Applied Business Forecasting
and Planning
Introduction To Business Forecasting
Chapter Overview




Introduce Business Forecasting.
Review Subjective Forecasting Methods.
Introduce two simple “Naïve” Forecasting
Models.
Develop Criteria for Evaluating Forecast
Accuracy
Introduction

What is forecasting?



“Forecasting is an attempt to foresee the future
by examining the past.”
Forecasts require judgment
Most estimates obtained in quality forecasting
are derived in an objective and systematic
fashion and do not depend solely on subjective
guesses and hunches of the analyst.
Forecasting and Decision Making

Example:


Decision to “Whether to build a new factory”
Requires forecasts on


Future demand, technological innovations, cost, prices,
competitor’s plan, labor, legislation, etc.
Most forecasting required for decision making is
handled judgmentally in an intuitive fashion, often
without separating the task of forecasting from
that of decision making.
Forecasting and Decision making



Systematic, explicit approaches to forecasting can
be used to supplement the common sense and
management ability of decision makers.
All types and forms of forecasting techniques are
extrapolation, that is, predicting within the
existing data.
Quantitative forecasting techniques should be used
in with analysis, judgment, common sense, and
business experience in order to produce an
effective forecasting outcome.
Advantages and Disadvantages of Subjective
Methods


Subjective (qualitative or judgmental) forecasting
methods are sometimes considered desirable
because they do not require any particular
mathematical background of the individuals
involved.
Subjectivity is the most important advantage of
this class of methods. There are often forces at
work that cannot be captured by quantitative
methods.
Advantages and Disadvantages of Subjective
Methods

The disadvantages of subjective methods
are:
1.
2.
3.
They are almost always biased
They are not consistently accurate overtime.
It takes yeas of experience for someone to learn
how to convert intuitive judgment into good
forecast.
Who needs forecasts?


Every organizations, large and small, private and
public.
Needs for forecasts cuts across all functional lines.

It applies to problems such as:




How much this company worth? (Finance)
Will a new product be successful? (Marketing)
What level of inventories should be kept? (Production)
How can we identify the best job candidates? (Personnel)
Naïve Method 1




It is based solely on the most recent
information available.
Suitable when there is small data set.
Some times it is called the “no change”
forecast.
The naïve forecast for each period is the
immediately proceeding observation.
Naïve Method 1

The simplest naïve forecasting model, in
which the forecast value is equal to the
previous observed value, can be described
in algebraic form as follows:
yˆ t  yt 1

Since it discards all other observations, it
tracks changes rapidly.
Example:Sales of saws for Acme Tool
Company,1994-2000



The following table shows the sales of saws for
the Acme tool Company. These data are shown
graphically ass well.
In both forms of presentation you can see that the
sales varied considerably throughout this period,
from a low of 150 in 1996Q3 to a high of 850 in
2000Q1.
The Fluctuations in most economic and business
series (variables) are best seen after converting the
data graphic form.
Example:Sales of saws for Acme Tool
Company,1994-2000
Year
Quarter
1994
1995
1996
1997
1998
1999
2000
t
sales
1
1
500
2
2
350
3
3
250
4
4
400
1
5
450
2
6
350
3
7
200
4
8
300
1
9
350
2
10
200
3
11
150
4
12
400
1
13
550
2
14
350
3
15
250
4
16
550
1
17
550
2
18
400
3
19
350
4
20
600
1
21
750
2
22
500
3
23
400
4
24
650
1
25
850
2
26
600
3
27
450
Example:Sales of saws for Acme Tool
Company,1994-2000
Sales of saws for the Acme Tool Company: 1994-2000
900
800
700
600
Saws
500
400
300
200
100
0
0
5
10
15
Year
20
25
30
Example:Sales of saws for Acme Tool
Company,1994-2000

