Peramalan Model Presentasi

8/19/2019 Peramalan Model Presentasi

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FORECASTING METHOD


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ACTIVITIES IN PRODUCTIO


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What Is ForecastingWhat Is Forecasting• Process of predictinga future event

• Underlying basis ofall business decisions

• Production

• Inventory• Personnel

• Facilities


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• Used when situationis vague & little dataexist

• New products

• New technology

• Involve intuition,experience

• e.g., forecastingsales on Internet

Qualitative Methods

Forecasting A!!roachesForecasting A!!roaches

Quantitative Metho


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• Used when situation is ‘stable & historicalexist

• !xisting products• Involve "athe"atical techni#ues

Quantitative Metho

Forecasting A!!roachesForecasting A!!roaches

• Used when situationis vague & little dataexist

• New products

• New technology

• Involve intuition,experience

Qualitative Methods


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"#antitati$e Forecasti"#antitati$e Forecasti

• $elect several forecasting "ethods• ‘Forecast the past

• !valuate forecasts

• $elect best "ethod

• Forecast the future• %onitor continuously forecast accuracy


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CausalModels

"#antitati$e ForecastingMetho%s"#antitati$e ForecastingMetho%s

QuantitativeForecasting

Time Series

Models

RegressionExponentialSmoothing

Trend

ModelsMovingAverage


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What is a Ti&e SeriesWhat is a Ti&e Series

• i"e series data is a se#uence of observacollected fro" a process

with e#ually spaced periods of ti"e F

Forecast based only on past values

• !xa"ple• 'ear( )**+)**)**-)**)***

• $ales( -.- /.+ *.- */.0 *0.)


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Ti&e Series Co&!onentsTi&e Series Co&!onents

Trend

Seasonal

Cyclical

Irregular


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Tren% Co&!onentTren% Co&!onent

• Persistent, overall upward or downwardpattern

• 1ue to population, technology etc.

• $everal years duration

Mo. Qtr. !r.

Response

© 1984-1994 T/Maker


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Tren% Co&!onent

• 2verall Upward or 1ownward %ove"ent

• 1ata a3en 2ver a Period of 'ears

Sales

Time

U p w a r d


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C'c(ica( Co&!onentC'c(ica( Co&!onent

• 4epeating up & down "ove"ents• 1ue to interactions of factors in5uencingecono"y

• Usually 06)7 years duration

Mo. Qtr. !r.

Response

Cycle


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C'c(ica( Co&!onent

• Upward or 1ownward $wings• %ay 8ary in 9ength

• Usually 9asts 0 6 )7 'ears

Sales

Tim

C y c l e


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Seasona( Co&!onentSeasona( Co&!onent

• 4egular pattern of up & down 5uctuations• 1ue to weather, custo"s etc.

• 2ccurs within one year

Mo. Qtr.

Response

Summer

© 1984-1994 T/Maker Co.


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Seasona( Co&!onen

• Upward or 1ownward $wings• 4egular Patterns

• 2bserved :ithin 2ne 'ear

Sales

Time "Monthly or Quarterly#

W i n t e r


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Irreg#(ar Co&!onentIrreg#(ar Co&!onent

• !rratic, unsyste"atic, ‘residual 5uctuations• 1ue to rando" variation or unforeseen events

• $hort duration &nonrepeating

INTRODUCTION TIME SERIES


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INTRODUCTION TIME SERIESMETHOD). i"e series are best when applied to short6ter"

forecasts.0. i"e series "odels prove "ost satisfactory when

historical data contain either no syste"atic datapattern or when the changes are occurring very sor consistently.

/. 1ata re#uire"ents and easy of i"ple"entation afunction of the speci;c ti"e series techni#ue sele


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NA)VE MODE*

• Uses recent past as the best indicator o

the future.

