Exam 16: Time-Series Forecasting

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 17 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 second- order autoregressive model?

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 X (0.012)in the regression equation is:

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 2014 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,the best model based on the residual plots is the linear-trend model.

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 second value?

A model that can be used to make predictions about long-term future values of a time series is

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 .

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 first month using a smoothing coefficient of W = 0.5?

A least squares linear trend line is just a simple regression line with the years recoded.

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 second 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 p-value of the t test statistic for testing the appropriateness of the second-order autoregressive model?

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 2013?

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 1994 is .

When a time series appears to be increasing at an increasing rate,such that percentage difference from value to value is constant,the appropriate model to fit is the

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 first quarter of 2016?

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 quadratic- trend model?

SCENARIO 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Scenario 16-1,does there appear to be a relationship between year and the number of cases of wine sold?

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 smoothed with a 5-term moving average.The last smoothed value will be .

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 forecast for profits in 2019 is .