Department of Business Administration
FALL 2010-2011
I see that you will
get an A this semester.
Chapter 5: Demand Forecasting
Outline: What You Will Learn . . .








Ch 5 : Demand Forecasting
List the elements of a good forecast.
Outline the steps in the forecasting process.
Describe at least three qualitative forecasting
techniques and the advantages and disadvantages of
each.
Compare and contrast qualitative and quantitative
approaches to forecasting.
Briefly describe averaging techniques, trend and
seasonal techniques, and regression analysis, and
solve typical problems.
Describe two measures of forecast accuracy.
Describe two ways of evaluating and controlling
forecasts.
Identify the major factors to consider when choosing
a forecasting technique
2
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
What is meant by Forecasting and Why?



Forecasting is the process of estimating a
variable, such as the sale of the firm at some
future date.
Forecasting is important to business firm,
government, and non-profit organization as a
method of reducing the risk and uncertainty
inherent in most managerial decisions.
A firm must decide how much of each product
to produce, what price to charge, and how
much to spend on advertising, and planning for
the growth of the firm.
3
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
The aim of forecasting


The aim of forecasting is to reduce the
risk or uncertainty that the firm faces in
its short-term operational decision
making and in planning for its long term
growth.
Forecasting the demand and sales of the
firm’s product usually begins with
macroeconomic forecast of general level
of economic activity for the economy as
a whole or GNP.
4
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
The aim of forecasting



The firm uses the macro-forecasts of general
economic activity as inputs for their microforecasts of the industry’s and firm’s demand
and sales.
The firm’s demand and sales are usually
forecasted on the basis of its historical market
share and its planned marketing strategy (i.e.,
forecasting by product line and region).
The firm uses long-term forecasts for the
economy
and
the
industry
to
forecast
expenditure on plant and equipment to meet its
long-term growth plan and strategy.
5
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecasting Process Map
Statistical
Model
Demand
History
Sales
Marketing
Causal
Factors
Product
Production &
Executive
Management
Inventory
Management
& Finance
Control
Consensus
Process
Consensus
Forecast
6
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Uses of Forecasts
Ch 5 : Demand Forecasting
Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services
7
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Features of Forecasts




Ch 5 : Demand Forecasting
Assumes causal system
past ==> future
Forecasts rarely perfect
because of
randomness
I see that you will
get an A this semester.
Forecasts more
accurate for
groups vs. individuals
Forecast accuracy
decreases
as time horizon
increases
8
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Elements of a Good Forecast
Timely
Accurate
Reliable
Written
9
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Make the forecast
Step 4 Obtain, clean and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
10
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecasting Techniques


A wide variety of forecasting methods are
available to management. These range from the
most naïve methods that require little effort to
highly complex approaches that are very costly
in terms of time and effort such as econometric
systems of simultaneous equations.
Mainly these techniques can break down into
three parts: Qualitative approaches (Judgmental
forecasts) and Quantitative approaches (Timeseries
forecasts)
and
Associative
model
forecasts).
11
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecasting Techniques



Judgmental - uses subjective inputs
such as opinion from consumer
surveys, sales staff etc..
Time series - uses historical data
assuming the future will be like the
past
Associative models - uses
explanatory variables to predict the
future
12
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts



Survey Techniques
Some of the best-know surveys
 Planned Plant and Equipment Spending
 Expected Sales and Inventory Changes
 Consumers’ Expenditure Plans
Opinion Polls
 Business Executives
 Sales Force
 Consumer Intentions
13
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
What are qualitative forecast ?



Qualitative forecast estimate variables
at some future date using the results of
surveys and opinion polls of business
and consumer spending intentions.
The rational is that many economic
decisions are made well in advance of
actual expenditures.
For example, businesses usually plan to
add to plant and equipment long before
expenditures are actually incurred.
14
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts





Surveys and opinion pools are often used to
make short-term forecasts when quantitative
data are not available.
Usually based on judgments about causal factors
that underlie the demand of particular products
or services.
Do not require a demand history for the product
or
service, therefore are useful for new
products/services.
Approaches
vary
in
sophistication
from
scientifically conducted surveys to intuitive
hunches about future events.
The approach/method that is appropriate
depends on a product’s life cycle stage.
15
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts


