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 appropriateness of the second-order autoregressive model?

The manager of a company believed that her company's profits were following an exponential trend.She used Microsoft Excel to obtain a prediction equation for the logarithm (base 10)of profits: log₁₀(Profits)= 2 + 0.3X The data she used were from 2007 through 2012 coded 0 to 5.The forecast for 2013 profits 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 moving average for 2009 is .

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,to obtain a forecast for the first quarter of 2014 using the model,which of the following sets of values should be used in the regression equation?

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 fitted values for the first-order autoregressive model are _____,_____,_____,_____,and_____ .

SCENARIO 16-9 Given below are EXCEL outputs for various estimated autoregressive models for a company's real operating revenues (in billions of dollars)from 1989 to 2012.From the data,you also know that the real operating revenues for 2010,2011,and 2012 are 11.7909,11.7757 and 11.5537,respectively. First-Order Autoregressive Model: Second-Order Autoregressive Model: -Referring to Scenario 16-9,if one decides to use the Third-Order Autoregressive model ,what will the predicted real operating revenue for the company be in 2014?

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 2013 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 third value?

The method of moving averages is used

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 2004 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 5-year moving average is to be constructed for the wine sales.The moving average for 2010 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 0.1.Then the forecast for the seventh 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,what is the exponentially smoothed value for the 12^th month using a smoothing coefficient of W = 0.25 if the exponentially smoothed value for the 10^th and 11^th month are 9,477.7776 and 9,411.8332,respectively?

Which of the following statements about moving averages is not true?

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,using the regression equation,what is the forecast for the revenues in the third quarter of 2014?

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,construct a centered 3-year moving average for the wine sales.

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 for Q₁ in the regression equation (- 0.083),the results were a t-statistic of - 0.66 and an associated p-value of 0.530.Which of the following is the best interpretation of this result?

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,using the regression equation,what is the forecast for the revenues in the fourth quarter of 2015?

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,how many values would it have?

When using the exponentially weighted moving average for purposes of forecasting rather than smoothing,