Exam 16: Time-Series Forecasting

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 3-year moving average is to be constructed for the wine sales.The moving average for 2004 is ________.

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.

The annual multiplicative time-series model does not possess ________ component.

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 first month is 0: -Referring to Table 16-13,if a five-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 first month is 0: -Referring to Table 16-13,you can reject the null hypothesis for testing the appropriateness of the third-order autoregressive model at the 5% level of significance.

After estimating a trend model for annual time-series data,you obtain the following residual plot against time. The problem with your model is that

TABLE 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 4-year period from 2005 to 2009.The following is the resulting regression equation: log₁₀ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 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 2005. 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 16-12,the best interpretation of the coefficient of Q₃ (0.098)in the regression equation 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 2008 to 2010.The following is the resulting regression equation: ln Ŷ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Ŷ 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. -Referring to Table 16-14,using the regression equation,which of the following values is the best forecast for the number of contracts in the second quarter of 2012?

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 2008 to 2010.The following is the resulting regression equation: ln Ŷ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Ŷ 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. -Referring to Table 16-14,to obtain a forecast for the fourth quarter of 2011 using the model,which of the following sets of values should be used in the regression equation?

TABLE 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 4-year period from 2005 to 2009.The following is the resulting regression equation: log₁₀ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 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 2005. 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 16-12,using the regression equation,what is the forecast for the revenues in the fourth quarter of 2011?

The effect of an unpredictable,rare event will be contained in the ________ component.

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 moving average for 2005 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 -Referring to Table 16-11,using the second-order model,the forecast of mean attendance for month 16 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 first month is 0: -Referring to Table 16-13,the best model based on the residual plots is the linear-trend model.

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 exponentially smoothed with a smoothing constant of 0.25.The smoothed value for the second Monday will be ________.

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: -Referring to Table 16-2,advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.

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 first month is 0: -Referring to Table 16-13,what is your forecast for the 13ᵗʰ month using the third-order autoregressive model?

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 exponentially smoothed with a smoothing constant of 0.1.The smoothed value for the second Monday will be ________.

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 2008 to 2010.The following is the resulting regression equation: ln Ŷ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Ŷ 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. -Referring to Table 16-14,the best interpretation of the constant 3.37 in the regression equation is

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 ________.