Bahan Rapat Gugus Inds Untuk Rapat Persiapan Kuliah 2012-2013 Semester Ganjil

7/28/2019 Bahan Rapat Gugus Inds Untuk Rapat Persiapan Kuliah 2012-2013 Semester Ganjil

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Selection and Control of Forecasting

MethodsTopic 10

Course : Supply Chain: Logistics


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Selecting a Forecasting Method

It should be based on the following considerations: Forecasting horizon (validity of extrapolating past

data)

Availability and quality of data

Lead Times (time pressures)

Cost of forecasting (understanding the value of

forecasting accuracy)

Forecasting flexibility (amenability of the model to

revision; quite often, a trade-off between filteringout noise and the ability of the model to respond to

abrupt and/or drastic changes)


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Data Pattern

A time series is likely to contain some or all of the following

components:

Trend

Seasonal

Cyclical

Irregular


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Data Pattern

Trendin a time series is the long-term change in the

level of the data i.e. observations grow or decline

over an extended period of time.

Positive trend When the series move upward over an extended period of time

Negative trend

When the series move downward over an extended period of time

Stationary When there is neither positive or negative trend.


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Data Pattern

Seasonalpattern in time series is a regular variation in the

level of data that repeats itself at the same time every year.

Examples:

Retail sales for many products tend to peak in

November and December.

Housing starts are stronger in spring and summer than

fall and winter.


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Data Pattern

Cyclicalpatterns in a time series is presented by

wavelike upward and downward movements of the

data around the long-term trend.

They are of longer duration and are less regular thanseasonal fluctuations.

The causes of cyclical fluctuations are usually less

apparent than seasonal variations.


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Data Pattern

Irregular pattern in a time series data are the fluctuations that

are not part of the other three components

These are the most difficult to capture in a forecasting model


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Example:GDP, in 1996 Dollars


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Example:Quarterly data on private housing starts


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Example:U.S. billings of the Leo Burnet

advertising agency


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Data Patterns and Model Selection The pattern that exist in the data is an important

consideration in determining which forecastingtechniques are appropriate.

To forecast stationary data; use the available history toestimate its mean value, this is the forecast for future

period.

The estimate can be updated as new information becomesavailable.

The updating techniques are useful when initial estimatesare unreliable or the stability of the average is in question.


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Data Patterns and Model Selection Forecasting techniques used for stationary time series data are:

Naive methods

Simple averaging methods,

Moving averages

Simple exponential smoothing

autoregressive moving average(ARMA)


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Data Patterns and Model Selection Methods used for time series data with trend are:

Moving averages

Holts linear exponential smoothing

Simple regression Growth curve

Exponential models

Time series decomposition

Autoregressive integrated moving average(ARIMA)


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Data Patterns and Model Selection For time series data with seasonal component the goal is

to estimate seasonal indexes from historical data.

These indexes are used to include seasonality in forecastor remove such effect from the observed value.

Forecasting methods to be considered for these type ofdata are:

Winters exponential smoothing

Time series multiple regression

Autoregressive integrated moving average(ARIMA)


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Data Patterns and Model Selection Cyclical time series data show wavelike fluctuation around the

trend that tend to repeat.

Difficult to model because their patterns are not stable.

Because of the irregular behavior of cycles, analyzing these

type data requires finding coincidental or leading economicindicators.


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Data Patterns and Model Selection Forecasting methods to be considered for these type of data

are:

Classical decomposition methods

Econometric models

Multiple regression

Autoregressive integrated moving average (ARIMA)


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Example:GDP, in 1996 Dollars For GDP, which has a trend and a cycle but no seasonality, the

following might be appropriate:

Holts exponential smoothing

Linear regression trend

Causal regression



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Example:Quarterly data on private housing starts

Private housing starts have a trend, seasonality, and a cycle.

The likely forecasting models are:

Winters exponential smoothing

Linear regression trend with seasonal adjustment

Causal regression



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Example:U.S. billings of the Leo Burnet

advertising agency For U.S. billings of Leo Burnett advertising, There is a non-linear trend, with no seasonality and no cycle, therefore the

models appropriate for this data set are:

Non-linear regression trend

Causal regression


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Autocorrelation

Correlation coefficient is a summary statistic that measures the

extent of linear relationship between two variables. As such

they can be used to identify explanatory relationships.

Autocorrelation is comparable measure that serves the same

purpose for a single variable measured over time.


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Autocorrelation In evaluating time series data, it is useful to look at the

correlation between successive observations over time.

