Analisis Deret Waktu: Materi minggu kedua

PendahuluanNave Models dan Moving Average Methods Exponential Smoothing MethodsRegresi dan Trend AnalysisRegresi Berganda dan Time Series RegresiMetode DekomposisiModel ARIMA Box-JenkinsStudi Kasus : Model ARIMAX (Analisis Intervensi, Fungsi Transfer dan Neural Networks)

Referensi Utama

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

Chapter 4: Exploring Data Pattern Measuring Forecasting Error

Chapter 5: Moving Average and Smoothing Methods Nave Models Averaging Methods Exponential Smoothing Methods

Kaitan Pola Data dengan Metode Peramalan

Nave Model

The recent periods are the best predictors of the future.

1. The simplest model for stationary data is

2. The simplest model for trend data is

or

3. The simplest model for seasonal data is

MINITAB implementationTime Series Plot

MINITAB implementation (continued)Nave 1Nave 2Nave 3

MINITAB implementation (continued)Nave 1Nave 2Nave 3

MINITAB implementation (continued)Nave 1Nave 2Nave 3MSE.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 and then using this mean to forecast the next period.

2. Moving Averages obtained by finding the mean for a specified set of values and then using this mean to forecast the next period.

for stationary datafor 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).

(iii).

(iv).

for a linear trend data

MINITAB implementation

MINITAB implementation (continued)

Case Study of Video Store: MINITAB implementationMoving AveragesDouble Moving Averages

Moving Averages Result (continued)

Moving Averages VS Double Moving Averages Results MA or Moving AveragesDMA or Double Moving AveragesMSE.MA = 132.67, MSE.DMA = 63.7

Exponential Smoothing Methods

Single Exponential Smoothing for stationary data

Exponential Smoothing Adjusted for Trend : Holts Method1. The exponentially smoothed series :At = Yt + (1) (At-1+ Tt-1)

2. The trend estimate :Tt = (At At-1) + (1 ) Tt-1

3. Forecast p periods into the future :

Exponential Smoothing Adjusted for Trend and Seasonal Variation : Winters Method

1. The exponentially smoothed series :

2. The trend estimate :

3. The seasonality estimate :

4. Forecast p periods into the future :Three parameters models

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

SES: MINITAB implementation (continued)

SES: MINITAB implementation (continued)

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

DES: MINITAB implementation (continued)

Winters Methods: MINITAB implementationWinters Methods dengan alpha 0,4; beta 0,1 dan gamma 0,3

Winters Methods: MINITAB implementation (continued)