Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	23	14	20	11	20	23	14

(a)	Compute MSE using the most recent value as the forecast for the next period.
	If required, round your answer to one decimal place.
	What is the forecast for month 8?
	If required, round your answer to one decimal place. Do not round intermediate calculation.
(b)	Compute MSE using the average of all the data available as the forecast for the next period.
	If required, round your answer to one decimal place. Do not round intermediate calculation.
	What is the forecast for month 8?
	If required, round your answer to one decimal place.
(c)	Which method appears to provide the better forecast?
	- Select your answer - (i) Naive (ii) All data average

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	13	16	11	17	14

(a)

Choose the correct time series plot.

(i)		(ii)
(iii)		(iv)

- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1

What type of pattern exists in the data?

- Select your answer -Horizontal PatternTrend PatternItem 2

(b)

Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7.

Do not round intermediate calculations. If required, round your answers to two decimal places.

Week	Value	Forecast
1	18
2	13
3	16
4	11
5	17
6	14

MSE:

The forecast for week 7:

(c)

Use= 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.

Do not round intermediate calculations. If required, round your answers to two decimal places.

Week	Value	Forecast
1	18
2	13
3	16
4	11
5	17
6	14

MSE:

The forecast for week 7:

(d)

Compare the three-week moving average forecast with the exponential smoothing forecast using= 0.2. Which appears to provide the better forecast based on MSE?

- Select your answer -Three-week moving averageExponential SmoothingItem 15

Explain.

Using this approach results in a - Select your answer -largersmallerItem 16 MSE.

(e)

Use trial and error to find a value of the exponential smoothing coefficientthat yields the minimum MSE. Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient.

alpha:

Refer to the gasoline sales time series data in the given table.

Click on the datafile logo to reference the data.

Week	Sales (1,000s of gallons)
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(a)

Compute four-week and five-week moving averages for the time series.

Do not round intermediate calculations. If required, round your answers to two decimal places.

Week	Sales	4-Week Moving Average	5-Week Moving Average
1	17
2	21
3	19
4	23
5	18
6	16
7	20
8	18
9	22
10	20
11	15
12	22

(b)

Compute the MSE for the four-week and five-week moving average forecasts.

Do not round intermediate calculations. If required, round your answers to two decimal places.

MSE for four-week moving average =

MSE for five-week moving average =

(c)

What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that the MSE for the three-week moving average is 10.22.

- Select your answer -

Three

Four

Five

Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.

Week	Sales (1,000s of gallons)
1	17
2	23
3	14
4	25
5	17
6	16
7	22
8	19
9	21
10	19
11	17
12	23

(a)

Show the exponential smoothing forecasts using = 0.1, and = 0.2.

	Exponential Smoothing
Week	= 0.1	= 0.2
13

(b)

Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of = 0.1 or = 0.2 for the gasoline sales time series?

An - Select your answer - = 0.1 = 0.2Item 3 smoothing constant provides the more accurate forecast, with an overall MSE of .

(c)

Are the results the same if you apply MAE as the measure of accuracy?

An - Select your answer - = 0.1 = 0.2Item 5 smoothing constant provides the more accurate forecast, with an overall MAE of .

(d)

What are the results if MAPE is used?

An - Select your answer - = 0.1 = 0.2Item 7 smoothing constant provides the more accurate forecast, with an overall MAPE of .

Thanks