Metode Pemulusan Eksponensial Sederhana

Transkripsi

1 Metode Pemulusan Eksponensial Sederhana (Single Exponential Smoothing) KULIAH 3 METODE PERAMALAN DERET WAKTU rahmaanisa@apps.ipb.ac.id

2 Review Untuk apa metode pemulusan (smoothing) dilakukan terhadap data deret waktu? Kapan metode rataan bergerak sederhana digunakan? Kapan metode rataan bergerak ganda digunakan?

3 Review: The Process of Smoothing Data Set

4 Outline Konsep dasar pemulusan eksponensial Pemulusan eksponensial sederhana Peramalan melalui pemulusan eksponensial sederhana Contoh aplikasi pada data

5 Moving Average Vs Exponential Smoothing

6 Moving Average Vs Exponential Smoothing n Period Moving Average hanya menggunakan n data Exponential Smoothing: menggunakan semua data bobot yg lebih besar diberikan pada data yg lebih up to date

7 What do you think about the MA forecasts?

8 Introduction Hasil smoothing tidak sesuai dgn pola data MENGAPA? karena data tidak lagi konstan Perubahan hasil smoothing terlalu lambat Bagaimana solusinya?

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10 Konsep Dasar Pemulusan Eksponensial

11 Exponential Smoothing It uses weighted averages of the past data The effect of recent observations is expected to decline exponentially over time The further back along the historical time path one travels, the less influence each observation has on the forecasts

12 Pemulusan Eksponensial Sederhana (SINGLE EXPONENTIAL SMOOTHING)

13 Single Exponential Smoothing give geometrically decreasing weights to the past observations. an exponentially weighted smoother is obtained by introducing a discount factor

14 Procedures of Single Exponential Smoothing Step 1: Compute the initial estimate of the mean (or level) of the series at time period t = 0 Step 2: Compute the updated estimate by using the smoothing equation l y (1 ) l T T T 1 where is a smoothing constant between 0 and 1. Slide 14

15 Procedures of Single Exponential Smoothing Note that l y (1 ) l T T T y (1 )[ y (1 ) l ] 1 T T 1 T 2 y (1 ) y (1 ) l 2 T T 1 T 2 y (1 ) y (1 ) y... (1 ) y (1 ) l 2 T 1 T T T 1 T The coefficients measuring the contributions of the observations decrease exponentially over time. Slide 15

16 Single Exponential Smoothing l y (1 ) l T T T 1 This can also be seen as the linear combination of the current observation and the smoothed observation at the previous time unit.

17 Comparison of Weights: MA Vs SES

18 Intial Value 1. Set l 0 = y 1, if the changes in the process are expected to occur early and fast 2. Take a subset of the avalaible data. Set l 0 = y, if the process is at least at the beginning locally constant.

19 Ilustrasi Data Dow Jones Actual SES(0.1) SES(0.9)

20 The Value of α α 0 maka hasil smoothing semakin smooth α 1 maka hasil smoothing semakin mendekati pola data aktual

21 The Value of α Perhatikan bahwa: α α α α α α α α α α Bagaimana pengaruh besarnya α terhadap Var y T?

22 The Value of α Thus the question will be how much smoothing is needed. In the literature, α values between 0.1 and 0.4 are often recommended and do indeed perform well in practice.

23 Peramalan

24 Single Exponential Smoothing Point forecast made at time T for y T+p yˆ ( T) l ( p 1,2,3,...) T p T Slide 24

25 Aplikasi pada Data

26 Example: Cod Catch The Bay City Seafood Company recorded the monthly cod catch for the previous two years, as follow: Cod Catch (In Tons) Month Year 1 Year 2 January February March April May June July August September October November December Slide 26

27 Time Series Plot Cod Catch Period

28 Time Series Plot Cod Catch Period

29 Single Exponential Smoothing Cod Period Catch Lt Forecast Period Cod Catch Lt Forecast

30 Single Exponential Smoothing Period Cod Catch Lt Forecast Period Cod Catch Lt Forecast

31 The Forecasts Aktual Forecast

32 Evaluasi

33 Latihan 1) Exercise 4.1 in Montgomery et al. (2015) 2) Exercise 4.2 in Montgomery et al. (2015)

34 Referensi Montgomery, D.C., Jennings, C.L., Kulahci, M Introduction to Time Series Analysis and Forecasting, 2 nd ed. New Jersey: John Wiley & Sons. 34

35 Materi perkuliahan dapat diakses pada: stat.ipb.ac.id/en 35

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