Forecasting
Why forecast?
Features Common to all Forecasts
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Conditions in the past will continue in the future
Rarely perfect
Forecasts for groups tend to be more accurate than forecasts for individuals
Forecast accuracy declines as time horizon increases
Elements of a Good Forecast
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Timely
Accurate
Reliable (should work consistently)
Forecast expressed in meaningful units
Communicated in writing
Simple to understand and use
Steps in Forecasting Process
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Determine purpose of the forecast
Establish a time horizon
Select forecasting technique
Gather and analyze the appropriate data
Prepare the forecast
Monitor the forecast
Types of Forecasts
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Qualitative
o Judgment and opinion
o Sales force
o Consumer surveys
o Delphi technique
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Quantitative
o Regression and Correlation (associative)
o Time series
Forecasts Based on Time Series Data
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What is Time Series?
Components (behavior) of Time Series data
o Trend
o Cycle
o Seasonal
o Irregular
o Random variations
Naïve Methods
Naïve Forecast – uses a single previous value of a time series as the basis of a
forecast.
Ft  yt 1
Techniques for Averaging
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What is the purpose of averaging?
Common Averaging Techniques
o Moving Averages
o Exponential smoothing
Moving Average
n
Ft 
A
i 1
i
n
Exponential Smoothing
Ft  Ft 1   ( At 1  Ft 1 )
Techniques for Trend
Linear Trend Equation
yt  a  bt
where :
t  specified number of time periods from t  0
yt  forecast for time period t
a  value of yt at t
b  slope of the line
Curvilinear Trend Equation
yt  a  bt  ct 2
where :
t  specified number of time periods from t  0
yt  forecast for time period t
a  value of yt at t
b  slope of the line
Techniques for Seasonality
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What is seasonality?
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What are seasonal relatives or indexes?
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How seasonal indexes are used:
o Deseasonalizing data
o Seasonalizing data
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How indexes are computed (see Example 7 on page 109)
Accuracy and Control of Forecasts
Measures of Accuracy
o Mean Absolute Deviation (MAD)
o Mean Squared Error (MSE)
o Mean Absolute Percentage Error (MAPE)
Forecast Control Measure
o Tracking Signal
Mean Absolute Deviation (MAD)
MAD 
 Actual  Forecast
n
Mean Squared Error (or Deviation) (MSE)
( Actual  Forecast )
MSE  
2
n 1
Mean Square Percentage Error (MAPE)
 Actual  Forecast
MAPE 
Actual
n
X 100
Tracking Signal
Tracking Signal 
 ( Actual  Forecast )
MAD
Problems:
2 – Plot, Linear, MA, exponential Smoothing
5 – Applying a linear trend to forecast
15 – Computing seasonal relatives
17 – Using indexes to deseasonalize values
26 – Using MAD, MSE to measure forecast accuracy
Problem 2 (110)
National Mixer Inc., sells can openers. Monthly sales for a seven-month period were as follows:
Month
Feb
March
April
May
June
July
August
Sales
(000 units)
19
18
15
20
18
22
20
(a) Plot the monthly data on a sheet of graph paper.
(b) Forecast September sales volume using each of the following:
(1) A linear trend equation
(2) A five-month moving average
(3) Exponential smoothing with a smoothing constant equal to 0.20, assuming March forecast of
19(000)
(4) The Naïve Approach
(5) A weighted average using 0.60 for August, 0.30 for July, and 0.10 for June
(c) Which method seems least appropriate? Why?
(d) What does use of the term sales rather than demand presume?
EXCEL SOLUTION
(a) Plot of the monthly data
How to superimpose a trend line on the graph
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Click on the graph created above (note that when you do this an item called CHART will appear
on the Excel menu bar)
Click on Chart > Add Trend Line
Click on the most appropriate Trend Regression Type
Click OK
(b) Forecast September sales volume using:
(1) Linear Trend Equation
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Create a column for time period (t) codes (see column B)
Click Tools > Data Analysis > Regression
Fill in the appropriate information in the boxes in the Regression box that appears
Sales data
Coded time period
Coded time period
(2) Five-month moving average
(3) Exponential Smoothing with a smoothing constant of 0.20, assuming March forecast of 19(000)
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Enter the smoothing factor in D1
Enter “19” in D5 as forecast for March
Create the exponential smoothing formula in D6, then copy it onto D7 to D11
(4) The Naïve Approach
(5) A weighted average using 0.60 for August, 0.30 for July, and 0.10 for June
Problem 5 (110)
A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to
predict annual sales of its popular Hand & Foot Cream.
yt =80 + 15 t
where: yt = Annual sales (000 bottles)
t0 = 1990
(a) Are the annual sales increasing or decreasing? By how much?
(b) Predict annual sales for the year 2006 using the equation
Problem 15 (113)
Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal, given the
following data. (Hint: Use a seven-day moving average)
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number
Served
80
75
78
95
130
136
40
82
77
80
94
125
135
42
Day
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Number
Served
84
77
83
96
135
140
37
87
82
98
103
144
144
48
Excel Solution
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Type a 7-day average formula in E6 ( =average(C3:c9) )
In F6, type the formula =C6/E6
Copy the formulas in E6 and F6 onto cells E7 to E27
Compute the average ratio for Day 1 (see formula in E12)
Copy and paste the formula in E12 onto E13 to E18 to complete the indexes for Days 2 to 7
Problem 17 (113) – Using indexes to deseasonalize values
New car sales for a dealer in Cook County, Illinois, for the past year are shown in the following table, along with
monthly (seasonal) relatives, which are supplied to the dealer by the regional distributor.
Month
Jan
Feb
Mar
April
May
Jun
Units
Sold
640
648
630
761
735
850
Index
0.80
0.80
0.70
0.94
0.89
1.00
Month
Jul
Aug
Sept
Oct
Nov
Dec
Units
Sold
765
805
840
828
840
800
Index
0.90
1.15
1.20
1.20
1.25
1.25
(a) Plot the data. Does there seem to be a trend?
(b) Deseasonalize car sales
(c) Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs.
Excel Solution
(a) Plot of original data (seasonalized car sales)
(b) Deseasonalized Car Sales
Create formula in F6 (see
circled formula), then copy
onto F7 to F17
(c) Graph of seasonalized car sales versus deseasonalized car sales
Problem 26 (115) – Using MAD, MSE, and MAPE to measure forecast accuracy
Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water. Actual
demand and the two sets of forecasts are as follows:
Period
1
2
3
4
5
6
7
8
Demand
68
75
70
74
69
72
80
78
Predicted Demand
F1
F2
66
66
68
68
72
70
71
72
72
74
70
76
71
78
74
80
(a) Compute MAD for each set of forecasts. Given your results, which forecast appears to be the most
accurate? Explain.
(b) Compute MSE for each set of forecasts. Given your results, which forecast appears to be the most
accurate? Explain.
(c) In practice, either MAD or MSE would be employed to compute forecast errors. What factors might lead
you to choose one rather than the other?
(d) Compute MAPE for each data set. Which forecast appears to be more accurate?
Excel Solution
=ABS(c7-d7)
=(c7-d7)^2
=ABS(c7-d7)/c7
=AVERAGE(G8:G15)
=SUM(J8:J15)/(COUNT(J8:J15)-1)
=AVERAGE(M8:M15)