This measure of correlation is called autocorrelation and maybe calculated as follows:

rk= autocorrelation coefficient for a k period lag.

mean of the time series. yt = Value of the time series at period t.

y t-k= Value of time series k periods before period t.

n

t

t

n

kt

ktt

k

yy

yyyy

r

1

2

1

)(

))((

y


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Autocorrelation

Autocorrelation coefficient for different time lags can be used

to answer the following questions about a time series data.

Are the data random?

In this case the autocorrelations between yt

and yt-k

for

any lag are close to zero. The successive values of a

time series are not related to each other.


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Correlograms: An Alternative Method of

Data Exploration Is there a trend? If the series has a trend, yt and y t-kare highly correlated

The autocorrelation coefficients are significantly

different from zero for the first few lags and then

gradually drops toward zero.

The autocorrelation coefficient for the lag 1 is often

very large (close to 1).

A series that contains a trend is said to be non-

stationary.


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Data Exploration Is there seasonal pattern? If a series has a seasonal pattern, there will be a

significant autocorrelation coefficient at the seasonal

time lag or multiples of the seasonal lag.

The seasonal lag is 4 for quarterly data and 12 for

monthly data.


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Data Exploration Is it stationary? A stationary time series is one whose basic statistical

properties, such as the mean and variance, remain

constant over time.

Autocorrelation coefficients for a stationary series

decline to zero fairly rapidly, generally after the second

or third time lag.


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Data Exploration To determine whether the autocorrelation at lag k issignificantly different from zero, the following hypothesis and

rule of thumb may be used.

H0: k= 0, Ha: k 0

For any k, reject H0 if

Where n is the number of observations.

This rule of thumb is for = 5%

n

rk

2


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Data Exploration The hypothesis test developed to determine whether aparticular autocorrelation coefficient is significantly different

from zero is:

Hypotheses

H0: k= 0, Ha: k 0

Test Statistic:

kn

rt k

1

0


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Data Exploration Reject H0 if

2;2; or knkn tttt


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Data Exploration The plot of the autocorrelation Function (ACF) versus time lagis called Correlogram.

The horizontal scale is the time lag

The vertical axis is the autocorrelation coefficient. Patterns in a Correlogram are used to analyze key features of

data.


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Example:Mobil Home Shipment

Correlograms for the mobile home shipment

Note that this is quarterly data

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12

ACF

Upper Limit

Low er Limit


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Example:Japanese exchange Rate

As the worlds economy becomes increasinglyinterdependent, various exchange rates betweencurrencies have become important in making businessdecisions. For many U.S. businesses, The Japaneseexchange rate (in yen per U.S. dollar) is an importantdecision variable. A time series plot of the Japanese-yen U.S.-dollar exchange rate is shown below. On the

basis of this plot, would you say the data is

stationary? Is there any seasonal component to thistime series plot?


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Japanese Exchange Rate

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30

Months

Exch

angeRate(yen

perU.S.

dollar)

EXRJ


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Here is the autocorrelationstructure for EXRJ.

With a sample size of 12,

the critical value is

This is the approximate

95% critical value forrejecting the nullhypothesis of zeroautocorrelation at lag K.

Obs ACF

1 .8157

2 .5383

3 .2733

4 .0340

5 -.1214

6 -.1924

7 -.2157

8 -.1978

9 -.1215

10 -.1217

11 -.1823

12 -.2593

408.024

22

n


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The Correlograms for EXRJ is given below

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12

ACF

Upper Limit

Lower Limit


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Since the autocorrelation coefficients fall to below the critical

value after just two periods, we can conclude that there is no

trend in the data.


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To check for seasonality at = .05

The hypotheses are:

H0;

12= 0 H

a:

12 0

Test statistic is:

Reject H0 if 899.01224/1

2595.

1

0

kn

rt k

2;2; or knkn tttt

179.2025.0;122; tt kn


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Since

We do not reject H0 , therefore seasonality does not appear to

be an attribute of the data.179.2899.0 025.0;12 tt


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ACF of Forecast Error

The autocorrelation function of the forecast errors is very

useful in determining if there is any remaining pattern in the

errors (residuals) after a forecasting model has been applied.

This is not a measure of accuracy, but rather can be used to

indicate if the forecasting method could be improved.

pp y ng a uan a ve orecas ngM th d


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pp y ng a uan a ve orecas ngMethod

Determine MethodTime SeriesCausal Model

Collect data:

Fit an analytical modelto the data:

F(t+1) = f(X1, X2,)

Use the model forforecasting futuredemand

Monitor error:

e(t+1) = D(t+1)-F(t+1)

Model

V lid?

Update Model

Parameters

Yes No

- Determinefunctional form

- Estimate parameters- Validate

Bahan Rapat Gugus Inds Untuk Rapat Persiapan Kuliah 2012-2013 Semester Ganjil

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