• he error associated with this "odel isco"puted as(

t t Y Y =

+1ˆ

t t t Y Y e ˆ−=


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E+a&!(e ,or theNa-$e Mo%e(

:ee3 $ales Forecast

) * 6

0 *

/ *

+ )0 * * )0

- )0 *

)) )0

* ? ))

E ( , th N -


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E+a&!(e ,or the Na-$eMo%e(

:ee3 $ales

Forecast !rror @bsolute

!rror

$#uared

!rror) *

0 * A) ) )

/ * ) ) )

+ )0 * / / *

* )0 A/ / *

- )0 * / / *

)) )0 A) ) )

$u" 0 )0 /7

%ean 7.// 0 +


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TIME SERIES METHOD

Also Known as Averaging methods:• he basic pre"ise of these "odels is that a weighte

average of past observations can be used to s"oot5uctuations in the data in the short ter"

• @veraging "ethods are suitable for stationary ti"edata where the series is in e#uilibriu" around a convalue < the underlying "ean> with a constant varianti"e.


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Mo$ing A$erage Gra!hMo$ing A$erage Gra!h

!ear

SalesActual


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Si&!(e A$erage Mo%e(

• $i"ilar to the naBve "odel, this "odeluses part of the historical data to "a3e forecast.

n

Y

Y

n

t

t

t

∑

= =+1

1ˆ


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Mo$ing A$erage Mo%e(

• 4ecent observations play an i"portant

the forecast.• @s new observations beco"e availableaverage is co"puted.

• he choice of using a s"aller or larger

of observations has i"plications for theforecast.


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• hen6period &o$ing a$erage builds a forecastaveraging the observations in the "ost recent n

periods(

• where x t represents the observation "ade in perand A

t denotes the "oving average calculated a

"a3ing the observation in period t .

The Mo$ing.A$erage Mo%e(


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Mo$ing A$erage/An E+a&!(e0Mo$ing A$erage/An E+a&!(e0

'ou wor3 for Firestone ire. 'ou want to s"ooth

rando" 5uctuations using

a /6period "oving average.

)**+07,777

)** 0C,777)**-00,777

)**0,777

)***0+,777


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Mo$ing A$erage/So(#tion0Mo$ing A$erage/So(#tion0

'ear $ales %@ in ),777

)**+07,777 N@

)** 0C,777 E/ 00

)**-00,777 E/ 0C

)**0,777 E/ 0C

)***0+,777 N@


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Mo$ing A$erageYear Response Moving

Ave

1994 2 NA

1995 5 3

199 2 3

199! 2 3.!

1998 ! 5

1999 NA94 95 9 9! 98

8

6

4

2

0

Sales


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Do#1(e Mo$ing A$erage Mo%• Used when we have a linear trend in the data

• wo diGerent "oving averages are co"puted in th

• he idea is to re"ove the trend.

Do#1(e Mo$ing


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Do#1(e Mo$ingA$erage Mo%e(

:ee3 $ales

$i"ple%oving@verage

$i"ple%oving@verage

Forecast

1ouble%oving@verag

) *

0 )) )7

/ )7 )7.+ )7 )7.0+

+ )C )0 )7.+ )).0+

) ) )0 )C

- 00 07 ) )

0/ 00.+ 07 0).0+

Do#1(e Mo$ing A$erage Mo%


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Do#1(e Mo$ing A$erage Mo%234


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Exponential Smoothing Method

• !hi method pro"ide an exponentially weighted mo"ing a"e

all pre"io$ly o%er"ed "al$e&

• 'ppropriate #or data with no predicta%le $pward or downwa

• !he aim i to etimate the c$rrent le"el and $e it a a #oreca

#$t$re "al$e&

EXPONENTIAL SMOOTHING METHOS


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EXPONENTIAL SMOOTHING METHOS

• he si"plest exponential s"oothing "ethod is th

s"oothing "ethod where only one para"etto be esti"ated

• Holts "ethod "a3es use of two diGerent para"eallows forecasting for series with trend.

