Metode Pemulusan Eksponensial Sederhana ( Single Exponential Smoothing) KULIAH 3|METODE PERAMALAN DERET WAKTU [email protected]
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Metode PemulusanEksponensial Sederhana(Single Exponential Smoothing)KULIAH 3|METODE PERAMALAN DERET WAKTU
Review Untuk apa metode pemulusan (smoothing)
dilakukan terhadap data deret waktu?
Kapan metode rataan bergerak sederhanadigunakan?
Kapan metode rataan bergerak gandadigunakan?
Review: The Process of Smoothing Data Set
Outline Konsep dasar pemulusan eksponensial
Pemulusan eksponensial sederhana
Peramalan melalui pemulusan eksponensialsederhana
Contoh aplikasi pada data
Moving Average Vs Exponential Smoothing
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 yglebih up to date
What do you think about the MA forecasts?
Introduction Hasil smoothing tidak sesuai dgn pola data
MENGAPA? karena data tidak lagi konstan
Perubahan hasil smoothing terlalu lambat
Bagaimana solusinya?
Konsep DasarPemulusan Eksponensial
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
Pemulusan EksponensialSederhana(SINGLE EXPONENTIAL SMOOTHING)
Single Exponential Smoothing
give geometrically decreasing weights to the past observations.
an exponentially weighted smoother is obtained by introducing a discount factor
Slide 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
where is a smoothing constant between 0 and 1.
1(1 )T T Ty l l
Slide 15
Procedures of Single Exponential Smoothing
Note that
The coefficients measuring the contributions of the observations decrease exponentially over time.
1(1 )T T Ty l l
1 2(1 )[ (1 ) ]T T Ty y l
2
1 2(1 ) (1 )T T Ty y l
2 1
1 2 1 0(1 ) (1 ) ... (1 ) (1 )T T
T T Ty y y y
l
Single Exponential Smoothing
This can also be seen as the linear combination of the current
observation and the smoothed observation at the previous time unit.
1(1 )T T Ty l l
Comparison of Weights: MA Vs SES
Intial Value
1. Set 𝑙0 = 𝑦1 , if the changes in the process are expected to occur early and fast
2. Take a subset of the avalaible data. Set 𝑙0 = 𝑦, if the process is at least at the beginning locally constant.
IlustrasiData Dow Jones
7000
8000
9000
10000
11000
12000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83
Actual SES(0.1) SES(0.9)
The Value of 𝛼 𝛼 → 0 maka hasil smoothing semakin smooth
𝛼 → 1 maka hasil smoothing semakin mendekatipola data aktual
The Value of 𝛼Perhatikan bahwa:
Bagaimana pengaruh besarnya 𝛼 terhadap 𝑉𝑎𝑟 𝑦𝑇 ?
𝛼 𝛼
𝛼 𝛼
𝛼𝛼
𝛼 𝛼
𝛼
𝛼
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.
Peramalan
Slide 24
Single Exponential Smoothing
Point forecast made at time T for yT+p
ˆ ( ) ( 1,2,3,...)T p Ty T p l
Aplikasi pada Data
Slide 26
Example: Cod CatchThe 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 362 276
February 381 334
March 317 394
April 297 334
May 399 384
June 402 314
July 375 344
August 349 337
September 386 345
October 328 362
November 389 314
December 343 365
Time Series Plot
275
295
315
335
355
375
395
415
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Period
Cod Catch
Time Series Plot
275
295
315
335
355
375
395
415
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Period
Cod Catch
Single Exponential SmoothingPeriod
Cod Catch
Lt Forecast
01 3622 3813 3174 2975 3996 4027 3758 3499 386
10 32811 38912 343
PeriodCod
CatchLt Forecast
13 27614 33415 39416 33417 38418 31419 34420 33721 34522 36223 31424 36525
Single Exponential SmoothingPeriod
Cod Catch
Lt Forecast
0 362.01 362 362.0 362.02 381 369.6 362.03 317 348.6 369.64 297 327.9 348.65 399 356.4 327.96 402 374.6 356.47 375 374.8 374.68 349 364.5 374.89 386 373.1 364.5
10 328 355.0 373.111 389 368.6 355.012 343 358.4 368.6
PeriodCod
CatchLt Forecast
13 276 325.4 358.414 334 328.9 325.415 394 354.9 328.916 334 346.5 354.917 384 361.5 346.518 314 342.5 361.519 344 343.1 342.520 337 340.7 343.121 345 342.4 340.722 362 350.2 342.423 314 335.7 350.224 365 347.4 335.725 347.4
The Forecasts
275.0
295.0
315.0
335.0
355.0
375.0
395.0
415.0
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
Aktual Forecast
Evaluasi
Latihan1) Exercise 4.1 in Montgomery et al. (2015)
2) Exercise 4.2 in Montgomery et al. (2015)
ReferensiMontgomery, D.C., Jennings, C.L., Kulahci, M. 2015.
Introduction to Time Series Analysis andForecasting, 2nd ed. New Jersey: John Wiley &Sons.
34
Materi perkuliahan dapatdiakses pada:
stat.ipb.ac.id/en
35
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