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, the Holt-Winters method for forecasting with smoothing constant of 0.8 for both level and trend will be used to forecast the wine sales. The forecast for 2002 is_____ .

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 16-11, the fitted values for the first-order autoregressive model are_____,_____ ,______ ,______ , and_____ .

The method of least squares is used on time-series data for

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 best interpretation of the coefficient of Q₂ (- 0.054) in the regression equation 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, 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 1998 are _____ and _____, respectively.

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 forecast the wine sales. The forecast for 1999 is_____ .

The annual multiplicative time-series model does not possess_____ component.

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, 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 September?

The base period should be recent so that a price index is not severely affected by change in technology, and consumer attitudes and habits.

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 1997 using 2000 as the base year?

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 this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the second 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, a centered 5-year moving average is to be constructed for the wine sales. The moving average for 1993 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, plot both the number of arrivals series and the series of Holt-Winters forecast for the seventh through twelfth Mondays using a smoothing constant of 0.9 for both level and trend.

The method of moving averages is used

You need to decide whether you should invest in a particular stock. You would like to invest if the price is likely to rise in the long run. You have data on the daily average price of this stock over the past 12 months. Your best action is to

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 Laspeyres price index for the group of three energy items in 1996 for a family that consumed 15 units of electricity, 24 units of natural gas and 200 units of fuel oil in 1992 using 1992 as the base year?

The Laspeyres price index uses the initial consumption quantities as the weights.

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 , the best interpretation of the constant 3.37 in the regression equation 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 1994 using 1996 as the base year?

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, plot both the number of arrivals series and the series of Holt-Winters forecast for the seventh through twelfth Mondays using a smoothing constant of 0.3 for both level and trend.