Transcript Chap003-Forecasting

Chapter 3
Forecasting
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 3: Learning Objectives
 You should be able to:
 List the elements of a good forecast
 Outline the steps in the forecasting process
 Describe qualitative forecasting techniques and the
advantages and disadvantages of each
 Compare and contrast qualitative and quantitative
approaches to forecasting
 Describe averaging techniques, trend and seasonal
techniques, and regression analysis, and solve typical
problems
 Explain three measures of forecast accuracy
 Compare two ways of evaluating and controlling forecasts
 Assess the major factors and trade-offs to consider when
choosing a forecasting technique
3-2
Forecast
 Forecast – a statement about the future
value of a variable of interest
 We make forecasts about such things as weather,
demand, and resource availability
 Forecasts are an important element in making
informed decisions
3-3
Two Important Aspects of
Forecasts
 Expected level of demand
 The level of demand may be a function of some
structural variation such as trend or seasonal
variation
 Accuracy
 Related to the potential size of forecast error
3-4
Features Common to All Forecasts
 Techniques assume some underlying causal
system that existed in the past will persist
into the future
 Forecasts are not perfect
 Forecasts for groups of items are more
accurate than those for individual items
 Forecast accuracy decreases as the
forecasting horizon increases
3-5
Elements of a Good Forecast
 The forecast
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



should be timely
should be accurate
should be reliable
should be expressed in meaningful units
should be in writing
technique should be simple to understand and
use
 should be cost effective
3-6
Steps in the Forecasting Process

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Determine the purpose of the forecast
Establish a time horizon
Obtain, clean, and analyze appropriate data
Select a forecasting technique
Make the forecast
Monitor the forecast
3-7
Forecast Accuracy and Control
 Forecasters want to minimize forecast errors
 It is nearly impossible to correctly forecast real-world
variable values on a regular basis
 So, it is important to provide an indication of the
extent to which the forecast might deviate from the
value of the variable that actually occurs
 Forecast accuracy should be an important
forecasting technique selection criterion
 Error = Actual – Forecast
 If errors fall beyond acceptable bounds, corrective
action may be necessary
3-8
Forecast Accuracy Metrics
Let et = Actualt – Forecastt, where t = given time period
e

MAD 
t
MAD weights all errors evenly
n
e 

MSE 
2
t
n 1
et
 Actual  100
t
MAP E 
n
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error
3-9
Forecast Error Calculation
Period
Actual
(A)
Forecast
(F)
(A-F)
Error
|Error|
Error2
[|Error|/Actual]x100
1
107
110
-3
3
9
2.80%
2
125
121
4
4
16
3.20%
3
115
112
3
3
9
2.61%
4
118
120
-2
2
4
1.69%
5
108
109
1
1
1
0.93%
Sum
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11.23%
n=5
n-1 = 4
n=5
MAD
MSE
MAPE
= 2.6
= 9.75
= 2.25%
3-10
Forecasting Approaches
 Qualitative Forecasting
 Qualitative techniques permit the inclusion of
soft information such as:
o Human factors
o Personal opinions
o Hunches
 These factors are difficult, or impossible, to
quantify
3-11
Forecasting Approaches
 Quantitative Forecasting
 Quantitative techniques involve either the
projection of historical data or the development
of associative methods that attempt to use causal
variables to make a forecast
 These techniques rely on hard data
3-12
Qualitative Forecasts
 Executive opinion
 Sales force opinion
 Consumer Survey
 Delphi method
3-13
Executive Opinion
 Involves small group of high-level experts and
managers
 Group estimates demand by working together
 Combines managerial experience with statistical
models
 Relatively quick
 ‘Group-think’ is a disadvantage
3-14
Sales Force Opinion
 Each salesperson projects his or her sales
 Combined at district and national levels
 Sales reps know customers’ wants
 Tends to be overly optimistic
3-15
Delphi Method
 Participants include
 Decision makers
 Staff
 Outside experts
 Anonymous iterative group process,
continues until consensus is reached
3-16
Consumer Survey
 Ask customers about purchasing plans
 Time consuming and expensive
 May require complex statistical analysis
 What consumers say, and what they actually
do are often different
3-17
Quantitative Forecasts
 Time series methods
 Associative forecasting techniques
3-18
Time-Series Forecasts
 Forecasts that project patterns identified in
recent time-series observations
 Time-series - a time-ordered sequence of
observations taken at regular time intervals
 Assume that future values of the time-series
can be estimated from past values of the
time-series
3-19
Time-Series Behaviors
 Trend
 Gradual increase or decrease over long period of
time
 Seasonality
 Regular and repeating changes
 Cycles
 Ups and downs due to economic cycles
3-20
Time-Series Behaviors
 Irregular variations
 Unexpected changes
 Random variation
3-21
Time-Series Behaviors
3-22
What model when
Seasonality not present
Trend not present
•
•
•
•
Trend is present
• Naive
• Trend projection using
Regression
Naive
Moving Average
Weighted Moving Average
Exponential smoothing
Seasonality is present
• Naive
• Seasonal index
• Seasonal index
• With trend projection
No trend and no seasonality
 Naïve Forecast
 Uses a single previous value of a time series as
the basis for a forecast
o The forecast for a time period is equal to the previous
time period’s value
 Ft+1 = At
3-24
Averaging forecasts
 These Techniques work best when a series
tends to vary about an average
 Averaging techniques smooth variations in the
data
 They can handle step changes or gradual changes
in the level of a series
 Techniques
o Moving average
o Weighted moving average
o Exponential smoothing
3-25
Moving Average
 Technique that averages a number of the
most recent actual values in generating a
n
forecast
Ft 1  MAn 
A
i 1
t i 1
n
where
Ft  Forecastfor timeperiodt
MAn  n periodmovingaverage
At  Actual value in periodt
n  Number of periodsin themovingaverage
3-26
Moving Average
 As new data become available, the forecast is
updated by adding the newest value and
dropping the oldest and then re-computing
the average
 The number of data points included in the
average determines the model’s sensitivity
 Fewer data points used-- more responsive
 More data points used-- less responsive
3-27
Weighted Moving Average
 The most recent values in a time series are
given more weight in computing a forecast
 The choice of weights, w, is somewhat arbitrary
and involves some trial and error
Ft 1  wt ( At )  wt 1 ( At 1 )  ...  wt n ( At n )
where
wt  weight for periodt , wt 1  weight for periodt  1, et c.
At  t heact ual value for periodt , At 1  t heact ual value for periodt  1, et c.
and Sum of weight s  1
3-28
Exponential Smoothing
 A weighted averaging method that is based
on the previous forecast plus a percentage of
the forecast error
Ft 1  At  (1   ) Ft
Ft 1  Ft   ( At  Ft )  Ft   ( et )
where
Ft 1  Forecast for periodt  1
Ft  Forecast for theperiodt
 = Smoothingconstant
At  Actual demand or sales for period just ended
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Techniques for Trend
 Linear trend equation
 Non-linear trends
3-30
Linear Trend
 A simple data plot can reveal the existence
and nature of a trend
 Naïve forecast with trend
 Ft+1 = At + (At – At-1)
3-31
Linear Trend - Regression
 Linear trend equation
Ft  a  bt
where
Ft  Forecastfor periodt
a  Value of Ft at t  0
b  Slope of theline
t  Specified number of timeperiodsfromt  1
3-32
Estimating slope and intercept
 Slope and intercept can be estimated from
historical data
b
n ty   t  y
n t 
2
 t
y  b t

