presentation - session 10

7/27/2019 Presentation - Session 10

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Forecasting Techniques

Part 2



© Copyright Coleago 2010

Learning Objectives

ExplanatoryMethods

How to use explanatory methods, notably regressionanalysis to make a forecast

Curve Fitting Using the product life cycle and s-shaped growth

curves to forecast take-up

Diffusion of

Innovation

The Bass model of diffusion of innovation to forecast

new demand for new services

Price Elasticity

of Demand

Price elasticity of demand in telecoms markets,

practical applications

1




Learning Objectives

ExplanatoryMethods




Diffusion of

Innovation



Price Elasticity

of Demand



2



Explanatory or causal methods

Explanatory or causal methods rely on observations that a change in one variable, for

example price, has an effect on the change in another variable, typically demand. Causal relationships are used to provide information that will help decision-making, for

example to predict the effect increasing advertising spend will have on sales.

We need to find an answer to

the following three questions:

– Is there a relationship? – What is the relationship?

– How good is the relationship?

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D e p e n d e n t V a r i a b l e

Explanatory Variable

© Copyright Coleago 2010 3



Using regression analysis to determining the type of relationship

between the causal and dependent variable

Regression analysis is used to determine how explanatory variables relate to thevariable to be forecast.

The objective of regression analysis is to find the function that best describes

the relationship between causal variables and a dependent variable.

This relationship can be described as function of the type y = a + f (x), where x

is the explanatory variable and y the dependent variable to be forecast.

Single variable linear regression is the simplest form of regression analysis. It is

also referred to as "simple regression“ which would give a formula of the type

y = a * x + b.

The calculations involved in regression analysis are extensive, but in practice

regression analysis can be performed easily using Excel.




The information required for regression analysis

A definition of the dependent variable, i.e. the variable to be forecast, for example

demand

An explanatory variable, for example the quarterly advertising expenditure

Sufficient data points to make statistical analysis meaningful

– For example, if there are only 5 or 6 observation, statistical analysis is useless.

With more than 20, several hundred or even thousands of observations, such as

past purchase data or usage data, statistical analysis is appropriate

The nature of the relationship between the variables, i.e. linear, exponential,

polynomial etc

– This helps to eliminate spurious results. For example by chance a polynomialfunction that waves about might fit the data, but in reality the relationship is linear




Two outputs from a regression analysis

A function or formula that describes the relationships between the explanatoryvariables and the dependent variable

– This formula can be readily used in spreadsheets for the purposes of

forecasting.

A measure of goodness of fit, i.e. how well the function fits the observed data

– As with time series analysis, some of the variation in the observed data will be

due to random events, i.e. error. Producing a good fit means minimising

error.




Practical exercise: Regression analysis using Excel

Open the Excel file “Forecasting Techniques”, tab Example 4 Highlight the data set (both columns) and create an XY graph

Click in the graph

Click a point on the series

Right click and select ADD TRENDLINE

Under TYPE tab select LINEAR

Check the bock to display the equation on the chart and check the box to display

the R2 value

Click OK

Try it now

You find the solution on tab Example 4S




Using the result of Excel generated regression analysis

The equation the form of y = ax + b can be used to make a forecast, with x being the

explanatory variable and y the dependent variable. R2 is called the coefficient of determination. The discussion of the detailed mathematics

to calculate R2 is beyond the scope of this course, but its interpretation is important.

The value of R2 ranges from

0 to 1.

1 means that all of thevariation in the data is

explained by the explanatory

variable.

0 means the variable does

not explain anything.

y = 1.4913x + 3.6692R² = 0.96

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S a l e s

Advertis ing Expenditure




Example of non-linear regression analysis. Excel File

“Forecasting Techniques”, tab Example 5

From the study of market behaviour it may be known that the type of function should

have a particular form. Demand for a product may be very high for high incomes and is

disproportional lower in lower income groups, but there is very limited demand even invery low income groups. This suggests an exponential curve with an R2 value close to 1.

The chart shows an analysis

based on actual data for

mobile users and their

monthly bill from the USA.

In 1999 a forecaster could

have used the formula

shown on the chart to make

a forecast of the expected

average month bill as a

function of the total mobileuser forecast.

Y = the bill amount and X =

the number of mobile users.

y = 1964.1x-0.343R² = 0.9943

0

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0 20,000 40,000 60,000 80,000

A v . M o n t h l y B i l l 1 9 9 9 R e a l U

S $

Subscribers '000

Aver Monthly Bill* and Installed Base of Mobile Subscribers USA

* Excluding long distance & roaming Source: CTIA





Learning Objectives

ExplanatoryMethods




Diffusion of

Innovation



Price Elasticity

of Demand



10



Market behaviour models: an overview

Economics and business studies provide a wealth of empirical data. From the

study of how markets, competitors and prices behave, a number of generallyaccepted models have emerged.

