Exam 16: Time-Series Forecasting and Index Numbers

A first-order autoregressive model for stock sales is: Sales_i = 800 + 1.2(Sales)_i-1. If sales in 1998 is 6000, the forecast of sales for 1999 is _______.

The cyclical component of a time series

The Paasche price index has the disadvantage that current consumption quantities are usually hard to obtain.

Given a data set with 15 yearly observations, there are only thirteen 3-year moving averages.

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. -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 1999 is_____

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 X (0.012) 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 16-7, 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 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, in testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.0000. Which of the following is the best interpretation of this result?

MAD is the summation of the residuals divided by the sample size.

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 unweighted aggregate price index for the basket of four food items in 1998 using 1996 as the base year?

TABLE 16-1 The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. Year Cases of Wine 1991 270 1992 356 1993 398 1994 456 1995 438 1996 478 1997 460 1998 480 -Referring to Table 16-1, set up a scatter diagram (i.e., a time-series plot) with year on the horizontal X-axis.

TABLE 16-12 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 second-order model, the forecast of average attendance for month 16 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 1995 using 1992 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 best interpretation of the coefficient of Q₃ (0.098) in the regression equation 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 second-order autoregressive model are______ ,_____ ____,_____ , and_____ .

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 are the simple price indexes for wheat, corn, soybeans and milk, respectively, in 2000 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, using the regression equation, what is the forecast for the revenues in the first quarter of 2005?

A model that can be used to make predictions about long-term future values of a time series is

TABLE 16-10 The manager of a marketing consulting firm has been examining his company's yearly profits. He believes that these profits have been showing a quadratic trend since 1980. He uses Microsoft Excel to obtain the partial output below. The dependent variable is profit (in thousands of dollars), while the independent variables are coded years and squared of coded years, where 1980 is coded as 0, 1981 is coded as 1, etc. SUMMARY OUTPUT Regression Statistics Multiple R 0.998 RSquare 0.996 Adjusted R Square 0.996 Standard Error 4.996 Observations 17 Coefficients Intercept 35.5 Coded Year 0.45 Year Squared 1.00 -Referring to Table 16-10, the forecast for profits in 2000 is_____ .

The method of least squares may be used to estimate both linear and curvilinear trends.