Exam 16: Time-Series Forecasting

TABLE 16-9 Given below are Excel outputs for various estimated autoregressive models for a company's real operating revenues (in billions of dollars)from 1985 to 2008.From the data,you also know that the real operating revenues for 2006,2007,and 2008 are 11.7909,11.7757 and 11.5537,respectively. First-Order Autoregressive Model: Second-Order Autoregressive Model: Third-Order Autoregressive Model: -Referring to Table 16-9 and using a 5% level of significance,what is the appropriate autoregressive model for the company's real operating revenue?

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 coefficient of X (0.117)in the regression equation 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,you can conclude that the quadratic term in the quadratic-trend model is statistically significant at the 5% level of significance.

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 conclude that the third-order autoregressive model is appropriate at the 5% level of significance.

The method of least squares is used on time-series data for

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 third 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,to obtain a forecast for the first quarter of 2011 using the model,which of the following sets of values should be used in the regression equation?

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 first-order model,the forecast of mean attendance for month 17 is ________.

TABLE 16-6 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1990.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 1990 is coded as 0,1991 is coded as 1,etc. -Referring to Table 16-6,the fitted trend value (in millions of dollars)for 1990 is ________.

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 1995.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 1995 is coded as 0,1996 is coded as 1,etc. -Referring to Table 16-7,the forecast for the demand in 2012 is ________.

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

The following is the list of MAD statistics for each of the models you have estimated from time-series data: Based on the MAD criterion,the most appropriate model 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,what is the exponentially smoothed forecast for the 13ᵗʰ month using a smoothing coefficient of W = 0.25 if the exponentially smooth value for the 10ᵗʰ and 11ᵗʰ month are 9,477.7776 and 9,411.8332,respectively?

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 the value of the t test statistic for testing the appropriateness of the second-order autoregressive model?

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,set up a scatter diagram (i.e.,a time-series plot)with year on the horizontal X-axis.

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 forecast wine sales.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 first month is 0: -Referring to Table 16-13,what is the exponentially smoothed value for the second month using a smoothing coefficient of W = 0.25?

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,construct a scatter plot (i.e.,a time-series plot)with month on the horizontal X-axis.

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 1995.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 1995 is coded as 0,1996 is coded as 1,etc. -Referring to Table 16-7,the forecast for the demand in 2009 is ________.

TABLE 16-10 -Referring to Table 16-10,the values of the MAD for the two models indicate that the first-order model should be used for forecasting.