Applications of Diffusion Models in Telecommunications Nigel Meade

Transcription

1 Applications of Diffusion Models in Telecommunications Nigel Meade

2 2 Introduction Recent examples of diffusion in telecomms Definition of diffusion model Survey of telecomms applications Extrapolation Use of explanatory variables Inter-market models Multi - national Multi - generation Multi - technology Strengths Weaknesses

3 Recent examples of diffusion in telecomms Financial Times 20/9/2004

4 Recent examples of diffusion in telecomms 1a Potential penetration of 20 million households 4 Rapid Growth Gradual growth Growth quickly evapoarates Financial Times 20/9/2004

5 Recent examples of diffusion in telecomms Financial Times 22/9/2004

6 Recent examples of diffusion in telecomms 2a No obvious limit to potential penetration 6 Rapid Exponential Growth Gradual linear growth Growth to a saturation level Financial Times 22/9/2004

7 Recent examples of diffusion in telecomms Financial Times 21/9/2004

8 Recent examples of diffusion in telecomms G starts to attract 2G customers Forbes 20/9/2004

9 Definition of Diffusion models 9 A new technology diffuses into a population Saturation level Early Adopters Early Majority Adoption per Period Cumulative Adoption Late Majority Laggards Time

10 10 Example UK Colour TV UK Adoption of Colour TV Early Adopters Early Majority Adoption per Period Cumulative Adoption Late Majority Laggards Time

11 Forecasting Issues of Interest 11 What will the rate of adoption be at a particular time? How many potential adopters are there in total? When will peak demand occur? How high is peak demand?

12 Problems in Forecasting 12 Identify the appropriate model Estimate its parameters Predict future adoption (with a prediction interval). Model identification is crucial the literature reveals 29 possible models there is no best single model

13 A selection of diffusion models 13 Logistic Gompertz Log Reciprocal Penetration (Xt) Penetration (Xt) Penetration (Xt) Time (t) Time (t) Time (t) Cumulative Lognormal Extended Logistic (A) Weibull Penetration (Xt) Penetration (Xt) Penetration (Xt) Time (t) Time (t) Time (t)

14 Model identification 14 Meade & Islam (Management Science 1998) The best fitting model is not necessarily the best forecasting model They propose combining criteria based on: Model fit (measured by R 2 Model stability (looks at one step ahead forecasts) These criteria suggest a subset of models which are used to produce a combined forecast

15 Forecasting Cable Television Penetration in US Forecast Region CATV Penetration in US Estimation Region Forecast of Best fitting model Combined Forecast Time

16 Applications in Telecomms 16 Variable Fixed line telephone penetration Business Telephones Author Chaddha & Chitgokepar (1971) Hyett & McKenzie (1975) Bewley & Fiebig (1988) Lee et al (1992) Meade & Islam (1995) Meade & Islam (1996) Model Logistic Logistic Flexible logistic Non-linear growth Comparison of 14 models Growth + econometric

17 Modelling approaches 17 Extrapolate from available data 12 UK Business Telephones (Mil) Fixed Saturation Level Actual Telephones Date

18 Modelling approaches 18 Dynamic saturation level by relation to environmental variables 12 UK Business Telephones (Mil) Implied Saturation Level (local logistic) Fixed Saturation Level Implied Saturation Level (NSRL) Actual Telephones Date

19 Multi national models Pooling data series from several countries is used to overcome data shortage 19 See Gatignon et al (1989) Islam et al (2002) Ln(no. of DCTs) The diffusion of Digital Cellular Telephones (DCT) Belgium Norway 10 Portugal 9 Sweden Switz. 8 UK 7 Hungary Turkey 6 Mar-92 Mar-93 Mar-94 Mar-95 Mar-96 Mar-97 Mar-98 Mar-99

20 20 Multi generation models Successive Generations of Technology Islam & Meade (1997) Third Generation Adopters Second Generation Adopters First Generation Adopters Time

21 21 3 Generations of Austrian Mobiles First & Second Generation Subscribers (000) Generation 1: nmt Generation 2: TACS Generation 3: GSM 50 Third Generation Subscribers 0 Dec-84 Dec-85 Dec-86 Dec-87 Dec-88 Dec-89 Dec-90 Dec-91 Dec-92 Dec-93 Dec-94 Dec-95 0

22 Multi technology models 22 Forecast international adoption of technology B using history of adoption of technology A (Meade & Islam, 2003) FAX Cellphone Frequency (% Hazard Rate - h(t) Conditional hazard t1 = 4 Marginal hazard Conditional hazard t1 = Time to adoption t Bivariate histogram of adoption times Hazard rates for early and late adopting countries

23 Conclusions 23 Strengths Intrinsic saturation level Data based forecasts grounded on actuality Prediction intervals can be provided Weaknesses Data based models prefer more data to less Forecasts made before point of inflexion have high uncertainty

24 The end 24