Polls can also be very useful in
supplementing
quantitative
forecasts,
anticipating changes in consumer tastes or
business
expectations
about
future
economic conditions, and forecasting the
demand for a new product.
Firms conduct opinion polls for economic
activities based on the results of published
surveys
of
expenditure
plans
of
businesses, consumers and governments.
16
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts


Survey Techniques– The rationale for
forecasting based on surveys of economic
intentions is that many economic decisions
are made in advance of actual expenditures
(Ex: Consumer’s decisions to purchase
houses, automobiles, TV sets, furniture,
vocation, education etc. are made months or
years in advance of actual purchases)
Opinion Polls– The firm’s sales are strongly
dependent on the level of economic activity
and sales for the industry as a whole, but also
on the policies adopted by the firm. The firm
can forecast its sales by pooling experts
within and outside the firm.
17
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts



Executive Polling- Firm can poll its top
management from its sales, production,
finance for the firm during the next
quarter or year.
Bandwagon effect (opinions of some
experts might be overshadowed by some
dominant personality in their midst).
Delphi Method – experts are polled
separately, and then feedback is
provided without identifying the expert
responsible for a particular opinion.
18
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Qualitative Forecasts or Judgmental Forecasts




Consumers intentions pollingFirms selling automobiles, furniture, etc.
can pool a sample of potential buyers on
their purchasing intentions. By using
results of the poll a firm can forecast its
sales for different levels of consumer’s
future income.
Sales force polling –
Forecast of the firm’s sales in each region
and for each product line, it is based on
the opinion of the firm’s sales force in the
field (people working closer to the market
and their opinion about future sales can
provide essential information to top
management).
19
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Quantitative Forecasting Approaches



Based on the assumption, the “forces”
that generated the past demand will
generate the future demand, i.e., history
will tend to repeat itself.
Analysis of the past demand pattern
provides a good basis for forecasting
future demand.
Majority of quantitative approaches fall
in the category of time series analysis.
20
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Time Series Analysis




A time series (naive forecasting) is a set of
numbers where the order or sequence of the
numbers is important, i.e., historical demand
Attempts to forecasts future values of the
time series by examining past observations
of the data only. The assumption is that the
time series will continue to move as in the
past
Analysis of the time series identifies patterns
Once the patterns are identified, they can be
used to develop a forecast
21
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecast Horizon

Short term


Medium term


Up to a year
One to five years
Long term

More than five years
22
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Reasons for Fluctuations in Time Series Data





Secular Trend are noted by an upward or downward
sloping line- long-term movement in data (e.g.
Population shift, changing income and cultural changes).
Cycle fluctuations is a data pattern that may cover
several years before it repeats itself- wavelike variations
of more than one year’s duration (e.g. Economic,
political and agricultural conditions).
Seasonality is a data pattern that repeats itself over
the period of one year or less- short-term regular
variations in data (e.g. Weekly or daily restaurant and
supermarket experiences).
Irregular variations caused by unusual circumstances
(e.g. Severe weather conditions, strikes or major
changes in a product or service).
Random influences (noise) or variations results from
random variation or unexplained causes. (e.g. residuals)
23
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecast Variations
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
24
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Uses for Naïve Forecasts
 Stable
time series data
 F(t) = A(t-1)
 Seasonal variations
 F(t) = A(t-n)
 Data with trends
 F(t) = A(t-1) + (A(t-1) – A(t-2))
25
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Techniques for Averaging
 Moving
average
 Weighted moving average
 Exponential smoothing
26
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Moving Averages

Moving average – A technique that
averages a number of recent actual values,
updated as new values become available.
Ft = MAn=
At-n + … At-2 + At-1
n
Weighted moving average – More recent
values in a series are given more weight in
computing the forecast.
wnAt-n + … wn-1At-2 + w1At-1
Ft = WMAn=
n=total amount of number of weights
n
27
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Simple Moving Average
Actual
MA5
47
45
43
41
39
37
MA3
35
1
2
3
4
5
6
7
8
9
10 11 12
At-n + … At-2 + At-1
Ft = MAn=
n
28
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Simple Moving Average






