Exam 16: Time-Series Forecasting and Index Numbers

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, use the Holt-Winters method of fitting wine sales to compute the smoothed level and trend with a smoothing constant of 0.8 for both level and trend.

Which of the following terms describes the overall long-term tendency of a time series?

Which of the following is not an advantage of exponential smoothing?

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 0.8 for both level and trend will be used to smooth the wine sales. The smoothed values of the level and trend for 1992 are ____ and ____, respectively.

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 forecast the number of arrivals. The forecast for the seventh Monday 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 16-7, 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 sixth Monday are ______ and ____, respectively.

TABLE 16-11 Business closures in Laramie, Wyoming from 1989 to 1994 were: 1993 10 1994 11 1995 13 1996 19 1997 24 1998 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT-2nd Order Model Coefficients Intercept -5.77 XVariable 1 0.80 XVariable 2 1.14 $\text {SUMMARY OUTPUT-1st Order}$ $\text {Model}$ Coefficients Intercept -4.16 $\underline{\text {XVariable 1 \quad 1.59}}$ -Referring to Table 16-11, the values of the MAD for the two models indicate that the first-order model should be used for forecasting.

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, plot both the wine sales series and the series of Holt-Winters forecast for 1999 to 2002 using a smoothing constant of 0.8 for both level and trend.

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 number of arrivals will be exponentially smoothed with a smoothing constant of 0.25. The smoothed value for the second Monday will be_____ .

TABLE 16-11 $\text { Businessclosures in Laramie, Wyomingfrom } 1989 \text { to } 1994 \text { were: }$ 1993 10 1994 11 1995 13 1996 19 1997 24 1998 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: \text {SUMMARY OUTPUT- 2 ^ { \text {nd } } Order Model} Coefficients Intercept -5.77 XVariable 1 0.80 XVariable 2 1.14 . \text {SUMMARY OUTPUT- 1 ^ { \text {st } } Order Model} Coefficients Intercept -4.16 X Variable 1 1.59 -Referring to Table 16-14, what are the simple price indexes for electricity, natural gas and fuel oil, respectively, in 1994 using 1992 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 0.2 will be used to smooth the wine sales. The value of E₂, the smoothed value for 1992 is______

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

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, suppose the last two smoothed values are 81 and 96 (Note: they are not). What would you forecast as the value of the time series for July?

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 number of arrivals will be smoothed with a 3-term moving average. There will be a total of _____ smoothed values.

TABLE 16-11 Business closures in Laramie, Wyoming from 1989 to 1994 were: 1993 10 1994 11 1995 13 1996 19 1997 24 1998 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: SUMMARY OUTPUT - 2nd Order Model Coefficients Intercept -5.77 XVariable 1 0.80 XVariable 2 1.14 SUMMARY OUTPUT - 1st Order Model Coefficients Intercept -4.16 XVariable 1 1.59 -Referring to Table 16-11, the residuals for the first-order autoregressive model are_____ ,____ _____,____ , and____ .

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 are the simple price indexes for wheat, corn, soybeans and milk, respectively, in 1998 using 2000 as the base year?

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 is the unweighted aggregate price index for the group of three energy items in 1994 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. Wheat Corn Soybeans Milk Year ( \/ Bushel) ( \/ Bushel) ( \/ Bushel) ( \/ 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 1999 that consisted of 60 bushels of wheat, 40 bushels of corn, 35 bushels of soybeans and 70 hundredweight of milk in 1999 using 1996 as the base year?

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, the estimated quarterly compound growth rate in revenues is around

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 third quarter of 2003 using the model, which of the following sets of values should be used in the regression equation?