Analisis Deret Waktu: Materi minggu kedua

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Pendahuluan Naïve Models dan Moving Average Methods Exponential Smoothing Methods Regresi dan Trend Analysis Model ARIMA Box-Jenkins



Regresi Berganda dan Time Series Regresi Metode Dekomposisi



Studi Kasus : Model ARIMAX (Analisis Intervensi, Fungsi Transfer dan Neural Networks)

Referensi Utama 

. Hanke, J.E. and Reitsch, A.G. ( 1995 “Business Forecasting” 5 th and 7 th edition, Prentice Hall. & 2001)

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Chapter 4: Exploring Data Pattern …



Measuring Forecasting Error

 

Chapter 5: Moving Average and Smoothing Methods

 

Naïve Models



Averaging Methods

 

Exponential Smoothing Methods



Kaitan Pola Data dengan Metode Peramalan

Stationer Time Series Patterns Trend Effect Seasonal Effect Trend and Seasonal

    Naïve Model  Simple Averages Moving Averages Single Exponential Smoothing   Naïve Model Double Moving Averages Double Exponential Smoothing   Naïve Model Winter’s Model

Naïve Model  The

recent periods

are the best predictors of the future.

1.

The simplest model

Y

ˆ

t

 1 

for stationary

Y t

data is 2.

The simplest model

Y

ˆ

t

 1 

for

Y t



trend data is

(

Y t



Y t

 1 ) or

Y

ˆ

t

 1 

Y t Y t Y t

 1

3.

The simplest model

Y

ˆ

t

 1 

for seasonal data is

Y

(

t

 1 ) 

s

MINITAB implementation

Time Series Plot

MINITAB implementation … (continued)

Naïve 1 Naïve 2 Naïve 3

MINITAB implementation … (continued)

Naïve 1 Naïve 2 Naïve 3

MINITAB implementation … (continued)

Naïve 1 Naïve 2 Naïve 3

MSE.1 = 28547.5 , MSE.2 = 53592.5 , MSE.3 = 4567.5

Measuring Forecasting Error …



MSE/MSD (mean squared error)

 rata-rata kuadrat kesalahan (residual atau error).



MAD



(mean absolute deviation)

ukuran kesalahan peramalan dalam unit ukuran yang sama dengan data aslinya.



MAPE



(mean absolute percentage error)

persentase kesalahan absolut rata-rata .



MPE



(mean percentage error)

persentase kesalahan rata-rata.

Average Methods

1. Simple Averages

 obtained by finding the

mean for all the relevant values

then

using this mean to forecast the next period

.

and

Y

ˆ

t

 1 

t n

  1

Y t n

for stationary data 2.

Moving Averages

 obtained by finding the

mean for a specified set of values

and then

using this mean to forecast the next period

.

M t



Y

ˆ

t

 1  (

Y t



Y t

 1   

Y t



n

 1 )

n

for stationary data

Average Methods … (continued)

3. Double Moving Averages

 one set of moving averages is computed , and then a second set is computed as a moving average of the first set .

(i).

(ii).

M t M t

 

Y

ˆ

t

 1   (

M t

(

Y t



Y t

 1

n

  

Y t



n

 1 ) 

M t

 1  

n



M t



n

 1 ) (iii).

a t

 2

M t



M t

 (iv).

b t



n

2  1 (

M t



M t

 )

Y

ˆ

t



p



a t



b t p

for a linear trend data

MINITAB implementation

MINITAB implementation … (continued)

Case Study of Video Store : MINITAB implementation

Moving Averages Double Moving Averages

Moving Averages Result … (continued)

Moving Averages

VS

Double Moving Averages Results

MA or Moving Averages DMA or Double Moving Averages

MSE.MA = 132.67 , MSE.DMA = 63.7

Exponential Smoothing Methods



Single Exponential

Y

ˆ

t

 1  

Y t



Smoothing

 ( 1   )

Y

ˆ

t

for stationary data  Exponential Smoothing Adjusted for Trend 1. The exponentially smoothed series : A t =  Y t + (1  ) (A t-1 + T t-1 ) :

Holt’s Method

2. The trend estimate : T t =  (A t  A t-1 ) + (1   ) T t-1 3. Forecast p periods into the future :

Y

ˆ

t



p



A t



pT t

Exponential Smoothing Adjusted for Trend and Seasonal Variation :

Winter’s Method

1. The exponentially

smoothed

series :

A t

 

Y t S t



L

 ( 1   ) (

A t

 1 

T t

 1 ) 2. The

trend

estimate :

T t

  (

A t



A t

 1 )  ( 1   )

T t

 1 3. The

seasonality

estimate :

S t

  4.

Forecast p

Y t A t

 ( 1   )

S t

 1 periods into the future :

Y

ˆ

t



p

 (

A t



pT t

)

S t



L



p

Three parameters models

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

SES : MINITAB implementation … (continued)

SES : MINITAB implementation … (continued)

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

DES : MINITAB implementation … (continued)

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

Winter’s Methods : MINITAB implementation … (continued)