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. Month Retail Sales 1 6,594 2 6,610 3 8,174 4 9,513 5 10,595 6 10,415 7 9,949 8 9,810 9 9,637 10 9,732 11 9,214 12 9,201 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 1st month is 0: $\text { Linear trend model: }$ Coefficients Standard Error t Stat P-value Intercept 7950.7564 617.6342 12.8729 0.0000 Coded Month 212.6503 95.1145 2.2357 0.0494 $\text { Quadratic trend model: }$ $\text { Exponential trend model: }$ Coefficients Standard Error t Stat P-value Intercept 3.8912 0.0315 123.3674 0.0000 Coded Month 0.0116 0.0049 2.3957 0.0376 $\text { First-order autoregressive: }$ Coefficients Standard Error t Stat P-value Intercept 3132.0951 1287.2899 2.4331 0.0378 YLag1 0.6823 0.1398 4.8812 0.0009 -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 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 -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?

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 16-15-A You are the CEO of a diary company. The total milk production (in gallons) from your company over the past 30 years are presented below and also contained in the Excel file SCENARIO 16- 15-A.XLSX. Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Milk 150201 172719 171357 157121 155727 152974 153443 158548 162614 164210 Prod 159127 153866 165992 177843 167477 163821 161700 170348 174105 185103 184670 173385 159695 173641 165706 171164 168706 150684 179314 163802 You want to predict your company's future total milk production using the linear trend, quadratic trend, exponential trend, first-order autoregressive, second-order autoregressive and third-order autoregressive model. -Referring to Scenario 16-15-A, what is the p-value of the t test statistic for testing the appropriateness of the third-order autoregressive model?

SCENARIO 16-10 Business closures in a city in the western U.S. from 2007 to 2012 were: 2007 10 2008 11 2009 13 2010 19 2011 24 2012 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT - Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Scenario 16-10, the value of the MAD for the second-order autoregressive model is ________.

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. Year Cases of Wine 2005 270 2006 356 2007 398 2008 456 2009 358 2010 500 2011 410 2012 376 -Referring to Scenario 16-4, exponentially smooth the wine sales with a weight or smoothing constant of 0.2.

SCENARIO 16-10 Business closures in a city in the western U.S. from 2007 to 2012 were: 2007 10 2008 11 2009 13 2010 19 2011 24 2012 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT - Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Scenario 16-10, the value of the MAD for the first-order autoregressive 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, exponentially smooth the number of arrivals using a smoothing constant of 0.1.

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

Based on the following scatter plot, which of the time-series components is not present in this quarterly time series?

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. Year Cases of Wine 2005 270 2006 356 2007 398 2008 456 2009 358 2010 500 2011 410 2012 376 -Referring to Scenario 16-4, construct a centered 5-year moving average for the wine sales.

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

SCENARIO 16-10 Business closures in a city in the western U.S. from 2007 to 2012 were: 2007 10 2008 11 2009 13 2010 19 2011 24 2012 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT - Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Scenario 16-10, the values of the MAD for the two models indicate that the first-order model should be used for forecasting.

SCENARIO 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. Year Cases of Wine 2005 270 2006 356 2007 398 2008 456 2009 358 2010 500 2011 410 2012 376 -Referring to Scenario 16-4, exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales. The value of E2, the smoothed value for 2006 is __________.

SCENARIO 16-13 Given below is the monthly time series data for U.S. retail sales of building materials over a specific year. Month Retail Sales 1 6,594 2 6,610 3 8,174 4 9,513 5 10,595 6 10,415 7 9,949 8 9,810 9 9,637 10 9,732 11 9,214 12 9,201 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 1st month is 0: $\text { Linear trend model: }$ Coefficients Standard Error t Stat P-value Intercept 7950.7564 617.6342 12.8729 0.0000 Coded Month 212.6503 95.1145 2.2357 0.0494 $\text { Quadratic trend model: }$ $\text { Exponential trend model: }$ Coefficients Standard Error t Stat P-value Intercept 3.8912 0.0315 123.3674 0.0000 Coded Month 0.0116 0.0049 2.3957 0.0376 $\text { First-order autoregressive: }$ Coefficients Standard Error t Stat P-value Intercept 3132.0951 1287.2899 2.4331 0.0378 YLag1 0.6823 0.1398 4.8812 0.0009 -Referring to Scenario 16-13, construct a scatter plot (i.e., a time-series plot) with month on the horizontal X-axis.

SCENARIO 16-10 Business closures in a city in the western U.S. from 2007 to 2012 were: 2007 10 2008 11 2009 13 2010 19 2011 24 2012 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT - Order Model Coefficients Intercept -5.77 X Variable 1 0.80 X Variable 2 1.14 SUMMARY OUTPUT - Order Model Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Scenario 16-10, the residuals for the second-order autoregressive model are ________, ________, ________, and ________.

SCENARIO 16-15-B You are the CEO of a diary company. The total milk production (in gallons) from your company over the past 30 years are presented below and also contained in the Excel file SCENARIO 16- 15-B.XLSX. Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Milk 150201 193718 212520 214553 237507 248069 241824 234627 252049 252029 Prod 263449 260689 247900 260059 268197 249477 246216 265236 256364 241705 245932 243529 241551 247697 248454 241974 235823 243517 238490 248606 You want to predict your company's future total milk production using the linear trend, quadratic trend, exponential trend, first-order autoregressive, second-order autoregressive and third-order autoregressive model. -Referring to Scenario 16-15-B, you can conclude that the second-order autoregressive model is appropriate at the 5% level of significance.

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 __________.

SCENARIO 16-15-B You are the CEO of a diary company. The total milk production (in gallons) from your company over the past 30 years are presented below and also contained in the Excel file SCENARIO 16- 15-B.XLSX. Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Milk 150201 193718 212520 214553 237507 248069 241824 234627 252049 252029 Prod 263449 260689 247900 260059 268197 249477 246216 265236 256364 241705 245932 243529 241551 247697 248454 241974 235823 243517 238490 248606 You want to predict your company's future total milk production using the linear trend, quadratic trend, exponential trend, first-order autoregressive, second-order autoregressive and third-order autoregressive model. -Referring to Scenario 16-15-B, you can conclude that the third-order autoregressive model is appropriate at the 5% level of significance.

SCENARIO 16-15-B You are the CEO of a diary company. The total milk production (in gallons) from your company over the past 30 years are presented below and also contained in the Excel file SCENARIO 16- 15-B.XLSX. Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Milk 150201 193718 212520 214553 237507 248069 241824 234627 252049 252029 Prod 263449 260689 247900 260059 268197 249477 246216 265236 256364 241705 245932 243529 241551 247697 248454 241974 235823 243517 238490 248606 You want to predict your company's future total milk production using the linear trend, quadratic trend, exponential trend, first-order autoregressive, second-order autoregressive and third-order autoregressive model. -Referring to Scenario 16-15-B, what is the exponentially smoothed value for 1987 using a smoothing coefficient of W = 0.25?