Transcript forecastingch3-16.ppt

Forecasting; Chapter3
Department of Business Administration
SPRING 2015-2016
I see that you will
get an A from this Course.
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Chapter 3: Forecasting
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Outline: What You Will Learn . . .
Forecasting; Chapter 3
 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
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Forecasting; Chapter 3
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.
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Forecasting; Chapter 3
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.
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Forecasting; Chapter 3
The aim of forecasting
 The firm uses the macro-forecasts of general economic
activity as inputs for their micro-forecasts 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.
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Forecasting; Chapter 3
Forecasting Process Map
Statistical
Model
Demand
History
Sales
Marketing
Causal
Factors
Product
Production &
Executive
Management
Inventory
Management
& Finance
Control
Consensus
Process
 This slide is excluded from the exam
Consensus
Forecast
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Features of Forecasts
Forecasting; Chapter 3
 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
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Forecasting; Chapter 3
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
 This slide is excluded from the exam
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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).
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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
 This slide is excluded from the exam
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Forecasting; Chapter 3
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.
 This slide is excluded from the exam
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Forecasting; Chapter 3
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.
 This slide is excluded from the exam
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Forecasting; Chapter 3
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.
 This slide is excluded from the exam
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
Forecast Horizon
 Short term
 Up to a year
 Medium term
 One to five years
 Long term
 More than five years
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Forecasting; Chapter 3
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)
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Forecasting; Chapter 3
Forecast Variations
Irregular
variation
Trend
Cycles
90
89
88
Seasonal variations
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Forecasting; Chapter 3
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))
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Forecasting; Chapter 3
Techniques for Averaging
Moving average
Weighted moving average
Exponential smoothing
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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)
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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.
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Forecasting; Chapter 3
Example-Moving Average
Days
1
2
3
4
5
6
7
8
9
10
11
12
Call Volume
159
217
186
161
173
157
203
195
188
168
198
159
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.
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Example-Moving Average
Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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).
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Forecasting; Chapter 3
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?
 F12 = 180.76 + .25(198 – 180.76) = 185.07
 F13 = 185.07 + .25(159 – 185.07) = 178.55
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Forecasting; Chapter 3
Example 2-Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
42
40
43
40
41
39
46
44
45
38
40
 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?
 Illustrate its graphical presentation on a diagram.
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Forecasting; Chapter 3
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
 what is the exponential smoothing forecast for the next periods?
 Using Alpha as 0.1
F12 = 41.92 + .10(40 – 41.92) = 41.73
 Using Alpha as 0.4
F12 = 41.53 + .40(40– 41.53) = 40.92
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Forecasting; Chapter 3
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
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Forecasting; Chapter 3
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.
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Forecasting; Chapter 3
Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5
t
 Ft = Forecast for period t
 t = Specified number of time periods
 a = Value of Ft at t = 0
 b = Slope of the line
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Forecasting; Chapter 3
Trend Projection
 Linear Trend:
St = S 0 + b t
b = Growth per time period
 Non-linear
St = S0 (1 + g)t
g = Growth rate
 Estimation of non linear form
ln St = ln S0 + t ln (1 + g)
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Forecasting; Chapter 3
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)
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Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
s yt =
r=
n t
2
Y
  a y  b ty
n2
Standard deviation
n ty   t  y
2
  t 
2
 n y   y 
2
2
Correlation coefficient
Determination of coefficient
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Forecasting; Chapter 3
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 t can be
entered into the regression equation
and a corresponding value of F (the
forecast) can be calculated.
a=
b=
2
t