An averaging period (AP) is given or selected
The forecast for the next period is the arithmetic
average of the AP most recent actual demands
It is called a “simple” average because each
period used to compute the average is equally
weighted
It is called “moving” because as new demand
data becomes available, the oldest data is not
used
By increasing the AP, the forecast is less
responsive to fluctuations in demand (low
impulse response and high noise dampening)
By decreasing the AP, the forecast is more
responsive to fluctuations in demand (high
impulse response and low noise dampening)
29
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
Ft = forecast for period t
Ft-1 = forecast for the previous period
= smoothing constant
At-1 = actual data for the previous period



Premise--The most recent observations might
have the highest predictive value. Therefore,
we should give more weight to the more
recent time periods when forecasting.
Weighted averaging method based on
previous forecast plus a percentage of the
forecast error
A-F is the error term,  is the % feedback
30
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Exponential Smoothing Forecasts





The weights used to compute the forecast
(moving average) are exponentially
distributed.
The forecast is the sum of the old forecast
and a portion (a) of the forecast error
(A t-1 - Ft-1).
The smoothing constant, , must be
between 0.0 and 1.0.
A large  provides a high impulse response
forecast.
A small  provides a low impulse response
forecast.
31
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Example-Moving Average
Ch 5 : Demand Forecasting
Central Call Center (CCC)
wishes to forecast the number of
incoming calls it receives in a day
from the customers of one of its
clients, BMI.
CCC schedules the appropriate
number of telephone operators
based on projected call volumes.
CCC believes that the
most recent 12 days of call
volumes (shown on the next
slide) are representative of
the near future call volumes.
32
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Moving Average





Moving Average
Use the moving average method with an
AP = 3
days to develop a forecast of the call
volume in Day 13 (The 3 most recent
demands)
compute a three-period average forecast
given scenario above:
F13 = (168 + 198 + 159)/3 = 175.0 calls
33
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Weighted Moving Average




Weighted Moving Average (Central Call Center )
Use the weighted moving average method with an
AP = 3 days and weights of .1 (for oldest datum),
.3, and .6 to develop a forecast of the call volume
in Day 13.
compute a weighted average forecast given
scenario above:
F13 = .1(168) + .3(198) + .6(159) = 171.6 calls
1

Note: The WMA forecast is lower than the MA
forecast because Day 13’s relatively low call
volume carries almost twice as much weight in the
WMA (.60) as it does in the MA (.33).
34
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Exponential Smoothing



Exponential Smoothing (Central Call Center)
Suppose a smoothing constant value of .25
is used and the exponential smoothing
forecast for Day 11 was 180.76 calls.
what is the exponential smoothing forecast
for Day 13?
Ft = Ft-1 + (At-1 - Ft-1)


F12 = 180.76 + .25(198 – 180.76) = 185.07
F13 = 185.07 + .25(159 – 185.07) = 178.55
35
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 2-Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12





Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
Alpha = 0.4 Error
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92
42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
Exponential Smoothing (Actual Demand forecasting )
Suppose a smoothing constant value of .10 is used and the
exponential smoothing forecast for the previous period was
42 units (actual demand was 40 units).
what is the exponential smoothing forecast for the next
periods?
F3 = 42 + .10(40 – 42) = 41.8
F4 = 41.8 + .10(43 – 41.8) = 41.92
© 2004, Managerial Economics, Dominick Salvatore
36
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 2-Exponential Smoothing
Graphical presentation
Actual
Demand
50
 = .4
45
 = .1
40
35
1
2
3
4
5
6
7
8
9 10 11 12
Period
37
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Trend Projection





The simplest form of time series is projecting
the past trend by fitting a straight line to the
data either visually or more precisely by
regression analysis.
Linear regression analysis establishes a
relationship between a dependent variable and
one or more independent variables.
In simple linear regression analysis there is
only one independent variable.
If the data is a time series, the independent
variable is the time period.
The dependent variable is whatever we wish to
forecast.
38
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5




Ft = Forecast for period t
t = Specified number of time
periods
a = Value of Ft at t = 0
b = Slope of the line
t
39
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Trend Projection



Linear Trend:
St = S0 + b t
b = Growth per time period
Constant Growth Rate(Non-linear)
St = S0 (1 + g)t
g = Growth rate
Estimation of Growth Rate
ln St = ln S0 + t ln (1 + g)
40
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Trend Projection- Simple Linear Regression







