TABLE E4.1 Data for Exercise 4.1 Period yt Period yt Period yt Period yt Period yt 1 48.7 11 49.1 21 45.3 31 50.8 41 47.9 2 45.8 12 46.7 22 43.3 32 46.4 42 49.5 3 46.4 13 47.8 23 44.6 33 52.3 43 44.0 4 46.2 14 45.8 24 47.1 34 50.5 44 53.8 5 44.0 15 45.5 25 53.4 35 53.4 45 52.5 6 53.8 16 49.2 26 44.9 36 53.9 46 52.0 7 47.6 17 54.8 27 50.5 37 52.3 47 50.6 8 47.0 18 44.7 28 48.1 38 53.0 48 48.7 9 47.6 19 51.1 29 45.4 39 48.6 49 51.4 10 51.1 20 47.3 30 51.6 40 52.4 50 47.7 4.2 Reconsider the time series data shown in Table E4.1. a. Use simple exponential smoothing with the optimum value of ? to smooth the first 40 time periods of this data (you can find the optimum value from Minitab). How well does this smoothing procedure work? Compare the results with those obtained in Exercise 4.1. b. Make one-step-ahead forecasts of the last 10 observations. Determine the forecast errors. Compare these forecast errors with those from Exercise 4.1. How much has using the optimum value of the smoothing constant improved the forecasts? 4.1 Consider the time series data shown in Table E4.1. a. Make a time series plot of the data. b. Use simple exponential smoothing with ? = 0.2 to smooth the first 40 time periods of this data. How well does this smoothing procedure work? c. Make one-step-ahead forecasts of the last 10 observations. Determine the forecast errors.
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1, we are given a time series data in Table E4.1. The data consists of 50 periods and the corresponding values for each period. Show more…
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Consider the following time series data. Week 1 2 3 4 5 6 Value 19 12 14 11 15 13 (a) Construct a time series plot. A B C D What type of pattern exists in the data? A The data appear to follow a trend pattern. B The data appear to follow a horizontal pattern. C The data appear to follow a cyclical pattern. D The data appear to follow a seasonal pattern. (b) Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.) Week Time Series Value Forecast 1 19 2 12 3 14 4 11 5 15 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. Week Time Series Value Forecast 1 19 2 12 3 14 4 11 5 15 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (Round your answer to two decimal places.) (d) Compare the three-week moving average approach with the exponential smoothing approach using α = 0.2. Which appears to provide more accurate forecasts based on MSE? Explain. A The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach. B The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach. C The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach. D The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. (e) Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts. Week Time Series Value Forecast 1 19 2 12 3 14 4 11 5 15 6 13 Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. A The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.4. B The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.4. C The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2. D The exponential smoothing using α = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.2.
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Consider the following time series data. Week 1 2 3 4 5 6 Value 16 12 14 11 15 13 (a) What type of pattern exists in the data? The data appear to follow a seasonal pattern. (b) Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.) Week Time Series Value Forecast 1 16 2 12 3 14 4 11 5 15 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. Week Time Series Value Forecast 1 16 2 12 3 14 4 11 5 15 6 13 Compute MSE. (Round your answer to two decimal places.) MSE = What is the forecast for week 7? (Round your answer to two decimal places.) (d) Compare the three-week moving average approach with the exponential smoothing approach using α = 0.2. Which appears to provide more accurate forecasts based on MSE? Explain. The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach. (e) Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts. Week Time Series Value Forecast 1 16 2 12 3 14 4 11 5 15 6 13 Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain. The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.4.
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The exponential smoothing method of forecasting is the most appropriate method for time series that exhibit: A. irregularity. B. seasonality. C. a constant downward trend. D. a constant upward trend. 1. The seasonal component in a time series reflects a long-term, relatively smooth pattern or direction. True False 2. Seasonality is a time-series component. True False 3. Which of the following components describe the up and down movements of a time series that vary both in length and in intensity? A. the cyclical component B. the trend component C. the seasonal component D. the irregular component 4. In which component of the time series will the effect of an unpredictable, rare event be contained? A. the seasonal component B. the irregular component C. the cyclical component D. the trend component 5. The irregular component of a time series exhibits a tendency to grow or decrease rather steadily over long periods of time. True False 6. We can smooth a time series using the method of moving averages, based on the idea that any large irregular component at any point in time will exert a smaller effect if we average the point with its immediate neighbors. True False 7. An apartment complex manager randomly selects 10 buildings from the complex's 30 buildings, and then interviews one household member from each apartment in the 10 buildings. This is an example of cluster sampling. True False 8. The Holt-Winters Exponential Smoothing procedure allows only the trend component in a time series. True False 9. Simple exponential smoothing provides a forecast based on a weighted average of current and past values. True False 10. If a time series is rather smooth, we would use a large value for the smoothing constant α in order to give more weight to the most recent observation. True False 11. The exponential smoothing method of forecasting is the most appropriate method for time series that exhibit: A. irregularity. B. seasonality. C. a constant downward trend. D. a constant upward trend.
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