Ten weeks of data on the Commodity Futures Index are 7.36, 7.41, 7.56, 7.57, 7.61, 7.53, 7.53, 7.71, 7.63, and 7.56.(a) Construct a time series plot.1234What type of pattern exists in the data?Week5The data appear to follow a horizontal pattern.O The data appear to follow a cyclical pattern.O The data appear to follow a trend pattern.O The data appear to follow a seasonal pattern.68.5-8.38.17.9+77.77.5-87.37.16.96.76.5 +01 23 4567 7 8 9 10 11Week98.5-8.3-108.17.97.7+7.5-7.37.16.96.76.50 1 2Time SeriesValue7.367.417.56(b) Use trial and error to find a value of the exponential smoothing coefficient a that results in a relatively small MSE. (Roundyour answers to two decimal places.)7.577.617.533 47.537.715 67 7 8 9 10 11Week7.637.56a = 0.1Forecastα = 0.3ForecastJCOIndexDICa = 0.8Forecast8.58.3-8.17.97.77.5-7.37.16.96.76.508.5 T8.3-8.17.9-7.7-7.57.37.16.9-6.7-6.512 3 4 5 678Week+0 1 2 3 48 9 10 115 66 7 8Week9 10 11What value of the smoothing constant provides the most accurate forecasts?O Exponential smoothing with a = 0.3 provides more accurate forecasts since its MSE is smaller than the MSE fora=0.1 or 0.8.O Exponential smoothing with a = 0.8 provides more accurate forecasts since its MSE is smaller than the MSE fora=0.1 or 0.3.O Exponential smoothing with a = 0.1 provides more accurate forecasts since its MSE is smaller than the MSE forα = 0.3 or 0.8.All three values of the smoothing constant provide the same MSE, so none provide a more accurate forecast than theothers.

Ten weeks of data on the Commodity Futures Index are 7.36, 7.41, 7.56, 7.57, 7.61, 7.53, 7.53, 7.71, 7.63, and 7.56. (a) Construct a time series plot. O Index Index 8.5 8.3 8.1 7.9 7.7 7.5 7.3 7.1 6.9 6.7 6.5 0 1 2 3 4 5 6 7 8 9 10 11 Week 1 8.5 8.3 8.1 7.9 7.7 7.5 7.3 7.1 6.9 6.7 6.5 2 66 Week 0 1 2 3 What type of pattern exists in the data? O The data appear to follow a horizontal pattern. The data appear to follow a cyclical pattern. The data appear to follow a trend pattern. The data appear to follow a seasonal pattern. Time Series Value 4 7.36 567 8 9 10 11 Week 7.41 a = 0.1 Forecast Index a = 0.3 Forecast Index (b) Use trial and error to find a value of the exponential smoothing coefficient a that results in a relatively small MSE. (Round your answers to two decimal places.) 8.5 8.3 a=0.8 Forecast 8.1 7.9 7.7- 7.5 7.3 7.1 6.9 6.7- 6.5 0 1 2 3 4 5 6 7 8 9 10 11 Week 8.5 8.3 8.1 7.9 7.7- 7.5- 7.3 7.1- 6.9 6.7 6.5 01 2 3 4 5 6 7 8 9 10 11 Week

Ten weeks of data on the Commodity Futures Index are 7.36, 7.41, 7.56, 7.57, 7.61, 7.53, 7.53, 7.71, 7.63, and 7.56. (a) Construct a time series plot. O Index Index 8.5 8.3 8.1 7.9 7.7 7.5 7.3 7.1 6.9 6.7 6.5 0 1 2 3 4 5 6 7 8 9 10 11 Week 1 8.5 8.3 8.1 7.9 7.7 7.5 7.3 7.1 6.9 6.7 6.5 2 66 Week 0 1 2 3 What type of pattern exists in the data? O The data appear to follow a horizontal pattern. The data appear to follow a cyclical pattern. The data appear to follow a trend pattern. The data appear to follow a seasonal pattern. Time Series Value 4 7.36 567 8 9 10 11 Week 7.41 a = 0.1 Forecast Index a = 0.3 Forecast Index (b) Use trial and error to find a value of the exponential smoothing coefficient a that results in a relatively small MSE. (Round your answers to two decimal places.) 8.5 8.3 a=0.8 Forecast 8.1 7.9 7.7- 7.5 7.3 7.1 6.9 6.7- 6.5 0 1 2 3 4 5 6 7 8 9 10 11 Week 8.5 8.3 8.1 7.9 7.7- 7.5- 7.3 7.1- 6.9 6.7 6.5 01 2 3 4 5 6 7 8 9 10 11 Week

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section13.7: Exponential Smoothing Models

Problem 27P: The file P13_27.xlsx contains yearly data on the proportion of Americans under the age of 18 living...

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The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?
The file P13_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b?
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The file P13_02.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least the near future. a. Explain briefly whether the plot of the series visually supports the companys suspicion. b. By what percentage are sales increasing each month? c. What is the MAPE for the forecast model in part b? In words, what does it measure? Considering its magnitude, does the model seem to be doing a good job? d. In words, how does the model make forecasts for future months? Specifically, given the forecast value for the last month in the data set, what simple arithmetic could you use to obtain forecasts for the next few months?
The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers). a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?
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The file P13_19.xlsx contains the weekly sales of a particular brand of paper towels at a supermarket for a one-year period. a. Using a span of 3, forecast the sales of this product for the next 10 weeks with the moving averages method. How well does this method with span 3 forecast the known observations in this series? b. Repeat part a with a span of 10. c. Which of these two spans appears to be more appropriate? Justify your choice.
The file P13_27.xlsx contains yearly data on the proportion of Americans under the age of 18 living below the poverty level. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Create a chart of the series with the forecasts superimposed from this optimal smoothing constant. Does it make much of an improvement over the model in part b? d. Write a short report to summarize your results. Considering the chart in part c, would you say the forecasts are good?
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