Regression Equation
This model is of the form:
Y = a + bX
Y = dependent variable (the value of time
series to be forecasted for period t)
X = independent variable ( time period in
which the time series is to be
forecasted)
a = y-axis intercept (estimated value of the
time series, the constant of the regression)
b = slope of regression line (absolute
amount of growth per period)
41
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Trend Projection- Calculating a and b



Constants a and b
The constants a and b
are computed using the
equations given:
Once the a and b
values are computed, a
future value of X can
be entered into the
regression equation
and a corresponding
value of Y (the
forecast) can be
calculated.
x  y- x xy

a=
n x -( x)
2
2
b=
2
n xy- x y
n x -( x)
2
2
42
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Trend Projection- Calculating a and b
Or If formula b is used first, it may
be used formula a in the following
format:
b=
n xy- x y
n x -( x)
2
2
Y  b X

a=
n
43
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 1 for Trend Projection-Electricity sales


Suppose we have the data show
electricity sales in a city between
1997.1 and 2000.4. The data are
shown in the following table. Use
time series regression to forecast the
electricity
consumption
(mn
kilowatt) for the next four quarters.
Do not forget to use the formulae a and b
44
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example1 for Trend Projection
TP
1997Q1
1997Q2
1997Q3
1997Q4
1998Q1
1998Q2
1998Q3
1998Q4
1999Q1
1999Q2
1999Q3
1999Q4
2000Q1
2000Q2
2000Q3
2000Q4
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Q
11
15
12
14
12
17
13
16
14
18
15
17
15
20
16
19
sq ( T )
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
Qx T
11
30
36
56
60
102
91
128
126
180
165
204
195
280
240
304
sum
x
136
y
244
sq x
1496
xy
2208
a
b
11.9
0.394118
a=
b=
2
x
  y- x xy
n x2 -( x)2
n xy- x y
n x2 -( x)2
sq sum x
18496
45
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example1 for Trend Projection
Y = 11.90 + 0.394X
Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001
Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001
Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001
Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001
Note: Electricity sales are expected to increase
by 0.394 mn kilowatt-hours per quarter.
46
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 2 for Trend Projection

Estimate a trend line using regression analysis
Year
2003
2004
2005
2006
2007
2008
Time
Period
(t)
1
2
3
4
5
6
Sales
(y)
20
40
30
50
70
65

Use time (t) as the
independent variable:
ŷ = b0  b1t
47
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 2 for Trend Projection
(continued)

2003
2004
2005
2006
2007
2008
1
2
3
4
5
6
Sales
(y)
20
40
30
50
70
65
ŷ = 12.333  9.5714 t
Sales trend
sales
Year
Time
Period
(t)
The linear trend model is:
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
48
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example 2 for Trend Projection
(continued)

Sales
(y)
2003
2004
2005
2006
2007
2008
2009
1
2
3
4
5
6
7
20
40
30
50
70
65
??
ŷ = 12.333  9.5714 (7)
= 79.33Sales
sales
Year
Time
Period
(t)
Forecast for time period 7:
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
49
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example for Trend Projection using-Non linear form
St = S0 (1 + g)t


Running the regression above in the form
of logarithms: ln St = ln S0 + t ln (1 + g)
to construct the equation which has
coefficients a and b.
Antilog of 2.49 is 12.06 and Antilog of
0.026 is 1.026.
Coefficients
Standard Error t Stat
Intercept 2.486914 0.062793 39.60489
T
0.026371 0.006494 4.060874
St = 12.06(1.026)t
50
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example for Trend Projection using St = S0 (1 + g)t




S17= 12.06(1.026)17 = 18.66 in the first
quarter of 2001
S18= 12.06(1.026)18 = 19.14 in the second
quarter of 2001
S19= 12.06(1.026)19 = 19.64 in the third
quarter of 2001
S20= 12.06(1.026)20= 20.15 in the fourth
quarter of 2001
These forecasts are similar to those obtained by
fitting a linear trend
51
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Evaluating Forecast-Model Performance



