Forecasting Practice Problems
1. Given the following actual sales,
t
A(t)
1
8
2
4
3
9
4
11
5
10
a. Use Simple Moving Average method (with n =
3) to forecast sales in periods 6, 7, and 8.
b. Use Weighted Moving Average method (with
weights of 0.6, 0.3, 0.1) to forecast sales in
periods 6, 7, and 8.
c. Use Exponential Smoothing method (with  =
0.4) to forecast sales in periods 6, 7, and 8.
(Hint: Use the first 2 data sets to initialize the
Exponential Smoothing forecasting model, then
update the forecasts in periods 3, 4, and 5.)
2. Given the data below, what is the Simple Linear
Regression model that can be used to predict sales?
t
A(t)
1
150
2
157
3
162
4
166
5
177
3. Given the following actual sales,
t
A(t)
1
2
2
6
3
5
4
8
5
10
6
13
7
15
8
14
a. Use the first 4 sets of data and Simple Linear
Regression to initialize the Holt’s Trend Model.
b. Use Holt’s Trend Model (with  = 0.2,  = 0.4)
to update the forecasts in periods 5, 6, 7, and 8.
c. Use Holt’s Trend Model (with  = 0.2,  = 0.4)
to make forecasts for periods 9, 10, 11, and 12.
4. Given the following actual sales,
2003
2004
Spring
Summer
Fall
Winter
Spring
Summer
A(t)
33
12
18
27
36
13
Fall
15
Winter
29
2005
Spring
34
Summer
10
Fall
16
Winter
30
a. Use the first 2 years of data to initialize the
Seasonal Model (without trend).
b. Use Seasonal Model (without trend), (with  =
0.3,  = 0.4) to update the forecasts in 2005.
c. Use Seasonal Model (without trend), (with  =
0.3,  = 0.4) to make forecasts for 2006.
5. Given the following actual sales,
A(t)
Spring
8
Summer
14
Fall
12
Winter
29
2004
Spring
11
Summer
19
Fall
13
Winter
32
2005
Spring
17
Summer
19
Fall
15
Winter
36
a. Use the first 2 years of data and the
Decomposition Forecasting method to initialize
the Winter’s Model.
b. Use Winter’s Model, (with  = 0.3,  = 0.4,  =
0.2) to update the forecasts in 2005.
c. Use Winter’s Model, (with  = 0.3,  = 0.4,  =
0.2) to make forecasts for 2006.
2003
6. Given the following actual sales,
t
A(t)
1
12
2
17
3
14
4
19
5
16
6
12
7
23
a. Use the first 2 data sets to initialize the
Exponential Smoothing forecasting model.
b. Use Exponential Smoothing method (with  =
0.3) to update the forecasts in periods 3, 4, 5, 6,
and 7.
c. Calculate the bias and MAD using the actual and
forecast sales in periods 3, 4, 5, 6, and 7.
d. Use Exponential Smoothing method (with  =
0.8) to update the forecasts in periods 3, 4, 5, 6,
and 7.
e. Calculate the bias and MAD using the actual and
forecast sales in periods 3, 4, 5, 6, and 7.
f. Comparing the bias and MAD from the two
forecasting models, what conclusion can you
make?
7. Continued from the previous problem,
a. Calculate the MPE and MAPE using the actual
and forecast sales (Exponential Smoothing
method with  = 0.3) in periods 3, 4, 5, 6, and 7.
b. Calculate the MPE and MAPE using the actual
and forecast sales (Exponential Smoothing
method with  = 0.8) in periods 3, 4, 5, 6, and 7.
c. Comparing the MPE and MAPE from the two
forecasting models, what conclusion can you
make?
8. Given the following actual and forecast sales,
t
A(t)
F(t)
1
4.0
2
8.0
6.0
3
7.0
6.8
4
9.0
6.8
5
12.0
7.6
6
11.0
9.3
7
13.0
9.9
8
12.0
11.1
a. Calculate the tracking signals starting from
period 3.
b. When will the tracking signal exceed 5.0?