Exam 16: Time-Series Forecasting

SCENARIO 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 Scenario 16-5,the number of arrivals will be exponentially smoothed with a smoothing constant of 0.25.The forecast of the number of arrivals on the seventh Monday will be .

SCENARIO 16-10 Business closures in a city in the western U.S.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: -Referring to Scenario 16-10,the value of the MAD for the first-order autoregressive model is .

In selecting a forecasting model,you should perform a residual analysis.

SCENARIO 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 Scenario 16-5,the number of arrivals will be smoothed with a 3-term moving average.The first smoothed value will be .

SCENARIO 16-9 Given below are EXCEL outputs for various estimated autoregressive models for a company's real operating revenues (in billions of dollars)from 1989 to 2012.From the data,you also know that the real operating revenues for 2010,2011,and 2012 are 11.7909,11.7757 and 11.5537,respectively. First-Order Autoregressive Model: Second-Order Autoregressive Model: -Referring to Scenario 16-9,if one decides to use the Third-Order Autoregressive model ,what will the predicted real operating revenue for the company be in 2015?

SCENARIO 16-12 A local store developed a multiplicative time-series model to forecast its revenues in future quarters,using quarterly data on its revenues during the 5-year period from 2009 to 2013.The following is the resulting regression equation: log₁₀ Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^ˆ is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2008. 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. Time-Series Forecasting 16-31 -Referring to Scenario 16-12,to obtain a fitted value for the fourth quarter of 2010 using the model,which of the following sets of values should be used in the regression equation?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is your forecast for the 13^th month using the first-order autoregressive model?

Which of the following terms describes the up and down movements of a time series that vary both in length and intensity?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,you can conclude that the quadratic term in the quadratic-trend model is statistically significant at the 5% level of significance.

SCENARIO 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 Scenario 16-5,the number of arrivals will be exponentially smoothed with a smoothing constant of 0.25.The smoothed value for the second Monday will be .

SCENARIO 16-10 Business closures in a city in the western U.S.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: -Referring to Scenario 16-10,the residuals for the second-order autoregressive model are _____,_____,_____,and _____.

The overall upward or downward pattern of the data in an annual time series will be contained in the _____ component.

SCENARIO 16-9 Given below are EXCEL outputs for various estimated autoregressive models for a company's real operating revenues (in billions of dollars)from 1989 to 2012.From the data,you also know that the real operating revenues for 2010,2011,and 2012 are 11.7909,11.7757 and 11.5537,respectively. First-Order Autoregressive Model: Second-Order Autoregressive Model: -Referring to Scenario 16-9 and using a 5% level of significance,what is the appropriate autoregressive model for the company's real operating revenue?

Microsoft Excel was used to obtain the following quadratic trend equation: Sales = 100 - 10X + 15X². The data used was from 2004 through 2013 coded 0 to 9.The forecast for 2014 is .

SCENARIO 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 2011 to 2013.The following is the resulting regression equation: ln Y^ˆ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Y^ˆ is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2011. 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 Scenario 16-14 ,the best interpretation of the constant 3.37 in the regression equation is:

SCENARIO 16-12 A local store developed a multiplicative time-series model to forecast its revenues in future quarters,using quarterly data on its revenues during the 5-year period from 2009 to 2013.The following is the resulting regression equation: log₁₀ Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^ˆ is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2008. 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. Time-Series Forecasting 16-31 -Referring to Scenario 16-12,to obtain a forecast for the third quarter of 2014 using the model,which of the following sets of values should be used in the regression equation?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is the exponentially smoothed value for the 12^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?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,the best autoregressive model using the 5% level of significance is

SCENARIO 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 Scenario 16-5,the number of arrivals will be smoothed with a 3-term moving average.The last smoothed value will be .

SCENARIO 16-12 A local store developed a multiplicative time-series model to forecast its revenues in future quarters,using quarterly data on its revenues during the 5-year period from 2009 to 2013.The following is the resulting regression equation: log₁₀ Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^ˆ is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2008. 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. Time-Series Forecasting 16-31 -Referring to Scenario 16-12,the best interpretation of the coefficient of Q₃ (0.098)in the regression equation is: