Exam 16: Time-Series Forecasting and Index Numbers

TABLE 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 Table 16-3, if a three-term moving average is used to smooth this series, what would be the second calculated term?

TABLE 16-13 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 1998 to 2002. The following is the resulting regression equation: log₁₀Y^{^} = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^{^} is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 1998. 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 16-13, using the regression equation, what is the forecast for the revenues in the fourth quarter of 2004?

The consumer price index is a Paasche price index.

Which of the following terms describes the up and down movements of a time series that vary both in length and intensity?

TABLE 16-7 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 16-7, the Holt-Winters method for forecasting with smoothing constant of 0.9 for both level and trend will be used to smooth the number of arrivals. The smoothed values of the level and trend for the second Monday are _____ and____ , respectively.

TABLE 16-13 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 1998 to 2002. The following is the resulting regression equation: log₁₀Y^{^} = 6.102 + 0.012 X - 0.129 Q₁ - 0.054 Q₂ + 0.098 Q₃ where Y^{^} is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 1998. 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 16-13, to obtain a forecast for the first quarter of 2002 using the model, which of the following sets of values should be used in the regression equation?

The Paasche price index is a form of unweighted aggregate price index.

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

TABLE 16-15 Given below are the prices of a basket of four food items from 1996 to 2000. Year Wheat ( \/ Bushel) Corn ( \/ Bushel) Soybeans ( \/ Bushel) Milk ( \/ hundredweight) 1996 4.25 3.71 7.41 15.03 1997 3.43 27 7.55 13.63 1998 2.63 23 6.05 15.18 1999 2.11 1.97 4.68 14.72 2000 2.16 1.9 4.81 12.32 -Referring to Table 16-15, what is the Laspeyres price index for the basket of four food items in 1998 that consisted of 50 bushels of wheat, 30 bushels of corn, 40 bushels of soybeans and 80 hundredweight of milk in 1996 using 1996 as the base year?

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, exponential smoothing with a weight or smoothing constant of 0.4 will be used to forecast wine sales. The forecast for 1999 is ______ .

The more expensive commodities are overly influential in an unweighted aggregate price index.

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, the Holt-Winters method for forecasting with smoothing constant of 0.2 for both level and trend will be used to forecast the wine sales. The forecast for 1999 is______ .

TABLE 16-9 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 1985. 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 1985 is coded as 0, 1986 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.996 RSquare 0.992 Adjusted R Square 0.991 Standard Error 0.02831 Observations 12 Coefficients Intercept 1.44 Coded Year 0.068 -Referring to Table 16-9, the fitted trend value for 1985 is ______.

Given a data set with 15 yearly observations, a 3-year moving average will have fewer observations than a 5-year moving average.

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

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. January 36 February 45 March 81 April 90 May 108 June 144 -Referring to Table 16-3, if a three-term moving average is used to smooth this series, what would be the last calculated term?

TABLE 16-6 $\text { The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. }$ 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, use the Holt-Winters method of fitting wine sales to compute the smoothed level and trend with a smoothing constant of 0.2 for both level and trend.

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: Month Expenditures (\ ) 1 1.4 2 1.8 3 1.6 4 1.5 5 1.8 6 1.7 7 1.9 8 2.2 9 1.9 10 1.9 11 2.1 12 2.4 13 2.8 14 3.1 -Referring to Table 16-2, advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.

TABLE 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 Table 16-5, the best interpretation of the coefficient of Q₃ (0.617) in the regression equation is

TABLE 16-8 The president of a chain of department stores believes that her stores' total sales have been showing a linear trend since 1980. 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 1980 is coded as 0, 1981 is coded as 1, etc. $\text {SUMMARY OUTPUT}$ 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 16-8, the estimate of the amount by which sales (in millions of dollars) is increasing each year is______ .