Exam 16: Time-Series Forecasting

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is the value of the t test statistic for testing the significance of the quadratic term in the quadratic-trend model?

SCENARIO 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. -Referring to Scenario 16-6,the fitted trend value (in millions of dollars)for 1998 is .

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Scenario 16-3,if this series is smoothed using exponential smoothing with a smoothing constant of 1/3,what would be the first value?

SCENARIO 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 2009 to 2013.The following is the resulting regression equation: log₁₀ Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^ˆ 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. Time-Series Forecasting 16-31 -Referring to Scenario 16-12,in testing the significance of the coefficient of X in the regression equation (0.012)which has a p-value of 0.0000.Which of the following is the best interpretation of this result?

SCENARIO 16-10 Business closures in a city in the western U.S.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: -Referring to Scenario 16-10,the residuals for the first-order autoregressive model are _____,_____,_____,_____,and _____ .

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is the p-value for the t test statistic for testing the significance of the quadratic term in the quadratic-trend model?

If the percentage differences between consecutive values are constant,which of the following models may be the most appropriate?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is the p-value of the t test statistic for testing the appropriateness of the third-order autoregressive model?

To assess the adequacy of a forecasting model,one measure that is often used is

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,if a five-month moving average is used to smooth this series,what would be the first calculated value?

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

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

SCENARIO 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 Scenario 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 .

SCENARIO 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. -Referring to Scenario 16-11,using the second-order model,the forecast of mean attendance for month 16 is .

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Scenario 16-4,a centered 3-year moving average is to be constructed for the wine sales.The result of this process will lead to a total of _____ moving averages.

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Scenario 16-4,a centered 5-year moving average is to be constructed for the wine sales.The number of moving averages that will be calculated is .

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is your forecast for the 13^th month using the third-order autoregressive model?

With a 15 year time duration and available time series data,how many five year moving average forecasts can be made?

SCENARIO 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 2009 to 2013.The following is the resulting regression equation: log₁₀ Y^ˆ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^ˆ 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. Time-Series Forecasting 16-31 -Referring to Scenario 16-12,to obtain the fitted value for the first quarter of 2013 using the model,which of the following sets of values should be used in the regression equation?

SCENARIO 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: Third-order autoregressive:: Below is the residual plot of the various models: -Referring to Scenario 16-13,what is the exponentially smoothed forecast for the 13^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?