• Holt6:inters "ethod involves three s"oothing pato s"ooth the data, the trend, and the seasonal in


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(o trend or

eaonal pattern)

SingleExponential

Smoothing

Method

*olt+ !rend

Corrected

Exponential

Smoothing

Method

*olt,Winter

Method

Ue -th

Method

.inear trend

and no eaonal pattern)

/oth trend

and eaonal pattern)

( ( (


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SINGLE EXPONENTIAL SMOOTHING METHO


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*olt+ Exponential moothing

• *olt+ two parameter exponential moothing method i an ex

imple exponential moothing&

• t add a growth #actor or trend #actor3 to the moothing e$

way o# ad5$ting #or the trend&

*olt+ Exponential Smoothing


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*olt Exponential Smoothing

• !hree e$ation and two moothing contant are $ed in the

• !he exponentially moothed erie or c$rrent le"el etimate&

• !he trend etimate&

• orecat m period into the #$t$re&


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• 't 7 Etimate o# the le"el o# the erie at time t

• α 7 moothing contant #or the data&

• yt 7 new o%er"ation or act$al "al$e o# erie in period t&

• β 7 moothing contant #or trend etimate

• !t 7 etimate o# the lope o# the erie at time t

• m 7 period to %e #orecat into the #$t$re&


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• !he weight α and β can %e elected $%5ecti"ely or %y minimmea$re o# #orecat error $ch a 9MSE&

• .arge weight re$lt in more rapid change in the componen

• Small weight re$lt in le rapid change&


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• !he initialiation proce #or *olt+ linear exponential moot

re$ire two etimate:

• -ne to get the #irt moothed "al$e #or .1

• !he other to get the trend %1&

• -ne alternati"e i to et '1 7 y1 and


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Winter+ Exponential Smoothing

• Winter+ exponential moothing model i the econd extenio %aic Exponential moothing model&

• t i $ed #or data that exhi%it %oth trend and eaonality&

• t i a three parameter model that i an extenion o# *olt+ m

• 'n additional e$ation ad5$t the model #or the eaonal co


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• !hree e$ation and two moothing contant are $ed in the

• !he exponentially moothed erie or c$rrent le"el etimate&

• !he trend etimate&

• orecat m period into the #$t$re&

33212 11 −− +−+= t t t t b L y L α α

11 313 −− −+−= t t t t b L Lb β β

t t mt mb L F +=

+


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• .t 7 Etimate o# the le"el o# the erie at time t

• α 7 moothing contant #or the data&

• yt 7 new o%er"ation or act$al "al$e o# erie in period t&

• β 7 moothing contant #or trend etimate

• %t 7 etimate o# the lope o# the erie at time t

•m 7 period to %e #orecat into the #$t$re&


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• !he weight α and β can %e elected $%5ecti"ely or %y minimmea$re o# #orecat error $ch a 9MSE&

• .arge weight re$lt in more rapid change in the componen

• Small weight re$lt in le rapid change&


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• !he initialiation proce #or *olt+ linear exponential moot

re$ire two etimate:

• -ne to get the #irt moothed "al$e #or .1

• !he other to get the trend %1&

• -ne alternati"e i to et .1 7 y1 and

0

;

1

14

1

121

=

−

=

−=

b

or

y yb

or

y yb


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• ' with *olt+ linear exponential moothing< the weight α<can %e elected $%5ecti"ely or %y minimiing a mea$re o# #

error $ch a 9MSE&

• ' with all exponential moothing method< we need initial "

the component to tart the algorithm&

• !o tart the algorithm< the initial "al$e #or . t< the trend %t< anindice St m$t %e et&

i i l hi


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• !o determine initial etimate o# the eaonal indice we need to $e at leat

complete eaon= data i&e& period3&!here#ore


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• We will apply Winter+ method to 'cme !ool company ale

"al$e #or α i &4< the "al$e #or β i &1< and the "al$e #or γ i &;• !he moothing contant α moothe the data to eliminate ran

• !he moothing contant β moothe the trend in the data et&

Wi + E i l S hi


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• !he moothing contant γ moothe the eaonality in the da

• !he initial "al$e #or the moothed erie .t< the trend %t< and

eaonal index St m$t %e et&

Meas#res o, Forecast Acc#rac'


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MA" 7 A#$%a& 'ore#as$−∑

n

M() 7 A#$%a& 'ore#as$3

,1

2−∑

n

MA*) 7 A#$%a& 'ore#as$−

n

/ A#$%a&+1,,∑(

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