8-1 Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 Using the nave method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. (a) Mean absolute error If required, round your answer to one decimal place. (b) Mean squared error If required, round your answer to one decimal place. (c) Mean absolute percentage error If required, round your intermediate calculations and final answer to two decimal places. (d) What is the forecast for week 7? Problem 8-5 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) What type of pattern exists in the data? (b) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places. Week Time Series Value 1 18 2 13 3 16 4 11 5 17 6 14 MSE: The forecast for week 7: Forecast (c) Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places. Week Time Series Value 1 18 2 13 3 16 4 11 5 17 6 14 Forecast 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? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (e) Use trial and error to find a value of the exponential smoothing coefficient that results in a smaller MSE than what you calculated for = 0.2. Problem 8-7 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 2 3 4 5 6 7 8 9 10 11 12 17 21 19 23 18 16 20 18 22 20 15 22 (a) Compute four-week and five-week moving averages for the time series. If required, round your answers to two decimal places. Week Sales 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 4 Period 5 period Moving Average Moving Average (b) Compute the MSE for the four-week and five-week moving average forecasts. If required, round your intermediate calculations to four decimal places and round your final answers to three 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. Problem 8-11 For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. Click on the datafile logo to reference the data. (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Compare a three-month moving average forecast with an exponential smoothing forecast for = 0.2. Which provides the better forecasts using MSE as the measure of model accuracy? Do not round your interim computations and round your final answers to three decimal places. Moving Average Exponential smoothing MSE (c) What is the forecast for next month? If required, round your answer to two decimal places. Problem 8-13 The values of Alabama building contracts (in millions of dollars) for a 12-month period are as follows. Click on the datafile logo to reference the data. 240 350 230 260 280 320 220 310 240 (a) Choose the correct time series plot. (i) (ii) 310 240 230 (iii) (iv) What type of pattern exists in the data? (b) Compare a three-month moving average forecast with an exponential smoothing forecast for = 0.2. Which provides the better forecasts based on MSE? Do not round your interim computations and round your final answers to two decimal places. Moving Average Exponential smoothing MSE (c) What is the forecast for the next month using exponential smoothing with = 0.2? If required, round your answer to two decimal places