a
n
2
or y  bt
where
n  Number of periods
y  Value of the time series
3-33
Techniques for Seasonality
 Seasonality – regularly repeating movements
in series values that can be tied to recurring
events
 Expressed in terms of the amount that actual
values deviate from the average value of a series
 Naïve forecast
 Ft+1 = At-s+1
where s = No. of periods
3-34
Techniques for Seasonality
 Models of seasonality
 Additive
o Seasonality is expressed as a quantity that gets added
to or subtracted from the time-series average in order
to incorporate seasonality
 Multiplicative
o Seasonality is expressed as a percentage of the
average (or trend) amount which is then used to
multiply the value of a series in order to incorporate
seasonality
3-35
Models of Seasonality
3-36
Seasonal Relatives
 Seasonal relatives
 The seasonal percentage used in the multiplicative
seasonally adjusted forecasting model
 Deseasonalizing data
o Done in order to get a clearer picture of the nonseasonal
(e.g., trend) components of the data series
o Divide each data point by its seasonal relative
 Incorporating seasonality in a forecast
o Obtain trend estimates for desired periods using a trend
equation
o Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative
Associative Forecasting Techniques
 Associative techniques are based on the
development of an equation that summarizes
the effects of predictor variables
 Predictor variables - variables that can be used to
predict values of the variable of interest
o Home values may be related to such factors as home
and property size, location, number of bedrooms, and
number of bathrooms
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Simple Linear Regression
 Regression - a technique for fitting a line to a
set of data points
 Simple linear regression - the simplest form of
regression that involves a linear relationship
between two variables
o The object of simple linear regression is to obtain an
equation of a straight line that minimizes the sum of
squared vertical deviations from the line (i.e., the least
squares criterion)
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Least Squares Line
yc  a  bx
where
yc  P redicted(dependent) variable
x  P redictor(independent) variable
b  Slope of theline
a  Value of yc when x  0 (i.e., theheight of theline at they intercept)
and
b
n xy    x  y 
n x    x 
2
2
y  b x

a
or y  b x
n
where
n  Number of pairedobservations
3-40
Monitoring the Forecast
 Tracking and analyzing forecast errors
provides insight into whether forecasts are
performing satisfactorily
 Sources of forecast errors
 The model may be inadequate
 Irregular variations may have occurred
 The forecasting technique has been incorrectly
applied
 Random variation
3-41
Choosing a Forecasting Technique
 Factors to consider
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Cost
Accuracy
Availability of historical data
Availability of forecasting software
Time needed to gather and analyze data and
prepare a forecast
 Forecast horizon
3-42