Exam 16: Time-Series Forecasting

TABLE 16-5 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60,72,96,84,36,and 48. -Referring to Table 16-5,exponentially smooth the number of arrivals using a smoothing constant of 0.25.

TABLE 16-11 The manager of a health club has recorded mean attendance in newly introduced step classes over the last 15 months: 32.1,39.5,40.3,46.0,65.2,73.1,83.7,106.8,118.0,133.1,163.3,182.8,205.6,249.1,and 263.5.She then used Microsoft Excel to obtain the following partial output for both a first- and second-order autoregressive model. SUMMARY OUTPUT - 2nd Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.276 Observations 15 Coefficients Intercept 5.86 X Variable 1 0.37 X Variable 2 0.85 SUMMARY OUTPUT - 1st Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.150 Observations 15 Coefficients Intercept 5.66 X Variable 1 1.10 -Referring to Table 16-11,using the first-order model,the forecast of mean attendance for month 16 is ________.

TABLE 16-11 The manager of a health club has recorded mean attendance in newly introduced step classes over the last 15 months: 32.1,39.5,40.3,46.0,65.2,73.1,83.7,106.8,118.0,133.1,163.3,182.8,205.6,249.1,and 263.5.She then used Microsoft Excel to obtain the following partial output for both a first- and second-order autoregressive model. SUMMARY OUTPUT - 2nd Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.276 Observations 15 Coefficients Intercept 5.86 X Variable 1 0.37 X Variable 2 0.85 SUMMARY OUTPUT - 1st Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.150 Observations 15 Coefficients Intercept 5.66 X Variable 1 1.10 -Referring to Table 16-11,using the second-order model,the forecast of mean attendance for month 16 is ________.

TABLE 16-14 A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters,using quarterly data on number of contracts during the 3-year period from 2010 to 2012.The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2010 Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise -Referring to Table 16-14,in testing the coefficient of X in the regression equation (0.117)the results were a t-statistic of 9.08 and an associated p-value of 0.0000.Which of the following is the best interpretation of this result?

TABLE 16-10 Business closures in Laramie,Wyoming from 2007 to 2012 were: Microsoft Excel was used to fit both first-order and second-order autoregressive models,resulting in the following partial outputs: SUMMARY OUTPUT - 2nd Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - 1st Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Table 16-10,the value of the MAD for the first-order autoregressive model is ________.

True or False: The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

The method of moving averages is used

Microsoft Excel was used to obtain the following quadratic trend equation: Sales = 100 - 10X + 15X². The data used was from 2001 through 2010 coded 0 to 9.The forecast for 2011 is ________.

TABLE 16-13 Given below is the monthly time-series data for U.S.retail sales of building materials over a specific year. The results of the linear trend,quadratic trend,exponential trend,first-order autoregressive,second-order autoregressive and third-order autoregressive model are presented below in which the coded month for the 1^st month is 0: Linear trend model: Quadratic trend model: Exponential trend model: First-order autoregressive: Second-order autoregressive: Third-order autoregressive: Below is the residual plot of the various models: -Referring to Table 16-13,what is the exponentially smoothed forecast for the 13^th month using a smoothing coefficient of W = 0.5 if the exponentially smooth value for the 10^th and 11^th month are 9,746.3672 and 9,480.1836,respectively?

TABLE 16-5 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60,72,96,84,36,and 48. -Referring to Table 16-5,the number of arrivals will be smoothed with a 3-term moving average.There will be a total of ________ smoothed values.

TABLE 16-13 Given below is the monthly time-series data for U.S.retail sales of building materials over a specific year. The results of the linear trend,quadratic trend,exponential trend,first-order autoregressive,second-order autoregressive and third-order autoregressive model are presented below in which the coded month for the 1^st month is 0: Linear trend model: Quadratic trend model: Exponential trend model: First-order autoregressive: Second-order autoregressive: Third-order autoregressive: Below is the residual plot of the various models: -True or False: Referring to Table 16-13,you can reject the null hypothesis for testing the appropriateness of the second-order autoregressive model at the 5% level of significance.

TABLE 16-10 Business closures in Laramie,Wyoming from 2007 to 2012 were: Microsoft Excel was used to fit both first-order and second-order autoregressive models,resulting in the following partial outputs: SUMMARY OUTPUT - 2nd Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - 1st Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Table 16-10,the residuals for the second-order autoregressive model are ________,________,________,and ________.

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. -Referring to Table 16-3,if a three-month moving average is used to smooth this series,what would be the last calculated value?

TABLE 16-13 Given below is the monthly time-series data for U.S.retail sales of building materials over a specific year. The results of the linear trend,quadratic trend,exponential trend,first-order autoregressive,second-order autoregressive and third-order autoregressive model are presented below in which the coded month for the 1^st month is 0: Linear trend model: Quadratic trend model: Exponential trend model: First-order autoregressive: Second-order autoregressive: Third-order autoregressive: Below is the residual plot of the various models: -True or False: Referring to Table 16-13,you can conclude that the second-order autoregressive model is appropriate at the 5% level of significance.

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales.The value of E₂,the smoothed value for 2006 is ________.

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,a centered 5-year moving average is to be constructed for the wine sales.The number of moving averages that will be calculated is ________.

TABLE 16-2 The monthly advertising expenditures of a department store chain (in $1,000,000s)were collected over the last decade.The last 14 months of this time series follows: -True or False: Referring to Table 16-2,advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.

TABLE 16-7 The executive vice-president of a drug manufacturing firm believes that the demand for the firm's most popular drug has been evidencing an exponential trend since 1999.She uses Microsoft Excel to obtain the partial output below.The dependent variable is the log base 10 of the demand for the drug,while the independent variable is years,where 1999 is coded as 0,2000 is coded as 1,etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.996 R Square 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefficients Intercept 1.44 Coded Year 0.068 -Referring to Table 16-7,the fitted trend value for 1999 is ________.

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. -Referring to Table 16-3,suppose the last two smoothed values are 81 and 96 (Note: they are not).What would you forecast as the value of the time series for July?

TABLE 16-14 A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters,using quarterly data on number of contracts during the 3-year period from 2010 to 2012.The following is the resulting regression equation: ln = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2010 Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise -Referring to Table 16-14 ,the best interpretation of the constant 3.37 in the regression equation is