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Moving Averages for the Time Series

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The following data represent revenues in thousands of dollars for a manufacturer of small electric appliances.

a. Calculate the moving averages for this time series.
Moving
Year Quarter Revenues Q Average
1996 1 514 1
1996 2 822 2
1996 3 648 3
1996 4 976 4
1997 1 616 5
1997 2 884 6
1997 3 678 7
1997 4 996 8
1998 1 658 9
1998 2 850 10
1998 3 714 11
1998 4 1052 12

b. Find the seasonal index for each quarter.

Quarter Seasonal index
1
2
3
4

c. From the fourth quarter of 1997 to the first quarter of 1998, revenues declined. What happened on a seasonally adjusted basis?

d. From the first quarter of 1998 to the second quarter of 1998, revenues increased. What happened on a seasonally adjusted basis?

e. The regression equation to predict the long term trend in the seasonally adjusted revenues. Seasonally adjusted revenues = 705.97 + 11.67*Q.

f. Compute the seasonally adjusted forecast for the fourth quarter of 2001.

g. Compute the forecast for the second quarter of 2002.

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Moving Averages:

Year Quarter Revenues Q Moving Average
1996 1 514 1 -
1996 2 822 ...

$2.19
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Multiple Choice questions on Forecasting: Time series, moving average

Please refer to the attached table.

Year Crop Yield Rainfall Temperature
1996 208 25 53.2
1997 215 28.2 58.5
1998 204 25.6 55.1
1999 196 23.5 52.6

25. We decide to construct a time series model to obtain a 2 and 3-period moving average to forecast student enrollments for next term. Which statement is true concerning the accuracy of each forecast?

a. The 2-period forecast will be more accurate than the 3-period forecast.
b. The 3-period forecast will be more accurate than the 2-period forecast.
c. Both forecasts will be equally accurate.
d. Either forecast could be more accurate than the other.
e. Can NOT be determined.

26. 15 months of time series data is available for the sales of a product. We apply a 5-month moving average model to the data. To obtain the mean square error (MSE) we must sum ___ squared error terms.

a. 15
b. 10
c. 9
d. 5
e. 12

27. What are the values of the weights applied to a simple moving average model?

a. They all equal 1.
b. They all equal 0.
c. They are all equal and they all sum to 1.
d. They are all equal and they all sum to 0.
e. None of the above

28. A _________ moving average model for time series data is a moving average model with _________ weights.

a. Simple, unequal
b. Weighted, equal
c. Weighted, unequal
d. Either simple, unequal or weighted, equal
e. Both b and c

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