Forecasting
Part 3
By
Anita Lee-Post
© 2003 Anita Lee-Post
Selecting a forecasting model
Qualitative
Model
Qualitative
Data
Type
Time series
Model
Level/Trend/
Seasonal
Model
Forecast
Accuracy
© 2003 Anita Lee-Post
Data
Pattern
* MAD/MSE
* Tracking
Signal
Quantitative
Quantitative
Model
Causal factors
Time series
Basis of
forecast
Linear
Regression
Model
Strength
Causal
Model
Linear
Relation
Correlation
Coefficient
Forecast accuracy
• A good forecast is accurate but not
perfect, i.e., actual value  forecast
value
• Overall accuracy measures:
1. Mean absolute deviation
2. Mean squared error
• Forecast accuracy has to be monitored
by using a “tracking signal”
© 2003 Anita Lee-Post
Overall error measures
1. Mean absolute deviation (MAD):
n
MAD 
 A F
t
t 1
t
, where At : Actual for period t ,
n
Ft : Forecast for period t , n : number of data points
2. Mean squared error (MSE):
n
  At  Ft 2
MSE  t 1
, where At : Actual for period t ,
n
Ft : Forecast for period t , n : number of data points
•
The forecast technique giving the lowest MAD/MSE is
preferred
•
MSE magnifies large errors through the squaring process
© 2003 Anita Lee-Post
Tracking signal
A way to monitor forecast accuracy is by
comparing a measure called:
Cumulative Sum of Forecast Error
Tracking Signal 
MAD
against predetermined control limits
(usually +/-4 MAD) in a control chart
© 2003 Anita Lee-Post
Tracking signal continued
Signal exceeded limit
+
Upper control limit = +4MAD
0
-
Tracking signal
0 MAD
Lower control limit = -4MAD
Time
© 2003 Anita Lee-Post
Correlation coefficient
• Correlation coefficient, r, measures the
direction and strength of the linear
relationship between the independent (x)
and dependent (y) variables
r
© 2003 Anita Lee-Post
n
n
n
i 
i 
i 
n  x i yi   x i  yi
 n   n   n   n  
n  x i    x i   n  yi    yi  
 i     i 
 i   
 i 
Correlation coefficient continued



r = +1: a perfect positive linear relationship
r = 0: no relationship
r = -1: a perfect negative linear relationship
Y
r=1
Y
r = -1
Yi = a + b X i
Yi = a + b X i
X
Y
r = .89
Yi = a + b X i
© 2003 Anita Lee-Post
X
Y
X
r=0
Yi = a + b X i
X
Using Excel for forecasting
1. Enter the following demand figures for
C&A’s product in an Excel worksheet
Jan
650
© 2003 Anita Lee-Post
Feb
700
Mar
810
Apr
800
May
900
Jun
700
Using Excel for forecasting continued
2. Invoke the data
analysis tool:
Tools  Data Analysis
If “Data Analysis” is not
found, then
 Tools  Add-ins 
select “Analysis
ToolPak”

© 2003 Anita Lee-Post
Using Excel for forecasting continued
3. Select “Moving Average” from the list
of data analysis options” to compute
a 3-month moving average:
© 2003 Anita Lee-Post
Using Excel for forecasting continued
4. Fill in the Moving Average Parameters:
•
Input Range: cell range of
the time series
•
Labels in First Row: leave
it unchecked if your cell
range above contains data
points only
•
Interval: parameter n
(number of data points
used in moving average
computation)
•
Output Range: starting
cell address for forecast
values (need to offset the
input range by one row)
© 2003 Anita Lee-Post
Using Excel for forecasting continued
• Excel-generated moving average forecasts:
© 2003 Anita Lee-Post
Using Excel for forecasting continued
4. Fill in the Exponential Smoothing Parameters:
•
Input Range: cell range of
the time series
•
Damping factor: 1-a, the
smoothing constant
•
Labels: leave it unchecked
if your cell range above
contains data points only
•
Output range: starting cell
address for forecast
values (no offset is
needed)
© 2003 Anita Lee-Post
Using Excel for forecasting continued
• Excel-generated exponential smoothing
forecasts:
Copy the formula in cell C7 to cell C8
to compute the forecast for July
© 2003 Anita Lee-Post
Using Excel for forecasting continued
4. Fill in the Regression Parameters:
•
Input Y Range: cell range
of the dependent variable
•
Input X Range: cell range
of the independent
variable
•
Labels: have it checked as
column headings are
included in our input
ranges
•
Output range: starting cell
address for regression
analysis output
© 2003 Anita Lee-Post
Excel-generated regression analysis report:
Enter the formula =D17+D18*A8 in cell
B8 to compute the forecast for July
© 2003 Anita Lee-Post
Excel can be used to compute MAD and MSE:
A
B
C
D
E
Month
Demand
3-month
Moving
Average
Absolute Deviation Squared Error
…
…
…
…
…
5
Apr
800
720
=ABS(B5-C5)
=(B5-C5)^2
6
May
900
770
=ABS(B6-C6)
=(B6-C6)^2
7
Jun
700
836.7
=ABS(B7-C7)
=(B7-C7)^2
1
8
9
MAD
10 MSE
© 2003 Anita Lee-Post
=AVERAGE(D5:D7)
=AVERAGE(E5:E7)
Excel can be used to compute MAD and MSE:
A
B
C
Month
Demand
Exp.
Smooth.
(a  0.
Absolute Deviation Squared Error
…
…
…
…
…
5
Apr
800
670.5
=ABS(B5-C5)
=(B5-C5)^2
6
May
900
683.5
=ABS(B6-C6)
=(B6-C6)^2
7
Jun
700
705.1
=ABS(B7-C7)
=(B7-C7)^2
1
D
E
8
9
MAD
10 MSE
© 2003 Anita Lee-Post
=AVERAGE(D5:D7)
=AVERAGE(E5:E7)
Excel can be used to compute Tracking Signals:
A
B
C
Month
Demand
3-month
Moving
Average
Error
Cumulative
Sum of Error
Tracking
Signal
…
…
…
…
…
…
5
Apr
800
720
=B5-C5
=D5
=E5/$D$9
6
May
900
770
=B6-C6
=E5+D6
=E6/$D$9
7
Jun
700
836.7
=B7-C7
=E6+D7
=E7/$D$9
1
D
8
9
MAD
© 2003 Anita Lee-Post
116
E
F