CH 15 - Time Series Analysis and Forecasting. Questions and Answers

True / False 1. If we focus upon the historical data, or past values of the variable to be forecast, we refer to this as a time series method of forecasting. a. True b. False 2. Quantitative forecastin ...

True / False 1. If we focus upon the historical data, or past values of the variable to be forecast, we refer to this as a time series method of forecasting. a. True b. False 2. Quantitative forecasting methods can be used when past information about the variable being forecast is unavailable. a. True b. False 3. Trend in a time series must always be linear. a. True b. False 4. All quarterly time series contain seasonality. a. True b. False 5. A four-period moving average forecast for period 10 would be found by averaging the values from periods 10, 9, 8, and 7. a. True b. False 6. If the random variability in a time series is great, a small value of the smoothing constant is preferred so that we do not overreact and adjust our forecasts too quickly. a. True b. False 7. With fewer periods in a moving average, it will take longer to adjust to a new level of data values. a. True b. False 8. Qualitative forecasting methods are appropriate when historical data on the variable being forecast are either unavailable or not applicable. a. True b. False 9. A sequence of observations on a variable measured at successive points in time or over successive periods of time is known as a time series. a. True b. False 10. Any recurring sequence of points above and below the trend line lasting less than one year can be attributed to the cyclical component of the time series. a. True b. False 11. Smoothing methods are more appropriate for a stable time series than when significant trend or seasonal patterns are present. a. True b. False 12. The exponential smoothing forecast for any period is a weighted average of all the previous actual values for the time series. a. True b. False 13. The mean squared error is obtained by computing the average of the squared forecast errors. a. True b. False 14. If a time series has a significant trend pattern, then one should not use a moving average to forecast. a. True b. False 15. For a time series with relatively little random variability, we should use larger values of the smoothing constant to provide the advantage of allowing the forecasts to react more quickly to changing conditions. a. True b. False 16. Time series data can exhibit seasonal patterns of less than one month in duration. a. True b. False 17. When using a moving average of order k to forecast, a small value for k is preferred if only the most recent values of the time series are considered relevant. a. True b. False 18. In situations where you need to compare forecasting methods for different time periods, relative measures such as mean absolute error (MAE) are preferred. a. True b. False 19. In order to use moving averages to forecast a time series, the first step is to select the order k, the number of time series values to be included in the moving average. a. True b. False 20. When forecasting, if a greater number of past values are considered relevant, then we generally opt for a larger value of k. a. True b. False Multiple Choice 21. All of the following are true about time series methods EXCEPT a. they discover a pattern in historical data and project it into the future. b. they involve the use of expert judgment to develop forecasts. c. they assume that the pattern of the past will continue into the future. d. their forecasts are based solely on past values of the variable or past forecast errors. 22. Gradual shifting of a time series to relatively higher or lower values over a long period of time is called a. periodicity. b. a cycle. c. seasonality. d. a trend pattern. 23. Seasonal patterns a. cannot be predicted. b. are regular repeated patterns. c. are multiyear runs of observations above or below the trend line. d. reflect a shift in the time series over time. 24. The focus of smoothing methods is to smooth out a. random fluctuations. b. wide seasonal variations. c. significant trend effects. d. long-range forecasts. 25. Forecast errors a. are the difference in successive values of a time series. b. are the differences between actual and forecast values. c. should all be nonnegative. d. should be summed to judge the goodness of a forecasting model. 26. Linear trend is calculated as . The trend projection for period 15 is a. 11.25. b. 28.50. c. 39.75. d. 44.25. 27. The trend pattern is easy to identify by using a. a moving average. b. exponential smoothing. c. regression analysis. d. a weighted moving average. 28. The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal pattern is a. moving average. b. mean squared error. c. mean average error. d. qualitative forecasting. 