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) / Forecast (Ft) / Error (et) = At – Ft / |et| / |et|/At
1 / 11
2 / 10
3 / 9
4 / 11
5 / 10
6 / 12

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 / Forecast 2-MA / Error (Et) / |Et| / |Et|/At
1 / 11
2 / 10
3 / 9
4 / 11
5 / 10
6 / 12
t / Sales / Forecast 3-MA / Error (Et) / |Et| / |Et|/At
1 / 11
2 / 10
3 / 9
4 / 11
5 / 10
6 / 12

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 / Forecast / Error (Et) / |Et|
1 / 11
2 / 10
3 / 9
4 / 11
5 / 10
6 / 12

4.  Carmen’s decides to forecast auto sales Exponential smoothing with a = 0.8. Assume initial of 10.

t / Sales / Forecast with a = 0.8 / Error (Et)
1 / 11 / Given: F1 = 10
2 / 10
3 / 9
4 / 11
5 / 10
6 / 12


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 / Change from previous value (At – At-1) / Forecast
1996 / 100
1997 / 110
1998 / 122
1999 / 130
2000 / 139
2001 / 152
2002 / 164

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 / X2 / XY
1996 / 100
1997 / 110
1998 / 122
1999 / 130
2000 / 139
2001 / 152
2002 / 164
Sum =

Forecast for year 2003 and 2004

Year / t / Ft
2003
2004


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
2 / Spring / 3800
Summer / 2900
Fall / 2000
Winter / 900
3 / Spring / 4100
Summer / 3100
Fall / 2100
Winter / 1010
4 / Spring / 4200
Summer / 3100
Fall / 2200
Winter / 1050

Naïve forecast:

Year 5 Quarter / Forecast
Spring
Summer

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
Winter / 800 / 900 / 1010 / 1050
Quarter / Season Average / SA Index
Spring
Summer
Fall
Winter

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 / Season / At / SA Index / Deseasonalized-At
1 / Spring / 3500
Summer / 2800
Fall / 1800
Winter / 800
2 / Spring / 3800
Summer / 2900
Fall / 2000
Winter / 900
3 / Spring / 4100
Summer / 3100
Fall / 2100
Winter / 1010
4 / Spring / 4200
Summer / 3100
Fall / 2200
Winter / 1050


Tracking Signal

10.  Given the forecast demand and demand for fishing boats, compute the tracking signal.

Week / Demand / Forecast / Error (Et) / CFEt / |Et| / CAEt / No. of Error / MADt / Tracking Signal = CFEt/MADt
1 / 71 / 78
2 / 80 / 75
3 / 101 / 101
4 / 80 / 88

Et = Error = Demand - Forecast

|Et| = Absolute error = |Demand – Forecast|

CFEt = Running Sum of Et

CAEt = Running Sum of |Et|

MADt = Running MAD for period t = CAEt/ No. of error

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 $) / XY / X2
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

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