Accuracy
 Accuracy is the typical criterion for judging
the performance of a forecasting approach
 Accuracy is how well the forecasted values
match the actual values
Accuracy of a forecasting approach needs to be
monitored to assess the confidence you can
have in its forecasts and changes in the market
may require reevaluation of the approach
Accuracy can be measured in several ways
 Standard error of the forecast (SEF)
 Mean absolute deviation (MAD)
 Mean squared error (MSE)
 Mean absolute percent error (MAPE)
 Root mean squared error (RMSE)
52
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Forecast Accuracy





Error - difference between actual value
and predicted value
Mean Absolute Deviation (MAD)
 Average absolute error
Mean Squared Error (MSE)
 Average of squared error
Mean Absolute Percent Error (MAPE)
 Average absolute percent error
Root Mean Squared Error (RMSE)
 Root Average of squared error
53
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
MAD, MSE, and MAPE
MAD
=
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
RMSE =
( Actual
 forecas
t
n
/ Actual)*100)
2
(
A

F
)
 t t
n
54
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
MAD, MSE and MAPE




MAD
 Easy to compute
 Weights errors linearly
MSE
 Squares error
 More weight to large errors
MAPE
 Puts errors in perspective
RMSE
 Root of Squares error
 More weight to large errors
55
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-MAD, MSE, and MAPE
Compute MAD, MSE and MAP for the following
data showing actual and the predicted numbers of
account serviced.
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Actual
217
213
216
210
213
219
216
212
2.75
10.86
1.28
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2 (|A-F|/Actual)*100
4
0.92
9
1.41
1
0.46
16
1.90
4
0.94
25
2.28
1
0.46
16
1.89
76
10.26
22/8=2.75
76/8-1=10.86
10.26/8=1.28 %
56
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example: Central Call Center-Forecast
Accuracy - MAD

Which forecasting method (the AP =
3 moving average or the a = .25
exponential smoothing) is preferred,
based on the MAD over the most
recent 9 days? (Assume that the
exponential smoothing forecast for
Day 3 is the same as the actual call
volume.)
57
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
E AP4 = 161-187.3=26.3
EEXP4 = 161-186=25.0
Ch 5 : Demand Forecasting
Example: Central Call Center-Forecast Accuracy - MAD
F4MA = (186 + 217 + 159)/3 = 187.33 calls
F4EXP = 186 + .25(186 – 186) = 186.00 calls
© 2004, Managerial Economics, Dominick Salvatore
MADMA = 20.5/9 = 2.27
MADEXP = 18.0/9= 2.0
58
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast
Accuracy - RMSE
1
2
Quarter Firm's ams (A)
1
20
2
22
3
23
4
24
5
18
6
23
7
19
8
17
9
22
10
23
11
18
12
23
13
3
Tqmaf (F)
4
A-F
5
6
sq(A-F) Fqmaf (F)
21.6666667
23
21.6666667
21.6666667
20
19.6666667
19.3333333
20.6666667
21
2.333333
-5
1.333333
-2.66667
-3
2.333333
3.666667
-2.66667
2
total
21.3333333
21.4
22
21.4
20.2
19.8
20.8
19.8
8
sq(A-F)
1.6
-3
-4.4
1.8
3.2
-2.8
3.2
total
2.56
9
19.36
3.24
10.24
7.84
10.24
62.48
20.6
AP = 3 moving average
© 2004, Managerial Economics, Dominick Salvatore
5.444444
25
1.777778
7.111111
9
5.444444
13.44444
7.111111
4
78.33333
7
A-F
AP = 5 moving average
59
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast
Accuracy - RMSE
RMSE =
(A  F )
t
2
t
n
RMSE for 3-qma=2.95 Sqroot of 78.33/9=2.95
RMSE for 5-qma=2.99
Sqroot of 62.48/7=2.98
Thus three-quarter moving average forecast is marginally
better than the corresponding five- moving average
forecast.
60
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
(20+22+...23)/12=21=F1
Ft 1 = wAt  (1  w) Ft
Ch 5 : Demand Forecasting
Example-Exponential Smoothing Forecast Accuracy - RMSE
1
2
3
QuarterFirm's ams (A)(F) w=0.3
1
20
21
2
22
20.7
3
23
21.09
4
24
21.663
5
18
22.3641
6
23
21.05487
7
19
21.63841
8
17
20.84689
9
22
19.69282
10
23
20.38497
11
18
21.16948
12
23
20.21864
13
4
A-F
-1
1.3
1.91
2.337
-4.3641
1.94513
-2.63841
-3.84689
2.30718
2.615026
-3.16948
2.781363
total
21
5
sq(A-F)
1
1.69
3.6481
5.461569
19.04537
3.783531
6.961202
14.79853
5.323078
6.838359
10.04562
7.735978
87.19
6
(F) w=0.5
21
20.5
21.25
22.125
23.0625
20.53125
21.76563
20.38281
18.69141
20.3457
21.67285
19.83643
8
sq(A-F)
1
2.25
3.0625
3.515625
25.62891
6.094727
7.648682
11.44342
10.94679
7.045292
13.48984
10.0082
101.5
21.5
F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3
F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5
© 2004, Managerial Economics, Dominick Salvatore
7
A-F
-1
1.5
1.75
1.875
-5.0625
2.46875
-2.76563
-3.38281
3.308594
2.654297
-3.67285
3.163574
total
61
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Exponential Smoothing Forecast Accuracy - RMSE
F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3
F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5
RMSE =
RMSE with w=0.3 is 2.70
(A
t
 Ft ) 2
n
RMSE with w=0.5 is 2.91
Both exponential forecasts are better than the
previous techniques in terms of average values.
62
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Seasonal Variation
63
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Seasonal Variation
Ratio to Trend Method
Actual
Trend Forecast
Ratio =
Seasonal
Adjustment =
Adjusted
Forecast
=
Average of Ratios for
Each Seasonal Period
Trend
Forecast
Seasonal
Adjustment
64
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Seasonal Variation
Ratio to Trend Method:
Example Calculation for Quarter 1
Trend Forecast for 2001.1 = 11.90 + (0.394)(17) = 18.60
Seasonally Adjusted Forecast for 2001.1 = (18.60)(0.887) = 16.50
YEAR Forecasted
1997Q1
12.29
1998Q1
13.87
1999Q1
15.45
2000Q1
17.02
Actual
11
12
14
15
AV
Act/Forec
0.895037
0.865177
0.906149
0.881316
0.88692
0.887
Deseasonalize data=actual sales/seasonal relative (index)
65
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Seasonal Variation






