2007/12/21 MR Final Report 1 An Evaluation of the Time-varying Extended Logistic, Simple Logistic,...

2007/12/21 MR Final Report 1

An Evaluation of the Time-varying Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products

Cindy Wu

Advisor: Charles V. Trappey,


Introduction

With the rapid introduction of new technologies, product life cycles (PLC) for electronic goods become shorter and shorter.

Less data becomes available for analysis

Using smaller data sets to forecast future trends is important


Research Purpose

This research studies the forecast accuracy of long and short lifecycle products data sets using the simple logistic, Gompertz, and extended logistic models.

Time series datasets for 22 electronic products and services were used to evaluate and compare the performance of the three models.


Product Life Cycle

Introduction: slow sales growth Growth: rapid sales growth Maturity: sales growth declines Decline: sales growth falls

IntroductoryStage

GrowthStage

MaturityStage

Decline Stage

Time

MarketSales


S-curve

Time

Cumulative sales

Introduction

Growth

Mature

Decline

Technology product growth follows S-curve Initial growth is often slow Followed by rapid exponential growth Falls off as a limit to market share is approached


Growth Curve Model

Growth curves models are widely used in technology forecasting and have been developed to forecast the penetration rate of technology based products.

Growth curve models are expressed by logistic form, so they are also referred as “S-shaped” curves.

Simple logistic curve and Gompertz curve are the most frequently referenced.


Technological Forecasting Models

Simple Logistic Curve Model

Gompertz Model

Extended Logistic Model


Simple Logistic Curve Model

btT ae

Ly

1

btayLyY ttt lnln

L ty: is the upper bound of

e : natural logarithm

a b : parameter

: the variable care to forecastty


Gompertz Model

btaet Ley

btayLY tt lnlnln

L ty: is the upper bound of

e : natural logarithm

a b : parameter

: the variable care to forecastty


Limitation of the Models

The upper limit of the curve should be set correctly or the prediction will become inaccurate.

Setting the upper limit to growth is difficult and ambiguous Necessity productShort life cycle product

L1

Time

L2

A

B



Meyer and Ausubel (1999)The upper limit of the curve is not

constant but dynamic over timeExtending the simple logistics model with

a carrying capacity

k

ybydt

df1

tk

ybydt

df1is extended to


Technological Forecasting Models


is the time-varying capacity and is the function which is similar to logistic curve

ateDtk 1

bt

at

btteC

eD

eC

tky

1

1

1


The Measurements of Fit and Forecast Performance

n

ff

MAD

n

iii

1

ˆ

n

ff

RMSE

n

iii

1

2ˆ

Mean Absolute Deviation (MAD)

Root Mean Square Error (RMSE)

The smaller the MAD and RMSE, the better performance


Data Collection - Penetration rate

Product SamplePeriod

SampleSize

Color TV 1974 ~ 2004 31

Telephone 1964 ~ 2004 35

Washing Machine 1974 ~ 2004 31

ADSL subscription 2000 ~ 2006 26

Mobile internet subscription 2000 ~ 2006 20

Broadband network 2000 ~ 2006 26


Data Collection – Cumulative sales


SampleSize

LCD-TV 2003 ~ 2007 18

19”LCD monitor 2003 ~ 2007 18

CCD DC 2003 ~ 2007 18

DC >5m 2003 ~ 2007 18

WLAN (802.11g) 2003 ~ 2007 18

Cable Modem 2003 ~ 2007 18

Combo ODD 2003 ~ 2007 18

Barebones 2003 ~ 2007 18


Data Collection – Cumulative sales


SampleSize

China PAS 2003 ~ 2007 18

LCD panel for TV 2003 ~ 2007 18

LCD panel for notebook 2003 ~ 2007 18

Color-65k mobile phone

2003 ~ 2007 18

Server 2003 ~ 2007 18

LCD-TV >30” 2004 ~ 2007 14

VoIP IAD 2004 ~ 2007 14

VoIP router 2004 ~ 2007 14


Market Growth for Saturation Data Sets

0

20

40

60

80

100

120

1964

1970

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

.06

2000

.12

2001

.06

2001

.12

2002

.06

2002

.12

2003

.06

2003

.12

2004

.06

2004

.12

2005

.06

2005

.12

2006

.06

Time

Satu

ratio

n (%

)