29. We can model a time series with a seasonal pattern by treating the season itself as a(n) a. categorical variable. b. qualitative variable. c. annual variable d. None of these are correct. 30. One measure of the accuracy of a forecasting model is the a. smoothing constant. b. linear trend. c. mean absolute error. d. seasonal index. 31. Using a naive forecasting method, the forecast for next week’s sales volume equals a. the most recent week’s sales volume. b. the most recent week’s forecast. c. the average of the last four weeks’ sales volumes. d. next week’s production volume. 32. All of the following are true about a cyclical pattern EXCEPT a. it is often due to multiyear business cycles. b. it is often combined with long-term trend patterns and called trend-cycle patterns. c. it usually is easier to forecast than a seasonal pattern due to less variability. d. it is an alternating sequence of data points above and below the trend line. 33. All of the following are true about a stationary time series EXCEPT a. its statistical properties are independent of time. b. a plot of the series will always exhibit a horizontal pattern. c. the process generating the data has a constant mean. d. there is no variability in the time series over time. 34. In situations where you need to compare forecasting methods for different time periods, the most appropriate accuracy measure is a. MSE. b. MAPE. c. MAE. d. ME. 35. Whenever a categorical variable such as season has k levels, the number of dummy variables required is a. k  1. b. k. c. k + 1. d. 2k. 36. To select a value for α for exponential smoothing a. use a small α when the series varies substantially. b. use a large α when the series has little random variability. c. use a value between 0 and 1. d. All of these are correct. 37. Which of the following forecasting methods puts the least weight on the most recent time series value? a. exponential smoothing with α = 0.3 b. exponential smoothing with α = 0.2 c. moving average using the most recent four periods d. moving average using the most recent three periods 38. Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for time period 9 plus a. α times the demand forecast for time period 8. b. α times the error in the demand forecast for time period 9. c. α times the observed demand in time period 9. d. α times the demand forecast for time period 9. 39. Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a five-period moving average? a. α = 0.2 b. α = 0.25 c. α = 0.75 d. α = 0.8 Subjective Short Answer 40. The number of cans of soft drinks sold in a machine each week is recorded below. Develop forecasts using a three-period moving average. 338, 219, 278, 265, 314, 323, 299, 259, 287, 302 41. Use a four-period moving average to forecast attendance at baseball games. Historical records show the following: 5346, 7812, 6513, 5783, 5982, 6519, 6283, 5577, 6712, 7345 42. A hospital records the number of floral deliveries its patients receive each day. For a two-week period, the records show the following: 15, 27, 26, 24, 18, 21, 26, 19, 15, 28, 25, 26, 17, 23 Use exponential smoothing with a smoothing constant of 0.4 to forecast the number of deliveries. 43. The number of girls who attend a summer basketball camp has been recorded for the seven years the camp has been offered. Use exponential smoothing with a smoothing constant of 0.8 to forecast attendance for the eighth year. 47, 68, 65, 92, 98, 121, 146 44. A trend line for the weekly attendance at a restaurant's Sunday brunch is given by the following: How many guests would you expect in Week 20? 45. The number of new contributors to a public radio station's annual fund drive over the last 10 years is as follows: 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Develop a trend equation for this information, and use it to predict next year's number of new contributors. 46. The average SAT verbal score for students from one high school over the last 10 exams is as follows: 508, 490, 502, 505, 493, 506, 492, 490, 503, 501 Do the scores support an increasing or a decreasing trend? 47. The number of properties newly listed with a real estate agency in each quarter over the last four years is given below. Assume the time series has seasonality without trend. Year Quarter 1 2 3 4 1 73 81 76 77 2 89 87 91 88 3 123 115 108 120 4 92 95 87 97 a. Develop the optimization model that finds the estimated regression equation that minimizes the sum of squared error. b. Solve for the estimated regression equation. c. Forecast the four quarters of Year 5. 48. Quarterly billing for water usage is shown below. Year Quarter 1 2 3 4 Winter 64 66 68 73 Spring 103 103 104 120 Summer 152 160 162 176 Fall 73 72 78 88 a. Solve for the forecast equation that minimizes the sum of squared error. b. Forecast the summer of Year 5 and spring of Year 6. 