Select a representative historical data set.
Develop a seasonal index for each season.
Use the seasonal indexes to deseasonalize the
data.
Perform linear regression analysis on the
deseasonalized data.
Use the regression equation to compute the
forecasts.
Use the seasonal indexes to reapply the
seasonal patterns to the forecasts.
66
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example: Computer Products Corp.


Seasonalized Times Series Regression Analysis
An analyst at CPC wants to develop next year’s quarterly
forecasts of sales revenue for CPC’s line of Epsilon
Computers. The analyst believes that the most recent 8
quarters of sales (shown on the next slide) are
representative of next year’s sales. Calculate the seasonal
indexes
67
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example: Computer Products Corp.
68
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example: Computer Products Corp.
69
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Unseasonalized vs. Seasonalized
1
2
3
4
5
6
7
8
9
10
11
…
Seasonal
Index
Deseasonalized
Sales
23
40
25
27
32
48
33
37
37
50
40
0.825
1.310
0.920
0.945
0.825
1.310
0.920
0.945
0.825
1.310
0.920
…
27.88
30.53
27.17
28.57
38.79
36.64
35.87
39.15
44.85
38.17
43.48
…
27.88 =
23
0.825
Sales: Unseasonalized vs. Seasonalized
Sales
Quarter
Seasonalized
Sales
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10 11
Quarter
Sales
Deseasonalized Sales
70
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Deflating a Time Series
Observed values can be adjusted to
base year equivalent
 Allows uniform comparison over time
 Deflation formula:

y adj t
yt
=
(100)
It
where
y adj t
= adjusted time series value at time t
yt = value of the time series at time t
It = index value at time t
71
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Deflating a Time Series: Example