The forecast for the first quarter of 2000 ,
using the naïve method is:
ˆ t  yt 1
y
ˆ 25  y24
y
ˆ 25  650
y
Example:Sales of saws for Acme Tool
Company,1994-2000
Year
Quarter
t
sales
1994
1
1
500
2
2
350
500
3
3
250
350
4
4
400
250
1
5
450
400
2
6
350
450
3
7
200
350
4
8
300
200
1
9
350
300
2
10
200
350
3
11
150
200
4
12
400
150
1
13
550
400
2
14
350
550
3
15
250
350
4
16
550
250
1
17
550
550
2
18
400
550
3
19
350
400
4
20
600
350
1
21
750
600
2
22
500
750
3
23
400
500
4
24
650
400
1
25
850
650
2
26
600
850
3
27
450
600
4
28
700
450
1995
1996
1997
1998
1999
2000
Forecast
Example:Sales of saws for Acme Tool
Company,1994-2000
Quarte rly Sale s of Saws for Acm toll Company 1994-2000
900
800
700
600
Sales
500
sales
Forecast
400
300
200
100
0
0
5
10
15
Quarters
20
25
30
Naïve Method 2


One might argue that in addition to considering
just the recent observation, it would make sense to
consider the direction from which we arrived at
the latest observation.
That is: if the series dropped to the latest point,
perhaps it is reasonable to assume further drop and
if we have observed an increase, it may make
sense to factor into our forecast some further
increase.
Naïve Method 2

In general algebraic terms the model
becomes
yˆt  yt 1  P( yt 1  yt 2 )

Where P is the proportion of the change
between period t-2 and t-1 that we choose to
include in the forecast.
We call this Naïve method(2).

Example:Sales of saws for Acme Tool
Company,1994-2000

The forecast for the first quarter of 2000
using the Naïve method(2) with P = 50% is:
yˆ 25  y251  0.5( y251  y25 2 )
yˆ 25  y24  0.5( y24  y23 )
yˆ 25  650  0.5(650  400)  775
Example:Sales of saws for Acme Tool
Company,1994-2000
Year
Quarter
t
sales
1994
1
1
500
2
2
350
3
3
250
275
4
4
400
200
1
5
450
475
2
6
350
475
3
7
200
300
4
8
300
125
1
9
350
350
2
10
200
375
3
11
150
125
4
12
400
125
1
13
550
525
2
14
350
625
3
15
250
250
4
16
550
200
1
17
550
700
2
18
400
550
3
19
350
325
4
20
600
325
1
21
750
725
2
22
500
825
3
23
400
375
4
24
650
350
1
25
850
775
2
26
600
950
3
27
450
475
4
28
700
375
1995
1996
1997
1998
1999
2000
Forecast (N2)
Example:Sales of saws for Acme Tool
Company,1994-2000
Quarte rlt sale s of Saws for Acme Toll Company 1994-2000
1000
900
800
700
Sales
600
sales
500
Forecast (N2)
400
300
200
100
0
0
5
10
15
Quarters
20
25
30
Evaluating Forecasts



We have looked at two alternative forecasts of the
sales for the Acme Tool Company. Which forecast
is best depends on the particular year or years you
look at.
It is not always possible to find one model that is
always best for any given set of business or
economic data.
But we need some way to evaluate the accuracy of
forecasting models over a number of periods so
that we can identify the model that generally
works the best.
Evaluating Forecasts
Among a number of possible criteria that
could be used, five common ones are:

1.
2.
3.
4.
5.
6.
Mean absolute error (MAE)
Mean percentage error (MPE)
Mean absolute percentage error (MAPE)
Mean squared Error (MSE)
Root Mean squared Error (RMSE)
Theil’s U-statistic
Evaluating Forecasts

To illustrate how each of these is calculated,
let



yt = Actual value in period t
ŷt = Forecast value in period t
n = number of periods used in the calculation
Mean Absolute Error


The mean absolute error (MAE)
Measures forecast accuracy by averaging
the magnitudes of the forecast errors.
1 n
MAE   yt  yˆ t
n t 1
Mean Percentage Error




The Mean Percentage Error (MPE)
Can be used to determine if a forecasting
method is biased (consistently forecasting
low or high)
Large positive MPE implies that the method
consistently under estimates.
Large negative MPE implies that the
method consistently over estimates.
Mean Percentage Error

The forecasting method is unbiased if MPE
is close to zero.
1 n ( yt  yˆ t )
MPE  
n t 1
yt
Mean absolute Percentage Error