49. A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that show the number of calls received every day for the last five weeks. Week Day Number Week Day Number 1 M 28 4 M 27 T 12 T 13 W 16 W 16 TH 15 TH 18 F 23 F 24 2 M 25 5 M 26 T 10 T 11 W 14 W 18 TH 14 TH 17 F 26 F 25 3 M 32 T 15 W 15 TH 13 F 21 a. Develop the optimization model that finds the estimated regression equation that minimizes the sum of squared error. b. Solve for the estimated regression equation. c. Forecast the five days of Week 6. 50. Monthly sales at a coffee shop have been analyzed. The seasonal index values are as follows: Month Index January 1.38 February 1.42 March 1.35 April 1.03 May 0.99 June 0.62 July 0.51 August 0.58 September 0.82 October 0.82 November 0.92 December 1.56 The trend line is 74,123 + 26.9t. Assume there is no cyclical component and forecast sales for Year 8 (months 97–108). 51. A 24-hour coffee/donut shop makes donuts every eight hours. The manager must forecast donut demand so that the bakers have the fresh ingredients they need. Listed below is the actual number of glazed donuts (in dozens) sold in each of the preceding 13 eight-hour shifts. Date Shift Demand (dozens) June 3 Day 59 Evening 47 Night 40 June 4 Day 64 Evening 43 Night 39 June 5 Day 62 Evening 46 Night 42 June 6 Day 60 Evening 45 Night 40 June 7 Day 58 a. Develop the optimization model that finds the estimated regression equation that minimizes the sum of squared error. b. Solve for the estimated regression equation. c. Forecast the demand for glazed donuts for the day, evening, and night shifts of June 8. 52. The number of plumbing repair jobs performed by Auger's Plumbing Service in each of the last nine months is listed below. Month Jobs Month Jobs Month Jobs March 353 June 374 September 399 April 387 July 396 October 412 May 342 August 409 November 408 a. Assuming a linear trend function, forecast the number of repair jobs Auger's will perform in December using the least squares method. b. What is your forecast for December using a three-period weighted moving average with weights of 0.6, 0.3, and 0.1? How does it compare with your forecast from part (a)? 53. Quarterly revenues (in $1,000,000s) for a national restaurant chain for a five-year period were as follows: Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 33 42 54 70 85 2 36 40 53 67 82 3 35 42 54 70 87 4 38 47 62 77 99 a. Solve for the forecast equation that minimizes the sum of squared error. b. Forecast the four quarters of Year 6. 54. Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November–December); (2) Father's Day (late May–mid-June); and (3) all other times. Average weekly sales (in $s) for each of these three seasons during the past four years have been as follows: Season Year 1 Year 2 Year 3 Year 4 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120 Determine a forecast for the average weekly sales in Years 5 and 6 for each of the three seasons. 55. Coyote Cable has been experiencing an increase in cable service subscribers over the last few years due to increased advertising and an influx of new residents to the region. The number of subscribers (in 1000s) for the last 16 months is as follows: Month Sales Month Sales Month Sales 1 12.8 7 20.6 12 23.8 2 14.6 8 18.5 13 25.1 3 15.2 9 19.9 14 24.7 4 16.1 10 23.6 15 26.5 5 15.8 11 24.2 16 28.9 6 17.2 Forecast the number of subscribers for Months 17, 18, 19, and 20. 56. Weekly sales of the Weber food processor for the past 10 weeks have been as follows: Week Sales Week Sales 1 980 6 990 2 1040 7 1030 3 1120 8 1260 4 1050 9 1240 5 960 10 1100 a. Determine, on the basis of minimizing the mean square error, whether a three- or four-period simple moving average model gives a better forecast for this problem. b. For each model, forecast sales for Week 11. 57. Below you are given information on John's Hair Salon's profit for the past seven years. Year Profit (in 1000s) 1 15.0 2 16.2 3 17.1 4 18.1 5 18.8 6 19.2 7 20.5 a. Use regression analysis to obtain an expression for the linear trend projection. b. Forecast John's Hair Salon's profit for the next five years. 58. The number of pizzas ordered on Friday evenings between 5:30 and 6:30 at a pizza delivery location for the last 10 weeks is shown below. Use exponential smoothing with smoothing constants of 0.2 and 0.8 to forecast a value for Week 11. Compare your forecasts using MSE. Which smoothing constant would you prefer? 58, 46, 55, 39, 42, 63, 54, 55, 61, 52 59. Sales (in 1000s) of the new Thorton Model 506 convection oven over the eight-week period since its introduction have been as follows: Week Sales 1 18.6 2 21.4 3 25.2 4 22.4 5 24.6 6 19.2 7 21.7 8 23.8 a. Which exponential smoothing model provides better forecasts, one using α = 0.6 or α = 0.2? Compare them using mean squared error. b. Using the two forecast models in part (a), what are the forecasts for Week 9?