Chapter 4: Forecasting
No trend and no seasonality models
1.
Auto sales at Carmen’s Chevrolet are shown below. Prepare a time-series plot.
Find a Naive forecast for week 7. Compute the MAD and MAPE values.
t
Auto Sales (At)
1
11
2
10
3
9
4
11
5
10
6
12
Forecast (Ft)
Error (et) = At – Ft
1
|et|
|et|/At
2.
Auto sales at Carmen’s Chevrolet are shown below. Find a 2 and 3-week and
moving average forecasts for week 7. Compute the MAD and MAPE values.
t
Sales
1
11
2
10
3
9
4
11
5
10
6
12
t
Sales
1
11
2
10
3
9
4
11
5
10
6
12
Forecast 2-MA
Forecast 3-MA
Error (Et)
Error (Et)
2
|Et|
|Et|/At
|Et|
|Et|/At
3.
Carmen’s decides to forecast auto sales by weighting the three weeks with a weight
of 2 for last week, 1 for two weeks ago and 1 for 3 weeks ago.
t
Auto Sales
1
11
2
10
3
9
4
11
5
10
6
12
Forecast
Error (Et)
3
|Et|
Carmen’s decides to forecast auto sales Exponential smoothing with  = 0.8.
Assume initial of 10.
4.
t
Sales
Forecast with  = 0.8
1
11
Given: F1 = 10
2
10
3
9
4
11
5
10
6
12
4
Error (Et)
Models for time series with trend and no seasonality
5.
Plot the sales data given below. Find a forecast for year 2003 using Naïve model.
Naïve forecast: Ft+1 = At + (At – At-1)
Year
Actual
sales
1996
100
1997
110
1998
122
1999
130
2000
139
2001
152
2002
164
Change from previous value
(At – At-1)
Forecast
5
6.
Use the sales data given below to determine: (a) the least squares trend line, and (b)
the predicted value for 2003 and 2004 sales. To minimize computations, transform
the value of x (time) to simpler numbers. In this case, designate year 1996 as year 1,
1997 as year 2, etc.
Year
t
Demand
1996
100
1997
110
1998
122
1999
130
2000
139
2001
152
2002
164
X2
XY
Sum =
Forecast for year 2003 and 2004
Year
t
Ft
2003
2004
6
Forecasts with seasonality
7.
The following table shows sales data for water pumps sold by a manufacturer. Fid
the Naïve forecast for Spring and Summer of Year 5.
Year
Quarter
At
1
Spring
3500
Summer
2800
Fall
1800
Winter
800
Spring
3800
Summer
2900
Fall
2000
Winter
900
Spring
4100
Summer
3100
Fall
2100
Winter
1010
Spring
4200
Summer
3100
Fall
2200
Winter
1050
2
3
Quarter
4
Spring
Summer
Fall
Winter
Naïve forecast:
Year 5 Quarter
Forecast
Spring
8.
Summer
7
Year 1
Year 2
Year 3
Year 4
8.
The following table shows sales data for water pumps sold by a manufacturer. Find
Seasonal Relatives using the simple average method.
Quarter
Year 1
Year 2
Year 3
Year 4
Spring
3500
3800
4100
4200
Summer
2800
2900
3100
3100
Fall
1800
2000
2100
2200
800
900
1010
1050
Winter
Quarter
Season Average
Spring
Summer
Fall
Winter
8
SA Index
9.
Deseasonalize the water pump sales data from problem #8 using the SA index.
Find Naïve forecast for Trend with the deseasonalized data. Then find a final
forecast adjusted for seasonality for the next quarter using the SA index from
problem #8.
Year
1
2
3
4
Season
At
Spring
3500
Summer
2800
Fall
1800
Winter
800
Spring
3800
Summer
2900
Fall
2000
Winter
900
Spring
4100
Summer
3100
Fall
2100
Winter
1010
Spring
4200
Summer
3100
Fall
2200
Winter
1050
SA Index
9
DeseasonalizedAt
Tracking Signal
10. Given the forecast demand and demand for fishing boats, compute the tracking
signal.
Week
Demand
Forecast
1
71
78
2
80
75
3
101
101
4
80
88
Et
|Et|
CFEt
CAEt
MADt
Error (Et)
CFEt
|Et|
CAEt
= Error = Demand - Forecast
= Absolute error = |Demand – Forecast|
= Running Sum of Et
= Running Sum of |Et|
= Running MAD for period t = CAEt/ No. of error
Tracking Signal = CFEt/MADt
10
No. of
Error
MADt
Tracking Signal =
CFEt/MADt
Associative Forecast
Regional Foods, Inc. sells organic soap products. A random sample of advertising
expense in thousand dollars for eight randomly selected months and corresponding sales
in million dollars is given below. Using the Associative model ausal approach determine
a forecast for the next month if the company is considering spending $15,000 on
advertising. What is the expected sales if the advertising is $22,500?
Month
Sales
($Million)
Advertising
expense (000 $)
1
2.56
25.0
2
1.74
17.0
3
2.11
21.0
4
1.37
15.0
5
1.42
13.0
6
1.66
14.0
7
1.01
10.0
8
2.26
20.0
XY
11
X2