The Mean Absolute Percentage Error
(MAPE)
Provides an indication of how large the
forecast errors are in comparison to actual
values of the series.
Especially useful when the yt values are
large.
Mean absolute Percentage Error

Can be used to compare the accuracy of the
same or different methods on two different
time series data.
1 n yt  yˆ t
MAPE  
n t 1
yt
Mean Squared Error

This approach penalizes large forecasting
errors.
1 n
MSE   ( yt  yˆ t ) 2
n t 1
Root Mean Squared Error

The RMSE is easy for most people to interpret because of
its similarity to the basic statistical concept of a standard
deviation, and it is one of the most commonly used
measures of forecast accuracy.
n
RMSE 
(y
t 1
t
 yˆ t ) 2
n
Theil’s U-statistic


This statistic allows a relative comparison
of formal forecasting methods with naïve
approaches and also squares the errors
involved so that large errors are given much
more weight than smaller errors.
Mathematically, Theil’s U-statistic is
defined as
ˆ
yt 1  yt 1 2
)
y
t 1
t
n 1
yt 1  yt 2
(
)

yt
t 1
n 1
U 
(
Theil’s U-statistic



U = 1 The naïve method is as good as the
forecasting technique being evaluated.
U < 1 The forecasting technique being used
is better than the naïve method.
U > 1 There is no point in using a formal
forecasting method since using a naïve
method will produce better results
Example:VCR data

Data was collected on the number of VCRs sold
last year for Vernon’s Music store.
Month
t
Sales
Forecast(N1)
A t - Ft
January
1
123
February
2
130
123
7
March
3
125
130
-5
April
4
138
125
13
May
5
145
138
7
June
6
142
145
-3
July
7
141
142
-1
August
8
146
141
5
September
9
147
146
1
October
10
157
147
10
November
11
150
157
-7
December
12
160
150
10
Example:VCR data
Monthly VCR Sales
180
160
140
VCR Sales
120
100
Sales
Forecast(N1)
80
60
40
20
0
0
2
4
6
8
Months
10
12
14
Example:VCR data
Month
t
Sales
Forecast (N2) At - Ft
January
1
123
February
2
130
March
3
125
133.5
-8.5
April
4
138
122.5
15.5
May
5
145
144.5
0.5
June
6
142
148.5
-6.5
July
7
141
140.5
0.5
August
8
146
140.5
5.5
September
9
147
148.5
-1.5
October
10
157
147.5
9.5
November
11
150
162
-12
December
12
160
146.5
13.5
Example:VCR data
Monthly VCR Sales
180
160
140
VCR Sales
120
100
Sales
Forecast (N2)
80
60
40
20
0
0
2
4
6
8
Months
10
12
14
Example:VCR data
Error analysis:
RMSE
7.24
8.97
Forecast (N1)
Forecast (N2)
Monthly VCR Sales
180
160
140
120
VCR Sales

100
Sales
Forecast(N1)
Forecast (N2)
80
60
40
20
0
0
2
4
6
8
Months
10
12
14
Evaluating Forecasts



We will focus on root-mean-squared error
(RMSE) to evaluate the relative accuracy of
various forecasting methods.
All quantitative forecasting models are developed
on the basis of historical data.
When RMSE are applied to the historical data,
they are often considered measures of how well
various models fit the data (how well they work in
the sample).
Evaluating Forecasts


To determine how accurate the models are
in actual forecast (out of sample) a hold out
period is often used for evaluation.
It is possible that the best model “in
sample” may not be the best in “out of
sample”.
Using Multiple Forecasts



When forecasting Sales or some other business
economic variables, it is best to consider more
than one model.
In our example of VCR sales, using the two naïve
model, we could take the lowest forecast value as
the most pessimistic, the highest as the most
optimistic, and the average value as the most
likely.
This is the simplest way to combine forecasts.
Sources of Data

The quantity and type of data needed in
developing forecasts can vary a great deal from
one situation to another.

Some forecasting techniques require only data series
that is to be forecasted


Naïve method, exponential smoothing, decomposition method.
Some , like multiple regression methods require a data
series for each variable included in the forecasting
model.
Sources of Data

Sources of data


Internal records of the organization.
Outside of the organization



Trade associations
Governmental and syndicated services
There is a wealth of data available on the
internet.