y + K+ Y ˆ t t 1 t n+ 1 t+ 1 = n ) for stationary data 29

30 AverageMethods (continued) 3. Double Moving Averages one set of moving averages is computed, and then a second set computed as a moving average of the first set. (i). (ii). (iii). (iv). ( Yt + Yt 1 + K+ Yt n+ M t = Yt + 1 = n ( M M M 1 M t + t 1 + K+ t n+ 1) t = n t ˆ 1 a = 2M M t b 2 t = ( M t M t ) n 1 t ) is ˆ t + p t + t p for a linear trend ddt data Y = a + b 30

31 MINITAB implementation 31

32 MINITAB implementation (continued) 32

33 Moving Averages Result (continued) 33

34 MovingAverages VS Double MovingAverages Results MA or Moving Averages DMA or Double Moving Averages MSE.MA = , MSE.DMA =

35 Exponential Smoothing Methods Single Exponential Smoothing for stationary data Yˆ t Yt (1 ) Yˆ + 1 = α + α t Exponential Smoothing Adjusted for Trend : Holt s Method 1. The exponentially smoothed series : A t = α Y t + (1 α) (A t 1 + T t 1 ) 2. The trend estimate : T t = β (A t A t 1 ) + (1 β) T t 1 3. Forecast p periods into the future : Y ˆ = A + t+ p t pt t 35

36 Exponential Smoothing Adjusted for Trend and Seasonal Variation : Winter s Method 1. The exponentially smoothed series : Y A t t α + 1 α) ( At + T S = ( 1 t 1 t L ) 2. The trend estimate : T t = β ( A t A t 1) + (1 β ) T t 1 3. The seasonality estimate : S Y = t t γ + ( 1 γ ) S t 1 At 4. Forecast p periods into the future : Y ˆ t + p = ( A t pt t ) S t L + p Three parameters models 36

37 SES: MINITAB implementation SES dengan alpha 0,1 SES dengan alpha 0,6 37

38 SES: MINITAB implementation (continued) 38

39 SES: MINITAB implementation (continued) 39

40 DES (Holt s Methods): MINITAB implementation (continued) DES dengan alpha 0,3 dan beta 0,1 40

41 DES: MINITAB implementation (continued) 41

42 Winter s Methods: MINITAB implementation Winter s Methods dengan alpha 0,4; beta 0,1 dan gamma 0,3 42

43 Winter s Methods: MINITAB implementation (continued) 43