Exam 16: Time-Series Forecasting

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 16-4 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 forecast wine sales.The forecast for 2013 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 0.25.

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 month is 0: Below is the residual plot of the various models: -Referring to Scenario 16-13, what is your forecast for the 13th month using the quadratic- trend model?

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 month is 0: Below is the residual plot of the various models: -Referring to Scenario 16-13, what is the exponentially smoothed value for the second month using a smoothing coefficient of W = 0.5?

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

A trend is a persistent pattern in annual time-series data that has to be followed for several years.

If the percentage differences between consecutive values are constant, which of the following models may be the most appropriate?

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 0.2 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. 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 month is 0: Below is the residual plot of the various models: -Referring to Scenario 16-13, what is the exponentially smoothed value for the second month using a smoothing coefficient of W = 0.25?

SCENARIO 16-5 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.

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. SUMMARY OUTPUT -Referring to Scenario 16-8, the fitted value for 1999 is __________.

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: where is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2008. is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Scenario 16-12, to obtain the fitted value for the first quarter of 2013 using the model, which of the following sets of values should be used in the regression equation?

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 month is 0: Below is the residual plot of the various models: -Referring to Scenario 16-13, the best model based on the residual plots is the exponential-trend regression model.

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 month is 0: 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 third-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. -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?

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

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. SUMMARY OUTPUT - Order Model SUMMARY OUTPUT - 1 Order Model -Referring to Scenario 16-11, using the first-order model, the forecast of mean attendance for month 17 is __________.

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: where is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2008. is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Scenario 16-12, to obtain a fitted value for the fourth quarter of 2010 using the model, which of the following sets of values should be used in the regression equation?

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. SUMMARY OUTPUT -Referring to Scenario 16-6, the fitted trend value (in millions of dollars)for 1998 is __________.