 y   t  ty
n  t  ( t )
2
2
n  ty   t  y
n t 2  ( t ) 2
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Forecasting; Chapter 3
Example 1 for Trend Projection- Electricity sales
Year
1997Q1
1997Q2
1997Q3
1997Q4
1998Q1
1998Q2
1998Q3
1998Q4
1999Q1
1999Q2
1999Q3
1999Q4
2000Q1
2000Q2
2000Q3
2000Q4
ELECSALE
(Y)
11
15
12
14
12
17
13
16
14
18
15
17
15
20
16
19
 Suppose we have the electricity sales
data in a city between 1997.1 and
2000.4. The data are shown in the
following table.
 Construct the forecast equation.
 Briefly explain the relationship in the
forecast equation.
 Calculate the next four quarters.
 Compute the correlation coefficient,
determination of coefficient and standard
deviation.
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Forecasting; Chapter 3
Example1 for Trend Projection
Year
Trent (t)
1997Q1
1
1997Q2
2
1997Q3
3
1997Q4
4
1998Q1
5
1998Q2
6
1998Q3
7
1998Q4
8
1999Q1
9
1999Q2
10
1999Q3
11
1999Q4
12
2000Q1
13
2000Q2
14
2000Q3
15
2000Q4
16
(SUM) Σ
136
a
11.9
b
0.394
Av
15.25
ELECSALE
(Y)
11
15
12
14
12
17
13
16
14
18
15
17
15
20
16
19
244
(t )SQ
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
1496
Y*t
11
30
36
56
60
102
91
128
126
180
165
204
195
280
240
304
2208
(y) SQ
121
225
144
196
144
289
169
256
196
324
225
289
225
400
256
361
3820
(Σt) SQ
(ΣY) SQ
a=
b=
18496
2
t
  y   t  ty
n  t 2  ( t ) 2
n  ty   t  y
n t 2  ( t ) 2
59536
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Forecasting; Chapter 3
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.
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Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Std.dev
s yt =
2
y
  a y  b ty
n2
 Syt = SQRT( [3820-(11.9) (244)- (0.394) (2208)]/(16-2))=1.82
 Syt is a measure of how historical data points have been dispersed about
the trend line. If it is large (reference point in mean of the data) , the
historical data points have been spread widely about the trend line and if
otherway around, the data points have been grouped tightly about the
trend.
43
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Corr. coef
r=
n t
n ty   t  y
2
  t 
2
 n y   y 
2
2
r= ((16) (2208)- (136) (244))/SQRT( [(16) (1496)-(18496)*((16)(3820-59536)]=0.73
r lies between -1 and 1, -1 is strong negative whereas 1 is
strong positive. 0 means that there is no relationship
between the two variables (x and y). In this case, there is a
strong positive relationship between the two variables and
if an increase in independent variable, it will be a rise in
dependent variable.
44
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Determination of coefficient
R2=0.533. It varies between 0 and 1. 0 means that there is
no relationship between the two variables whereas 1
indicates that there is a perfect relationship. 53.3%
variation in dependent variable can be explained by the
variation happened in the independent variable. It is worth
to emphasize that 46.7% shows unexplained part of the
relationship.
45
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
Year
Time
Period
(t)
Sales
(F)
2003
2004
2005
2006
2007
2008
1
2
3
4
5
6
20
40
30
50
70
65
 Estimate the forecast equation
 Predict the next period
 Compute the correlation
coefficient, determination of
coefficient and standard
deviation.
F = a  bt
46
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
(continued)
 The linear trend model is:
2003
2004
2005
2006
2007
2008
1
2
3
4
5
6
Sales
(F)
20
40
30
50
70
65
F = 12.333  9.5714 t
Sales trend
sales
Year
Time
Period
(t)
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
47
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
Year
Time
Period
(t)
Sales
(F)
2003
2004
2005
2006
2007
2008
2009
1
2
3
4
5
6
7
20
40
30
50
70
65
??
(continued)
 Std dev=8.91
 R2=0.83
 r=0.91
 Forecast for time period 7:
F = 12.333  9.5714 (7)
= 79.33
sales
Sales
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
48
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
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)
49
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
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
MGMT 405, POM, 2014/15. Lec Notes
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50
Forecasting; Chapter 3
MAD, MSE, and MAPE
=
MAD
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
RMSE =
 Actual
 forecast / Actual*100)
2
(
A

F
)
 t t
MGMT 405, POM, 2014/15. Lec Notes
n
n
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
51
Forecasting; Chapter 3
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
52
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
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
Actual
217
213
216
210
213
219
216
212
Forecast
215
216
215
214
211
214
217
216
53
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
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=
RMSE
Actual
217
213
216
210
213
219
216
212
2.75
10.86
1.28
3.08
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
4
9
1
16
4
25
1
16
76
(|A-F|/Actual)*100
0.92
1.41
0.46
1.90
0.94
2.28
0.46
1.89
10.26
22/8=2.75
76/8-1=10.86
10.26/8=1.28
Sqroot(76/8)=3.08
54
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
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
a) Using MA3 and MA5 to forecast
next period.
b) Conduct RMSE technique to check
which model measures the forecasting
results more sensitive.
c) Using ESW3 and ESW5 to forecast
next period.
d) Conduct RMSE technique to check
which model measures the forecasting
results more sensitive.
e) Briefly explain the case.
55
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy – RMSE
(a)
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
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
5
6
sq(A-F) Fqmaf (F)
5.444444
25
1.777778
7.111111
9
5.444444
13.44444
7.111111
4
78.33333
21.4
22
21.4
20.2
19.8
20.8
19.8
7
A-F
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
56
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy – RMSE
(b)
RMSE =
2
(
A

