Exam 16: Time-Series Forecasting

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 forecast for sales (in millions of dollars)in 2015 is .

Which of the following is not an advantage of exponential smoothing?

SCENARIO 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 2011 to 2013.The following is the resulting regression equation: ln Y^ˆ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 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 2011. 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 Scenario 16-14,using the regression equation,which of the following values is the best forecast for the number of contracts in the third quarter of 2014?

SCENARIO 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 1994.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 1994 is coded as 0,1995 is coded as 1,etc. -Referring to Scenario 16-8,the fitted value for 1999 is .

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,based on the parsimony principle,the second- order model is the better model for making forecasts.

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 0.1.The smoothed value for the sixth Monday will be .

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,you can reject the null hypothesis for testing the appropriateness of the second-order autoregressive model at the 5% level of significance.

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

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,the best interpretation of the coefficient of Q₂ (-0.054)in the regression equation 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,suppose the last two smoothed values are 81 and 96 (Note: they are not).What would you forecast as the value of the time series for September?

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

The method of least squares may be used to estimate both linear and curvilinear trends.

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,exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales.The value of E₂,the smoothed value for 2006 is .

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 1993 is .

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.

SCENARIO 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. -Referring to Scenario 16-7,the fitted trend value for 1999 is .

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

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 last calculated value?

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 exponential- trend model?

SCENARIO 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 2011 to 2013.The following is the resulting regression equation: ln Y^ˆ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 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 2011. 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 Scenario 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?