Exam 16: Time-Series Forecasting

TABLE 16-2 The monthly advertising expenditures of a department store chain (in $1,000,000s) were collected over the last decade. The last 14 months of this time series follows: -Referring to Table 16-2, advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.

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, you can conclude that the second-order autoregressive model is appropriate at the 5% level of significance.

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -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

TABLE 16-6 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1990. 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 1990 is coded as 0, 1991 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.604 R Square 0.365 Adjusted R Square 0.316 Standard Error 4.800 Observations 17 Coefficients Intercept 31.2 Coded Year 0.78 -Referring to Table 16-6, the estimate of the amount by which sales (in millions of dollars) is increasing each year is ________.

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, to obtain a fitted value for the fourth quarter of 2006 using the model, which of the following sets of values should be used in the regression equation?

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 16-13 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 third-order autoregressive model?

TABLE 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 1995. 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 1995 is coded as 0, 1996 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.996 R Square 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefficients Intercept 1.44 Coded Year 0.068 -Referring to Table 16-7, the forecast for the demand in 2012 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, the best model based on the residual plots is the exponential-trend regression model.

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 5-term moving average. The first smoothed value will be ________.

TABLE 16-10 Business closures in Laramie, Wyoming from 2005 to 2010 were: -Referring to Table 16-10, the value of the MAD for the first-order autoregressive model is ________.

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. -Referring to Table 16-1, set up a scatter diagram (i.e., a time-series plot) with year on the horizontal X-axis.

TABLE 16-10 Business closures in Laramie, Wyoming from 2005 to 2010 were: -Referring to Table 16-10, the residuals for the second-order autoregressive model are ________, ________, ________, and ________.

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. -Referring to Table 16-11, using the first-order model, the forecast of mean attendance for month 17 is ________.

TABLE 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 2008 to 2010. The following is the resulting regression equation: ln Ŷ = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Ŷ 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. -Referring to Table 16-14, the best interpretation of the constant 3.37 in the regression equation is

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

TABLE 16-9 Given below are Excel outputs for various estimated autoregressive models for a company's real operating revenues (in billions of dollars) from 1985 to 2008. From the data, you also know that the real operating revenues for 2006, 2007, and 2008 are 11.7909, 11.7757 and 11.5537, respectively. First-Order Autoregressive Model: Second-Order Autoregressive Model: Third-Order Autoregressive Model: -Referring to Table 16-9 and using a 5% level of significance, what is the appropriate autoregressive model for the company's real operating revenue?

The MAD is a measure of the mean of the absolute discrepancies between the actual and the fitted values in a given time series.

The manager of a company believed that her company's profits were following an exponential trend. She used Microsoft Excel to obtain a prediction equation for the logarithm (base 10) of profits: log₁₀(Profits) = 2 + 0.3X The data she used were from 2005 through 2010 coded 0 to 5. The forecast for 2011 profits is ________.