– Examples are the product life cycle, diffusion of innovation etc.

These models are similar to the laws of natural science and provide a useful tool

box for the forecaster.

Market behaviour models fall into the category of qualitative forecast methods.

Market behaviour models share similarities with time series and causal models,

because they explain what happens over time and how different factors are

related.

– For example, price elasticity is an observation that describes how demand

reacts to price and it may be possible to determine the price elasticity

coefficient using regression analysis.




Using the product life cycle for forecasting

Observed market behaviour: Markets for products grow in an s-shaped manner and

eventually decline to be replaced by new products.

For the purposes of market forecasting, the product life cycle is best analysed in five

phases:

Introduction: Sales volumes

are low and increase in a near

linear fashion. There are few

competitors, the product may

suffer from quality problems

and there is li ttle variety

between different versions of

the product. Unit costs and

prices are high

Accelerating Growth Phase:

Buyer groups widen and sales

increase rapidly. Moresuppliers enter the market and

prices start to fall. A greater

variety of product forms start to

appear.

Decelerating growth phase: Penetration is still

increasing, but at a declining rate. Prices are falling

quicker and become a significant issue. Variety

increases further and there is an increased focus on

product quality. Late adopters buy the product.

Maturity: When penetration

is no longer increasing.

There may be consolidation.

Prices are declining further,

but at a slower rate.

Decline: Prices are

low, but no longer

declining. Some

competitors may exit

the market

I n t r o d u c t i o n

A c c e l e r a t i n g

G r o w t h

M a t u r i t y

D e c l i n e

Time

I n d u s t r y R e v e n

u e

D e

c e l e r a t i n g

G r o w t h




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2 0 1 6

2 0 1 8

M o b i l e U s e

r s ' 0 0 0

Curve fitting relies on a small number of historic data points, for

example mobile users numbers during the past few years

Actual observedhistoric data

Past Future




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r s ' 0 0 0

Curve fitting requires an estimate for the upper asymptote of the

curve, i.e. the line that describes demand at maturity


Past Future

Maximum

potential

demand




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M o b i l e U s e

r s ' 0 0 0

Curve fitting is a form of extrapolation based on the observation that

market developments follow an s-curve


Past Future

Forecast Using

S Curve

Select S curve that

fits well with actual

historic data




Pearl’s equation can be used in a practical manner to produce an s-curve

yt = m * ( 1 / (1 + a * e^ (-b * t)))

where

yt = the penetration in year t

m = the demand at maturity

a = a factor giving more / less growth later or earlier, the neutral value is 99

t = number of years after launch

b = a factor shortening or lengthening the time to maturity (calculated, see

below)

b = 1 / T * ( ln ( a / ( 1/0.99 - 1)))

where

a = a factor giving more / less growth later or earlier, the neutral value is 99

T = the total years to maturity




Fitting the curve

The essence of curve fitting is to select a particular s-curve that fits well with the

historic data points.

Assuming you have determined the maximum potential demand, i.e. the

demand at maturity, you now have to vary in the s-curve formula the values for

the parameters

– A (the curve skew value) to give more or less growth earlier or later

– And the time to maturity, fore example the number of years.

The effect of varying the curve skew value a and the time to maturity is show on

the following two slides.




The curve skew value a gives more or less growth earlier or later, but

maturity is reached at the same time

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10%

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40%

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60%

70%

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90%

100%

0 1 2 3 4 5 6 7 8 9 10Years

% o

f M a t u r i t y

A = 25 A = 99

A = 400

a = 99 produces a

symmetrical curve

higher values delay growth

lower values bring growth

forward


Th ti t t it b l th d h t d b i th



The time to maturity can be lengthened or shortened by varying the

factor t. T can be years or any other suitable interval.

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10%

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90%

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0 1 2 3 4 5 6 7 8 9 10Years

% o

f M a

t u r i t y

Years to Mature = 5

Years to Mature = 10

Years to Mature = 15




Excel File “Forecasting Techniques”, tab Example 6




Excel File “Forecasting Techniques”, tab Example 6

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2 0 1 8

I n s t a l l e d

B a s e

Actual Model





Learning Objectives

Explanatory

Methods

How to use explanatory methods, notably regression

analysis to make a forecast



Diffusion of Innovation

The Bass model of diffusion of innovation to forecastnew demand for new services

Price Elasticity

of Demand



22



Diffusion of innovation model of market behaviour

The Bass model is based on the observation that there are some innovators who adopt

products early and imitators who adopt the products as a result of having seen other

people using the product.

