Exam 16: Time-Series Forecasting

TABLE 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 4-year period from 2005 to 2009.The following is the resulting regression equation: log₁₀ = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where is the estimated number of contracts in a quarter. X is the coded quarterly value with X = 0 in the first quarter of 2005. 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 Table 16-12,the best interpretation of the coefficient of X (0.012)in the regression equation is

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,construct a centered 3-year moving average for the wine sales.

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,exponential smoothing with a weight or smoothing constant of 0.2 will be used to forecast wine sales.The forecast for 2011 is ________.

TABLE 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 - 2ⁿᵈ Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.276 Observations 15 Coefficients Intercept 5.86 X Variable 1 0.37 X Variable 2 0.85 -Referring to Table 16-11,based on the parsimony principle,the second-order model is the better model for making forecasts.

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.

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,construct a centered 5-year moving average for the wine sales.

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

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales.The value of E₄,the smoothed value for 2006 is ________.

TABLE 16-4 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-4,a centered 5-year moving average is to be constructed for the wine sales.The moving average for 2008 is ________.

TABLE 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 Table 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 ________.

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

TABLE 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 first month is 0: -Referring to Table 16-13,if a five-month moving average is used to smooth this series,how many moving averages can you compute?

TABLE 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 first month is 0: -Referring to Table 16-13,what is your forecast for the 13ᵗʰ month using the second-order autoregressive model?

TABLE 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 - 2ⁿᵈ Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.276 Observations 15 Coefficients Intercept 5.86 X Variable 1 0.37 X Variable 2 0.85 -Referring to Table 16-11,using the second-order model,the forecast of mean attendance for month 17 is ________.

A second-order autoregressive model for average mortgage rate is: Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂. If the average mortgage rate in 2010 was 7.0,and in 2009 was 6.4,the forecast for 2011 is ________.

TABLE 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 first month is 0: -Referring to Table 16-13,you can conclude that the second-order autoregressive model is appropriate at the 5% level of significance.

TABLE 16-10 -Referring to Table 16-10,the fitted values for the second-order autoregressive model are ________,________,________,and ________.

TABLE 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 Table 16-5,the number of arrivals will be smoothed with a 3-term moving average.The last smoothed value will be ________.

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

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