Exam 16: Time-Series Forecasting

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 1986 using a smoothing coefficient of W = 0.5?

After estimating a trend model for annual time-series data, you obtain the following residual plot against time, the problem with your model is that:

A second-order autoregressive model for average mortgage rate is: $\text { Rate } \left. \left. _ { i } = - 2.0 + 1.8 \text { (Rate } \right) _ { i - 1 } - 0.5 \text { (Rate } \right) _ { i - 2 } .$ . 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. 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, how many moving averages can you compute?

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, what is your forecast for the $13 ^ { \text {th } }$ month using the quadratic- trend model?

The overall upward or downward pattern of the data in an annual time series will be contained in the ____________ component.

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 -Referring to Scenario 16-14, the best interpretation of the coefficient of $Q _ { 3 }$ (0.617) 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. 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 0.4 will be used to smooth the wine sales. The value of E5, the smoothed value for 2009 is __________.

Given a data set with 15 yearly observations, there are only seven 9-year moving averages.

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, how many values would it have?

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

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 a three-month moving average is used to smooth this series, how many values would it have?

The following is the list of MAD statistics for each of the models you have estimated from time-series data: Model MAD Linear Trend 1.38 Quadratic Trend 1.22 Exponential Trend 1.39 Second-order Autoregressive 0.71 Based on the MAD criterion, the most appropriate model 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, you can conclude that the second-order autoregressive model is appropriate at the 5% level of significance.

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, what is the exponentially smoothed value for the second month using a smoothing coefficient of W = 0.25?

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 forecast for the demand in 2013 is __________.

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 your forecast for 2016 using the quadratic-trend model?

Which of the following methods should not be used for short-term forecasts into the future?

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, what is the exponentially smoothed value for the first month using a smoothing coefficient of W = 0.5?

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 __________.