Exam 16: Time-Series Forecasting

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -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 16-12 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

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 16-4 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 0.2 will be used to smooth the wine sales. The value of E₄, the smoothed value for 2006 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, if a three-month moving average is used to smooth this series, what would be the last calculated value?

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, exponentially smooth the wine sales with a weight or smoothing constant of 0.4.

TABLE 16-8 The manager of a marketing consulting firm has been examining his company's yearly profits. He believes that these profits have been showing a quadratic trend since 1990. He uses Microsoft Excel to obtain the partial output below. The dependent variable is profit (in thousands of dollars), while the independent variables are coded years and squared of coded years, where 1990 is coded as 0, 1991 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.998 R Square 0.996 Adjusted R Square 0.996 Standard Error 4.996 Observations 17 Coefficients Intercept 35.5 Coded Year 0.45 Year Squared 1.00 -Referring to Table 16-8, the forecast for profits in 2015 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 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. -The cyclical component of a time series

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -Which of the following terms describes the overall long-term tendency of a time series?

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 third-order autoregressive 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 first month is 0: -Referring to Table 16-13, what is the exponentially smoothed value for the 12ᵗʰ month using a smoothing coefficient of W = 0.5 if the exponentially smooth value for the 10ᵗʰ and 11ᵗʰ month are 9,746.3672 and 9,480.1836, 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 your forecast for the 13ᵗʰ month using the second-order autoregressive model?

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, 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 16-13 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 16-6 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. 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 1995 is ________.

In selecting an appropriate forecasting model, the following approach is suggested.

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. 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 1990 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, exponentially smooth the number of arrivals using a smoothing constant of 0.25.

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, 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?