Questions and Answers of Forecasting Predictive Analytics

2. Using Minitab or equivalent software, fit an model to Mary Beasley’s data, and generate forecasts for the next 12 months. Examine the residuals to check for adequacy of fit. Should Mary be happy
1. Using Mary Beasley’s data in Table 13, construct a time series plot, and compute the sample autocorrelations and sample partial autocorrelations for the total billable visits, ; the differenced
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4. Do you have any reservations about using ARIMA modeling in this situation? Discuss.
forecasts.
3. Using the model you have developed in Question 2, generate forecasts of contacts for the next 12 months. Include the forecasts on a plot of the original contacts series.Write a brief report
2. Is the model suggested in Question 1 adequate? Discuss with reference to residual plots, residual autocorrelations, and the Ljung-Box chi-square statistics. If the model is not adequate, modify
1. Using Minitab or equivalent software, fit an model to the data in Table 24. Why does this model seem to be a reasonable initial choice? Is there another candidate model that you might consider?
4. Write a report summarizing your findings. Include in your report a plot of the original series and the forecasts.
3. Using the model you have developed in Question 2, generate forecasts for the funding requirements for the next 12 months.
2. Is the model suggested in Question 1 adequate? Discuss with reference to residual plots, residual autocorrelations, and the Ljung-Box chi-square statistics. If the model is not adequate, modify
1. Using Minitab or equivalent software, fit an model to the data in Table 22. Do you think a constant term is required in the model? Explain.
3. Write a brief memo summarizing your findings.
2. Using your model, generate forecasts of revenue for the next 12 months. Append these forecasts to the end of the series, and plot the results. Are you happy with the pattern of the forecasts?
1. Develop an ARIMA model for sales tax revenue using the Box-Jenkins methodology.
3. The Lydia Pinkham data are interesting due to the unique (unchanging) nature of the product and marketing for the 54-year period represented. What factors might affect annual sales data for
2. There is some evidence that the Lydia Pinkham data may be nonstationary. For example, the sample autocorrelations tend to be large (persist) for several lags. Difference the data. Construct a
1. After this analysis was completed, the figure for sales in 1961 became available: $1,426. What is the model’s forecast for 1961? If this year were added to the testing data set, what would the
3. Write Dorothy a second memo that summarizes the results of this analysis
2. Develop an ARIMA model using the BoxJenkins methodology, and forecast the monthly number of new clients for the rest of 1993.
1. Write Dorothy a memo that explains the BoxJenkins methodology.
3. Using a program for ARIMA modeling, fit and check an ARIMA model for Mr. Tux sales. Generate forecasts for the next 12 months.
2. Given the autocorrelations in Figure 39 and the partial autocorrelations in Figure 40, what regular (nonseasonal) terms might John include in an ARIMA model for Mr. Tux sales? What seasonal terms
1. Discuss the problems, if any, of explaining the Box-Jenkins method to John’s banker and others on his management team.
5. Would you use the same Box-Jenkins model if the new data were combined with the old data?
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3. How do these forecasts compare with actual sales?
2. What are your forecasts for the first four weeks of January 1983?
1. What is the appropriate Box-Jenkins model to use on the original data?
23. Figure P-23 is a time series plot of the weekly number of Influenza A Positive cases in a region of Texas from the week of September 2, 2003, to the week of April 10, 2007. The number of cases
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16. Use the Box-Jenkins methodology to model and forecast the monthly sales of the Cavanaugh Company given in Table P-14. (Hint: Consider a log transformation before modeling these data.)TABLE P-14
15. Table P-15 gives the 120 monthly observations on the price in cents per bushel of corn in Omaha, Nebraska. Determine the best ARIMA model for these data. Generate forecasts of the price of corn
14. The data in Table P-14 are weekly automobile accident counts for the years 2006 and 2007 in Havana County. Determine the appropriate ARIMA model, and forecast accidents for the 91st week. Comment
13. The data in Table P-13 are closing stock quotations for the DEF Corporation for 150 days. Determine the appropriate ARIMA model, and forecast the stock price TABLE P-13 Period DEF Period DEF
12. The data in Table P-12 are weekly prices for IBM stock.a. Using a program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations, and the sample partial autocorrelations. Use
11. Table P-11 contains a time series of 96 monthly observations. Using a computer program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations,and the sample partial
10. Table P-10 contains a time series of 80 observations. Using a computer program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations, and the sample partial autocorrelations.
9. Table P-9 contains a time series of 80 observations. Using a computer program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations, and the sample partial autocorrelations.
8. Table P-8 contains a time series with 126 observations. Using a computer program for ARIMA modeling, obtain a plot of the data, the sample autocorrelations, and the sample partial
7. Chips Bakery has been having trouble forecasting the demand for its special highfiber bread and would like your assistance. The data for the weekly demand and the autocorrelations of the original
6. An ARIMA(1, 1, 0) model (AR(1) model for first differences) is fit to observations of a time series. The first 12 residual autocorrelations are shown in Figure P-6. The model was fit with a
5. Given the graphs in Figure P-5 of the sample autocorrelations and the sample partial autocorrelations, tentatively identify an ARIMA model from each pair of graphs.
4. Fill in the missing information in Table P-4, indicating whether the theoretical autocorrelations and partial autocorrelations die out or cut off for these models.
