Exam 16: Time-Series Forecasting

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 appropriateness of the second-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 0.25.The smoothed value for the third Monday will be ________.

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,the best interpretation of the coefficient of Q₃ (0.098)in the regression equation is

TABLE 16-10 Business closures in Laramie,Wyoming 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: SUMMARY OUTPUT - 2nd Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - 1st Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Table 16-10,the residuals for the first-order autoregressive model are ________,________,________,________,and ________.

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 12^th month using a smoothing coefficient of W = 0.25 if the exponentially smooth value for the 10^th and 11^th month are 9,477.7776 and 9,411.8332,respectively?

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 sixth 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,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?

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 this series is smoothed using exponential smoothing with a smoothing constant of ,what would be the second value?

In selecting an appropriate forecasting model,the following approaches are suggested:

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 this series is smoothed using exponential smoothing with a smoothing constant of ,what would be the first value?

The fairly regular fluctuations that occur within each year would be contained in the ________ component.

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 16-6 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 1993 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: -Referring to Table 16-13,what is the p-value of the t test statistic for testing the appropriateness of the second-order autoregressive model?

A first-order autoregressive model for stock sales is: Sales_i = 800 + 1.2(Sales)_i-1. If sales in 2012 is 6,000,the forecast of sales for 2013 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 this series is smoothed using exponential smoothing with a smoothing constant of ,how many values would it have?

A second-order autoregressive model for average mortgage rate is: Rate_i = -2.0 + 1.8 (Rate)_i-1 - 0.5 (Rate)_i-2. If the average mortgage rate in 2012 was 7.0,and in 2011 was 6.4,the forecast for 2013 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: -Referring to Table 16-13,what is the exponentially smoothed value for the second month using a smoothing coefficient of W = 0.5?

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 forecast for the demand in 2016 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 2008 is ________.