F
)
 t 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 due to results of RMSE. The less error calculated,
the better results forcasted.
57
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© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
(20+22+...23)/12=21=F1
Ft = Ft-1 + (At-1 - Ft-1)
Forecasting; Chapter 3
Example-Exponential Smoothing Forecast Accuracy – RMSE
(c)
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
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
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
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
21.5
F2= 21+(0.3) (20-21)=20.7 with w=α=0.3
F2= 21+(0.5) (20-21)=20.5 with w=α=0.5
MGMT 405, POM, 2014/15. Lec Notes
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58
Forecasting; Chapter 3
Example-Exponential Smoothing Forecast Accuracy – RMSE
(d)
RMSE =
(A
t
 Ft ) 2
n
RMSE= SQRT(87.19/12)= 2.6955
RMSE= SQRT(101.5/12)=2.908
RMSE with α=0.3 is 2.6955
RMSE with α=0.5 is 2.908
 Both Exponential smoothing techniques are better than
three-quarter moving average forecast techniques because
the latter one gives less error than the former one.
59
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example: Unseasonalized vs. Seasonalized
Quar
ter
1
2
3
4
5
6
7
8
9
10
11
…
Seasonalized Sales
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
 This topic is excluded from the exam.
MGMT 405, POM, 2014/15. Lec Notes
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60
Forecasting; Chapter 3
Example: Unseasonalized vs. Seasonalized
Sales
Sales: Unseasonalized vs. Seasonalized
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
Quarter
Sales
Deseasonalized Sales
 This topic is excluded from the exam.
61
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for Trend Projection- Petrol sales
Year
PETROLSALE
(Y)
2004
1
2005
3
2006
4
2007
2
2008
1
2009
3
2010
5
2011
3
 Suppose we have the petrol sales
data in a city between 2004 and
2011. The data are shown in the
following table.
Construct the forecast equation.
Briefly explain
Calculate the next four years.
Briefly explain.
Compute the correlation coefficient,
determination of coefficient and
standard deviation. Briefly explain.
62
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example1 for Trend Projection
Year
Trent (t) PETROLSALE (Y) (t )SQ
Y*t
(y) SQ (Σt) SQ (ΣY) SQ
2004
1
1
1
1
1
2005
2
3
4
6
9
2006
3
4
9
12
16
2007
4
2
16
8
4
2008
5
1
25
5
1
2009
6
3
36
18
9
2010
7
5
49
35
25
2011
8
3
64
24
9
(SUM) Σ
36
22
204
109
74
a
1.678
b
0.238
a=
2
t

b=
1296
 y   t  ty
n  t  ( t )
2
2
n  ty   t  y
n t 2  ( t ) 2
484
63
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example1 for Trend Projection
Y = 1.678 + 0.238t
Y9 = 1.678 + 0.238(9) = 3.83 in 2012
Y10 = 1.678 + 0.238(10) = 4.06 in 2013
Y11 = 1.678 + 0.238(11) = 4.30 in 2014
Y12 = 1.678 + 0.238(12) = 4.54 in 2015
Note: Petrol sales are expected to increase by
0.238 mn gallons per year.
64
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Std.dev
 Syt =
s yt =
2
y
  a y  b ty
n2
1.36
 Syt is a measure of how historical data points have been dispersed about
the trend line. If it is large (reference point in mean of the data) , the
historical data points have been spread widely about the trend line and if
otherway around, the data points have been grouped tightly about the
trend.
65
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Corr. coef
r=
n t
n ty   t  y
2
  t 
2
 n y   y 
2
2
r=0.42
r lies between -1 and 1, -1 is strong negative whereas 1 is
strong positive. 0 means that there is no relationship
between the two variables (x and y). In this case, there is a
moderate positive relationship between the two variables
and if an increase in independent variable, it will be a rise
in dependent variable.
66
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
The correlation coefficient, determination of
coefficient and standard deviation
Determination of coefficient
R2=0.18. It varies between 0 and 1. 0 means that there is
no relationship between the two variables whereas 1
indicates that there is a perfect relationship. 18.0%
variation in dependent variable can be explained by the
variation happened in the independent variable. It is worth
to emphasize that 82% shows unexplained part of the
relationship.
67
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for MA, WMA and ES
period No of law case
1
60
2
64
3
55
4
58
5
64
(a) Use a simple three-month moving average
to find the next period
(b) Use a weight average method conducting
0.50 (for most recent datum), 0.30 , and 0.20
to find the next period.
(c) Use single exponential smoothing
technique to find the next period employing
smoothing constant and 5. period forecast
value are 0.4 and 58.60 respectively.
(d) Use RMSE error model and decide which
technique is better explain the data (MA and
ES).
(e) Plot the monthly data, three-month moving
average estimates as as well as exponential
smoothing estimates. Briefly explain the
patterns.
68
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© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for MA, WMA and ES
a-b-c
period No of law case MA3 WMA3
ES 0.4
1
60
60.2
2
64
60.12
3
55
61.672
4
58
59.67
59.0032
5
64
59
58.60192
next period
59
60.4
60.761152
The first forecasting number for ES is calculated as average of series (60+64....+64)/5=60.2.
69
MGMT 405, POM, 2014/15. Lec Notes
© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for MA, WMA and ES
-dErrorMA3
sq(ErrorMA3) ErrorES0.4 sq(ErrorES0.4)
-0.2
0.04
3.88
15.0544
-6.672
44.515584
-1.666666667
2.777777778
-1.0032
1.00641024
5
25
5.39808
29.13926769
sum
27.77777778
30.14567793
RMSE
3.726779962
2.455429817
 Exponential smoothing technique is better than three-quarter moving average
forecast technique because the former one gives less error than the latter one.
70
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© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for MA, WMA and ES
-e-
66
64
62
60
No of law case
58
MA3
ES 0.4
56
54
52
50
1
2
3
4
5
6
71
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© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Thanks
72
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© Stevenson, McGraw Hill, 2010- Prof. Dr. Sami Fethi, EMU, All Right Reserved.