3. A time series model has been fit and checked with historical data yielding Suppose at time the observation is .a. Determine forecasts for periods 61, 62, and 63 from origin 60.b. Suppose the
2. Suppose the following time series model has been fit to historical data and found to be an adequate model. The first four observations are and Assuming and , calculate forecasts for periods 5, 6,
1.a. For a sample of 100 observations of random data, calculate a 95% confidence interval for the autocorrelation coefficient at any lag.b. If all the autocorrelation coefficients are within their
5. Which model, the dummy variable regression or the autoregression, do you prefer? Why?
4. Fit an autoregressive model to Jame’s data with sales lagged 12 months as the predictor variable.Is this model reasonable? Generate forecasts for the remaining seven months of 2003 using your
3. Using Jame’s fitted model in Table 23, generate forecasts for the remaining seven months of 2003.
2. Are you happy with Jame’s regression model? What changes would you make, if any?
1. All the coefficients of the dummy variables in Jame’s regression are negative except that for Nov. Does this make sense? Explain.
4. What conditions might prompt Julie to reexamine her regression model or, perhaps, to look for another method of forecasting sales?
3. How might Julie’s model be used to determine future amounts spent on newspaper and TV advertising?
2. Assuming there are no additional important predictor variables, are you satisfied with Julie’s forecasting model? How would you “sell” the model to management (and Jackson Tilson)?
1. Julie has collected data on other variables that were not included in her multiple regression model. Should one or more of these other variables be included in her model? More generally, how can
3. Prepare a memo to Michael recommending the regression model you believe is more appropriate for predicting the cyclical nature of emergency road service call volume.
2. Is serial correlation a problem? If any coefficients are not significantly different from zero, try running a regression without these independent variables. Try experimenting with different
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1. Analyze the significance of the variables in Dorothy’s regression model. Develop a regression model (be sure to include additive dummy variables for the seasonal component, if necessary), and
1. Write a memo to John with a careful analysis of the results of his two attempts to develop a seasonal forecasting model. Which model is better? Be sure your discussion includes an evaluation of
4. Would another type of forecasting model be more effective for forecasting weekly sales?
3. Do you agree with Jim’s conclusions?
2. Was it correct for Jim to use sales lagged one week as a predictor variable?
1. Was Jim’s use of a dummy variable correct?
6. What conclusions can be drawn from a comparison of the Spokane County business activity index and the GNP?
5. Is there any potential for the use of lagged data?
4. Should the regression done on the first differences have been through the origin?
3. How does the small sample size affect the analysis?
2. Would it have been better to eliminate multicollinearity first and then tackle autocorrelation?
1. Why did Young choose to solve the autocorrelation problem first?
7. Examine the residuals from your fitted model. In particular, check for autocorrelation. Once you are satisfied with your forecasting equation, generate forecasts for the next six time periods. If
6. Develop a forecasting equation for your dependent variable using one or more of the identified predictor variables.
5. Identify several potential predictor variables for your dependent variable. You may use company records and other data sources in this process.
4. Compute the first differences for your data, and construct the autocorrelation function for the differenced data. Describe the resulting patterns in the time series of first differences.
3. Based on the pattern of the autocorrelation function, describe the patterns in your time series.
2. Calculate several autocorrelation coefficients, and plot the autocorrelation function.
1. Identify a company or organization that interests you.The company can be a local or national company that has published records, including the measurement of time series variables. Identify a key
24. Consider the bivariate system where are each independently distributed with mean zero and variance . Develop an expression for , and show that X and Y are cointegrated. What is the cointegrating
23. Refer to Problem 20. Run a simple linear regression of chicken consumption on chicken consumption lagged one time period. Examine the residuals. Interpret the results of your regression analysis.
22. Refer to Problem 20. Consider only the variables chicken consumption, income, and chicken price in the original units. Compute simple differences for each of the variables. Using the differenced
21. Repeat parts b and c of Problem 20 with the log-transformed data. Give an interpretation of the coefficients of income and chicken price in terms of elasticities. Using your final fitted
20. The demand for a commodity typically depends on the income of the consumer, the real price of the commodity, and the real price of complementary or competing products. Table P-20 gives the per
19. Circuit City Inc. is a retailer of video and audio equipment and other consumer electronics and office products. Recently, sales have been weak, declining by a total TABLE P-19 Year May 31 Aug 31
18. Although the time series data in Table P-18 are old, they provide the basis for some interesting regression modeling. Using the data in Table P-18, attempt to relate personal savings to personal
17. Refer to Example 5. Using the Sears data in Table 5, convert the sales and disposable income values to simple differences. That is, create the numbers and . Fit a simple linear regression model
16. The data in Table P-16 show seasonally adjusted quarterly sales for Dickson Corporation and for the entire industry for 20 quarters.a. Fit a linear regression model, and store the residuals. Plot
15. National Presto is a manufacturer of small electrical appliances and housewares, including pressure cookers, heaters, canners, fry pans, griddles, roaster ovens, deep fryers, corn poppers, can
14. Thomas Furniture Company concludes that production scheduling can be improved by developing an accurate method of predicting quarterly sales. The company analyst, Mr. Estes, decides to
13. Thompson Airlines has determined that 5% of the total number of U.S. domestic airline passengers fly on Thompson planes. You are given the task of forecasting the number of passengers who will
12. Paul Raymond, president of Washington Water Power, was worried about the possibility of a takeover attempt and the fact that the number of common shareholders has been decreasing since 1983.
11. Jim Jackson, a rate analyst for the Washington Water Power Company, while preparing for a rate case needed to forecast electric residential revenue for 1996. Jim decided to investigate three

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