Color TV Telephone Washing machine ADSL Mobile internet Broadband network


Market Growth for Cumulative Data Sets

0

20000

40000

60000

80000

100000

120000

140000

160000

2003

Q1

2003

Q2

2003

Q3

2003

Q4

2004

Q1

2004

Q2

2004

Q3

2004

Q4

2005

Q1

2005

Q2

2005

Q3

2005

Q4

2006

Q1

2006

Q2

2006

Q3

2006

Q4

2007

Q1

2007

Q2

Time

Cum

ulat

ive

sale

s vo

lum

e (t

hous

and)

LCD-TV 19”LCD monitor CCD DC DC >5mWLAN (802.11g) Cable Modem Combo ODD BareboneChina PAS LCD panel for TV LCD panel for notebook Mobile color-65kServer LCD-TV >30” VoIP IAD VoIP Router

Note: the unit of wireless internet is ten thousand. Source: ASIP, Market Intelligence Center, Taiwan


Analysis Steps

The first step (Fit performance) Reserve the last five data points Fit the remaining data points into the three models Compute the coefficients of the models and the

statistics for MAD and RMSE

The second step (Forecast performance) Uses the derived models to forecast the five data

points Compare the forecast with the true observations Compute MAD and RMSE for forecast performance


Results (Penetration Data Set)

Product

Fitting Forecasting

Extended logistic

GompertzSimple logistic

Extended logistic


Color TV 1 2 3 1 2 3

Phone 1 2 3 1 2 3

Washing Machine

1 2 3 1 2 3

ADSL 1 2 3 1 2 3

Mobile Internet

1 2 3 1 2 3

BroadbandNetwork

1 3 2 1 2 3


Results (Cum. Sales Data Set)

Product

Fitting Forecasting

Extended logistic


Extended logistic


LCD-TV 1 2 3 1 2 3

19”LCD monitor 1 2 3 2 1 3

CCD DC 1 2 3 1 2 3

DC >5m 1 2 3 2 1 3

WLAN (802.11g) 1 2 3 1 2 3

Cable Modem 1 2 3 1 2 3

Combo ODD 1 2 3 1 2 3

Barebones 1 2 3 1 2 3

China PAS 1 2 3 1 2 3

LCD panel for TV 1 2 3 2 1 3

LCD-TV >30” 1 3 2 3 2 1

VoIP IAD 1 2 3 2 1 3


Conclusion

This study compares the fit and prediction performance of the simple logistic, Gompertz, and the extended logistic models for four electronic products.

Since the simple logistic and Gompertz curves require the correct setting of upper limits for accurate market growth rate predictions, these two models may not be suitable for short life cycle products with limited data.


Conclusion

The time-varying extended logistic model fits short life cycle product datasets better than the simple logistic, and Gompertz models for 70% of the 18 product data sets for which the extended logistic model could be fitted.

Besides, the time-varying extended logistic model is better suited to predict market capacity with limited historical data as is typically the case for short lifecycle products and services.


Limitations

Since the capacity of extended logistic model is time-varying and is a logistics function of time, it is not suitable for the data with linear curve.

The data sets for LCD panel for notebooks, color-65k mobile phones, servers, and VoIP routers would not converge when using the time-varying extended logistic model to estimate the coefficients.


Limitations

LCD panel for notebooks, servers, and VoIP routers data sets are linear

The curve for the color-65k mobile phone has an obvious jump

0

20000

40000

60000

80000

100000

120000

140000

160000

2003Q1 2003Q2 2003Q3 2003Q4 2004Q1 2004Q2 2004Q3 2004Q4 2005Q1 2005Q2 2005Q3 2005Q4 2006Q1 2006Q2 2006Q3 2006Q4 2007Q1 2007Q2Time

Cu

mu

lati

ve

sale

s v

olu

me

(th

ou

san

d)

LCD panel for notebook Mobile color-65k Server VoIP Router

Note: the unit of wireless internet is ten thousand. Source: ASIP, Market Intelligence Center, Taiwan


Meade & Islam (1995)

Source: Meade N, Islam T. Forecasting with growth curves: An empirical comparison. International Journal of Forecasting 1995;11:199-215.

Using telephone data from Sweden to compare the simple logistic, extended logistic, and the local logistic models

The extended logistic model had the worst performance


Future Research

A possible solution for those types of data sets with linear data or with many anomalous data points may be to apply smoothing techniques or data re-interpretation techniques.

Further research can be conducted using Tukey smoothing and data re-interpretation to see if the extended logistic model can be forced to converge and therefore find broader applications for short life cycle data sets.


Thank you.

2007/12/21 MR Final Report 1 An Evaluation of the Time-varying Extended Logistic, Simple Logistic,...

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