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 5-year moving average is to be constructed for the wine sales.The moving average for 2007 is ________.

True or False: If a time series does not exhibit a long-term trend,the method of exponential smoothing may be used to obtain short-term predictions about the future.

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,if a five-month moving average is used to smooth this series,what would be the last calculated value?

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 16-13 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,if a five-month moving average is used to smooth this series,what would be the first calculated value?

TABLE 16-6 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1993.She uses Microsoft Excel to obtain the partial output below.The dependent variable is sales (in millions of dollars),while the independent variable is coded years,where 1993 is coded as 0,1994 is coded as 1,etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.604 R Square 0.365 Adjusted R Square 0.316 Standard Error 4.800 Observations 17 Coefficients Intercept 31.2 Coded Year 0.78 -Referring to Table 16-6,the fitted trend value (in millions of dollars)for 1998 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: -True or False: 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.

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 exponential trend equation to predict Y 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.The first smoothed value will be ________.

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 quadratic term in the quadratic-trend model is statistically significant at the 5% level of significance.

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 -True or False: Referring to Table 16-11,based on the parsimony principle,the second-order model is the better model for making forecasts.

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 16-13 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 third-order autoregressive model is appropriate at the 5% level of significance.

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 5-year period from 2008 to 2012.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 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 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 third quarter of 2013?

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 17 is ________.

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-1,does there appear to be a relationship between year and the number of cases of wine sold?

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 5-year period from 2008 to 2012.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 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 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise -Referring to Table 16-12,in testing the significance of the coefficient for Q₁ in the regression equation (-0.129)which has a p-value of 0.492.Which of the following is the best interpretation of this result?

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 value of the t test statistic for testing the significance of the quadratic term in the quadratic-trend model?

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,the best model based on the residual plots is the quadratic-trend regression model.

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 value for the first month using a smoothing coefficient of W = 0.5?