It a useful techniques for new products and services, i.e. where curve fitting does not

work because there is no historic data

nt = nt-1 + p (m – nt-1) + q (nt-1 / m) (m – nt-1)

where:nt = the number of users in year t

m = the maximum penetration or market potential, i.e. the total number of

people who will eventually use the product or service

p = the coefficient of external influence or coefficient of innovation, which is the

probability that an individual will start using the product or service because

of advertising or other external factors

q = the coefficient of internal influence or imitation, which is the probability that

individuals buy the product because of "word-of-mouth" or other influence

from those who already have the product.


Bass model curves worked example Excel File “Forecasting Techniques”



Bass model curves, worked example. Excel File Forecasting Techniques ,

tab Example 7

Estimates for p and q can be obtained by looking at similar products or through market

research. An estimate for m (the maximum potential penetration) can also be obtained

through market research.

The Bass model explains

how innovation diffuses,

but there is uncertainty of

knowing the values for p

and q.

The innovators “p” could

be identified through

market research i.e. those

who say they would adopt

within 1 year of

availability.

0%

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40%

50%

60%

70%

80%

90%

100%

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p = 0.02, q = 0.60

p = 0.04, q = 0.30


The speed of diffusion of innovation varies between countries and is



The speed of diffusion of innovation varies between countries and is

similar for different products within the same country

A recent study found that the speed diffusion of innovation varies between

countries depending on the cultural factors. Detailed insight is provided by the

research findings published by Trellis, Stremersch and Yin 1.

This shows that time to take-off varies, among other things, substantially by

country. In Scandinavian countries time to take-off was almost as half long as in

Mediterranean countries. The mobile market does not appear to be an

exception to this.

In order to gain insight into the speed of adoption of a new services, apart from

looking at market research you might analyse diffusion curves of other

technology services and products or other consumer products in your country.

1) Trellis, Stremersch and Yin; “The International Takeoff of New Products: The Role of Economics,

Culture, and Country Innovativeness”, Marketing Science, Vol. 22 No. 2, Spring 2003, pp 188-208.

The research paper is included in the course pack.


C l i f “Th I t t i l T k Off f N P d t ”



Conclusions from “The Internat ional Take-Off of New Produ cts ”

Products take-off faster in wealthier countries than in poorer countries

Products take-off faster in industrious countries

Products take-off faster in high media intensity countries

Products take-off faster in highly educated economies

PC and Internet penetration would be an interesting new variable to include in

the analysis


L i Obj ti




Learning Objectives

Explanatory

Methods

How to use explanatory methods, notably regression

analysis to make a forecast



Diffusion of Innovation

The Bass model of diffusion of innovation to forecastnew demand for new services

Price Elasticity

of Demand



27

D d l ti iti



Demand elasticities

Elasticities are a measure of how a change in a variable affects demand.

There are many different types of elasticities:

– price elasticity of demand

– cross price elasticity of demand

– income elasticity of demand

– elasticity to advertising expenditure

– etc…..


In the context of market forecasting the most important elasticity is



price elasticity of demand (PED)

Quantity

P r i c e

∆ Price

∆ Quantity

Inelastic Demand: Change in price yields

small change in demand

Quantity

P r i c e

∆ Price

∆ Quantity

Elastic Demand: Change in price yields big

change in demand

PED =∆ Q

∆ P= gradient of blue line =

Q2 – Q1

Q1

P2 – P1

P1© Copyright Coleago 2010 29

In practice elasticities have to be estimated rather than measured



In practice elasticities have to be estimated rather than measured

It is unlikely that the there is no effect on demand if prices change, i.e. the price

elasticity coefficient is unlikely to be 0.

Equally, it is unlikely that if prices decline, demand increases in exactly the same

proportion, i.e. the price elasticity coefficient is unlikely to be -1.

Studies have produced estimates for price elasticity coefficients in telecoms market

ranging from:

– - 0.8 for international calls

– to - 0.1 for local calls

Elasticities are generally not constant. The law of diminishing return applies, e.g. if

prices fall to zero demand would be infinite.

If prices are very low in the context of the expenditure of an individual, changes in

price will have little effect on demand, i.e. the price elasticity coefficient is close to 0.


In any forecast it is good practice to use price elasticity explicitly



In any forecast, it is good practice to use price elasticity explicitly

Although the price elasticity coefficient may not be known, in any forecast an assumption

must be made that a change in price has some effect on demand.

– For example, if a forecast assumes that if prices drop by 10%, revenue will decline by

10%, i.e. the quantity demanded remains constant, implicitly the price elasticity

coefficient is 0.

Even if the price elasticity

coefficient is not an explicit

input, it should be calculatedas an output.

Open the Excel file

“Forecasting Techniques” and

go to the tab Example 8.

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100 105 110 116 122 128 134 141 148 155Quantity

U n i t P r i c e

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3,000

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7,000

8,000

9,000

10,000

R e v e n u e

Unit Price

RevenuePrice Elasticity Coefficient = -0.40




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