Which movie made more money (in real terms)?
Movie
Title
Total
Gross $
1939
Gone With
the Wind
199
1977
Star Wars
461
1997
Titanic
601
Year
(Total Gross $ = Total domestic gross ticket receipts in $millions)
72
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Deflating a Time Series: Example
Year
Movie
Title
Gone
1939 With the
Wind
Star
1977
Wars
1997
Titanic
GWTW adj 1984
Total
Gross
CPI
(base year =
1984)
Gross
adjusted
to 1984
dollars
199
13.9
1431.7
461
60.6
760.7
601
199
=
(100) = 1431.7
13.9
160.5
 GWTW
374.5
made
about twice
as much as Star Wars,
and about 4 times as
much as Titanic when
measured in equivalent
dollars
73
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Barometric Methods







National Bureau of Economic Research
Department of Commerce
Leading Indicators
Lagging Indicators
Coincident Indicators
Composite Index
Diffusion Index
74
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Barometric Methods




As conducted today, is primarily the result of the
work conducted at the National Bureau of
Economic Research (NBER) and the Conference
Board.
Leading economic indicators – is used to forecast
an increase in general business activity, and vice
versa. (Ex: an increase in building permits can be
used to forecast an increase in housing
construction)
When some time series move in step or coincide
with movements in general economic activity are
called coincident indicators
Indicators which follow or lag movements in
economic activity and are called lagging indicators
75
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Leading indicators (10 series)
Average weekly hours, manufacturing
Initial claims for unemployment insurance, thousands
Manufacturers’ new orders, consumer goods and materials
Vendor performance, slower deliveries diffusion index
Manufacturers’ new orders, nondefense capital goods
Building permits, new private housing units
Stock prices, 500 common stocks
Money supply, M2
Interest rate spread, 10-year Treasury bonds less federal funds
Index of consumer expectations
76
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.

Ch 5 : Demand Forecasting
Coincident indicators (4 series)
Employees on nonagricultural payrolls
Personal income less transfer payments
Industrial production
Manufacturing and trade sales

Lagging indicators (7 series)
Average duration of unemployment, weeks
Ratio, manufacturing and trade inventories to sales
Change in labor cost per unit of output, manufacturing
Average prime rate charged by banks
Commercial and industrial loans outstanding
Ratio, consumer installment credit to personal income
Change in consumer price index for services
77
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
78
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Econometric Models


The
characteristic
that
distinguishes
econometric model from other forecasting
methods is that they seek to identify and
measure the relative importance (elasticity)
of the various determinants of demand or
other economic variables to be forecasted.
Econometric
forecasting
frequently
incorporates or uses the best features of
other forecasting techniques, such as trend
and
seasonal
variations,
smoothing
techniques, and leading indicators
79
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Econometric Models
Single Equation Model of the
Demand For Cereal (Good X)
QX = a0 + a1PX + a2Y + a3N + a4PS + a5PC + a6A + e
QX = Quantity of X
PS = Price of Muffins
PX = Price of Good X
PC = Price of Milk
Y = Consumer Income
A = Advertising
N = Size of Population
e = Random Error
80
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Econometric Models
Multiple Equation Model of GNP
Ct = a1  b1GNPt  u1t
I t = a2  b2 t 1  u2t
GNPt  Ct  It  Gt
Reduced Form Equation
Gt
a1  a2 b2 t 1
GNPt =
1  b1

1
 b1 
1  b1
81
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Econometric Models







Suppose we have the following equation and
the estimated results for air travel between the
USA and Europe from 1965 to 1978:
Q= 2.737-1.247 ln Pt + 1.905 ln GNPt
Q is number of passengers per year traveling
between the two continents.
Pt is the average yearly air fare
GNPt is U.S gross national product
Suppose the estimated Pt+1 and GNPt+1 in 1979
are $ 550 and $ 1480 respectively.
Forecast the number of passengers in 1979.
82
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
Example-Econometric Models

Qt+1= 2.737-1.247 (antilog of 550) + 1.905 (antilog of 1480)
= 2.737-1.247 (6.310) + 1.905 (7.300)
=8.775
The antilog of 8.775= 6,470,000 passengers for 1979
The accuracy of the forecast depends on the
accuracy of estimated demand coefficients and
the estimated values of both the independent
and explanatory variables in the demand
equation.
83
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.
Ch 5 : Demand Forecasting
The End
Thanks
84
© 2004, Managerial Economics, Dominick Salvatore
© 2010/11, Sami Fethi, EMU, All Right Reserved.