Exam 16: Time-Series Forecasting and Index Numbers

TABLE 16-5 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 1996 to 1998. The following is the resulting regression equation: ln Y^{^} = 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 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 1996. 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 16-5, in testing the coefficient for Q₁ in the regression equation (- 0.083), the results were a t-statistic of - 0.66 and an associated p-value of 0.530. Which of the following is the best interpretation of this result?

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, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?

The Paasche price index reflects more accurately the consumption cost at a point in time because it uses the consumption quantities in the initial year as the base.

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 forecast the number of arrivals. The forecast for the seventh Monday is ____.

TABLE 16-14 Given below are the average prices for three types of energy products in the United States from 1992 to 1995. Year Electricity N atural Gas Fuel Oil 1992 43.205 25.893 0.892 1993 16.959 28.749 0.969 1994 47.202 28.933 1.034 1995 48.874 29.872 0.913 1996 48.693 28.384 0.983 -Referring to Table 16-14, what are the simple price indexes for electricity, natural gas and fuel oil, respectively, in 1993 using 1996 as the base year?

The effect of an unpredictable, rare event will be contained in the component.

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 0.3 for both level and trend will be used to smooth the number of arrivals. The smoothed values of the level and trend for the sixth Monday are _____ and_____ , respectively.

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 unweighted aggregate price index for the basket of four food items in 2000 using 1996 as the base year?

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. SUMMARY OUTPUT Regression Statistics Multiple R 0.604 RSquare 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 forecast for sales (in millions of dollars) in 2005 is ______.

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 this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the first term?

TABLE 16-12 The manager of a health club has recorded average 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 Coetficients Intercept 5.86 XVariable 1 0.37 XVariable 2 0.85 $\text {SUMMARY}$ $\text {OUTPUT - 1st Order}$ $\text {Model Regression}$ Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.150 Observations 15 Coefficients Intercept 5.66 XVariable 1 1.10 -Referring to Table 16-12, using the first-order model, the forecast of average attendance for month 16 is _____.

The Laspeyres price index has the disadvantage that the consumption pattern in the initial period might be quite different from that in the current period and, hence, does not reflect accurately the current consumption cost.

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 smooth the wine sales. The smoothed values of the level and trend for 1998 are _____ and ____, respectively.

TABLE 16-14 Given below are the average prices for three types of energy products in the United States from 1992 to 1995. Year Electricity N atural Gas Fuel Oil 1992 43.205 25.893 0.892 1993 16.959 28.749 0.969 1994 47.202 28.933 1.034 1995 48.874 29.872 0.913 1996 48.693 28.384 0.983 -Referring to Table 16-14, what are the simple price indexes for electricity, natural gas and fuel oil, respectively, in 1996 using 1992 as the base year?

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 Paasche 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 1998 using 1996 as the base year?

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. 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 fitted trend value (in millions of dollars) for 1985 is ____.

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 16-6, a centered 5-year moving average is to be constructed for the wine sales. The number of moving averages that will be calculated is_____ .

Unweighted aggregate price indexes account for differences in the magnitude of prices per unit and differences in the consumption levels of the items in the market basket.

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

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 -A second-order autoregressive model for average mortgage rate is: Rate_i = - 2.0 + 1.8(Rate)_i-1 - 0.5 (Rate)_i-2^. If the average mortgage rate in 1998 was 7.0, and in 1997 was 6.4, the forecast for 2000 is_____ .