Question

Suppose that you work for a major U.S. retail department store that has outlets nationwide. The store offers credit to customers in various forms, including store credit cards, and over the years has seen a substantial increase in credit purchases. The manager of credit sales is concerned about the degree to which consumers are using credit and has started to track the ratio of consumer installment credit to personal income. She calls this ratio the credit percent, or CP, and has asked that you forecast that series for year 8. The available data are:

Year CP

1. 12.96

2. 14.31

3. 15.34

4. 15.49

5. 15.70

6. 16.00

7. 15.62

1. Use the first naive model presented in this chapter to prepare forecasts of CP for years 2 through 8.

2. Plot the actual and forecast values of the series for the years 1 through 8. (You will not have an actual value for year 8 or a forecast value for year 1.)

3. Calculate the MAPE for your forecasts for years 2 through 7.

( please show through excel with plugin values.)

Answer 1

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Answer(a):

Using the first naive model as defined, the forecasted value at any time period - t (F_t) will be actually equal to previous period of time period (A_t-1) (Acording to Naive Model)

=>  F_t = A_t-1

Using the statement above, we insert the data entries into excel for the forecasts from time - t ( 2 to 8 )

A B co Year | 4 2 Actual CP Forecast (4) (F) 12.96 14.31 =C3 15.34 =c4 15.49 =C5 15.7 =C6 16 =C7 15.62 =C8 =09

A B с Actual CP Year Forecast (F) 5 3 $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 9 7 10 8

Answer (b):

$16.50 Year Forecast (F.) $26 8 8 Actual CP (4.) $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 8 8 $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 Sales / Forecast Actual CP (At) 8 8 Forecast (Ft) 8 8 8 02 2 4 6 8 10 Year

I have plotted a scatter plot for the actual and forecasted values using Scatter function in Excel

Answer (c):

(4,-F) RMSE = 1-2

We use the following formula for calculating Root Mean Square Error, where n is the timer period from t = (2 to 7)

Using excel, to compute the formulation, we get

Actual CP Forecast Year (4,-F,)? | $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 $12.96 $14.31 $15.34 $15.49 $15.70 $16.00 $15.62 Average RMSEL 1.8225 1.0609 0.0225 0.0441 0.09 0.1444 0.531 0.73