Ec 178 Old Exams

# Ec 178 Old Exams - Ec 178 RECENT EXAMS Midterm Winter 2006...

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Ec 178 RECENT EXAMS Midterm -- Winter 2006 Problem 1 You have data y t , t = 1…6, in Table A. A. Compute simple moving average (m = 2), EWMA (α = 0.4), CMA (m = 3), and 1 st differences. B. Use SES (α = 0.4) to compute forecast ŷ 7 . Problem 2 Lake level data y t , t = 1…13, are shown in Table B. The series was smoothed and forecasted by Holt’s Two-Parameter DES with α = 0.6 and β = 0.2. A. Fill in the unshaded blank cells in the table, including ex ante fore- casts ŷ 14 and ŷ 15 . B. Explain how you could compute an approximately 95% prediction interval forecast for any future time period n+h. Problem 3 Fig. 1 shows a firm called “Victim.” They introduced a new product and sales grew well until an outside party allegedly injured the company, giving rise to a “business interruption” lawsuit. Your consulting team is to forecast what sales would have been if the interruption had NOT occurred. You have the following data: y t = sales, t = 1…37 lny t = Ln(y t ) Table A -- Filters t y t (2) t (0.4) t CMA(3) t (1-L)y t 1 107 2 126 3 132 4 106 5 118 6 105 7 < ---- Forecast Table B – Lake Level t y t S t D t ŷ t-1,1 1 31 2 28 28.000 -3.000 3 28 26.800 -2.640 4 27 25.864 -2.299 5 26 25.026 -2.007 6 25 24.208 -1.769 23.019 7 16 18.575 -2.542 22.438 8 18 17.213 -2.306 16.033 9 18 16.763 -1.935 14.908 1 0 12 13.131 -2.274 14.828 1 1 11 1 2 7 7.674 -2.459 8.686 1 3 5 5.086 -2.485 5.215 1 4 < --- Ex ante forecasts 1 5 Fig. 1 -- Victim Sales (\$1000/month) \$0 \$100 \$200 \$300 \$400 \$500 \$600 \$700 \$800 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 y y-fit y-f'cast

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Ec 178 Recent Exams p. 2 d t = interruption dummy variable, d = 0 before the interruption (t = 1…20) and d = 1 after the interruption began (t = 21…37) You ran the following regression in S TATA over period t = 1…37: nl (lny = {b0} + {b1}*d + {b2}/t + {b3}*d/t) The regression results are in Table C. In Fig. 1, fitted values from this regression are shown as “y-fit” and your forecast of sales if no interruption had occurred are “y-f’cast.” A. What is the name of the curve you used to represent Victim’s uninterrupted sales pattern? B. If the interruption had not occurred, your model predicts that Victim sales would eventually reach what level? C. Compute the forecasted (uninterrupted) value of sales for period t = 30. ŷ 30 = __________ Problem 4 A school has three 4-month trimesters each year. Let y t = number of students enrolled/trimester. Table D shows the results of three regressions based on the seasonal dummy variable model: y t = β 1 + β 2 A(2) t + β 3 A(3) t + β 4 t + β 5 t 2 + u t , t = 1 …15. Table D Estimated Coefficient (|t-stats| in parentheses) Regression β 1 β 2 β 3 β 4 β 5 R 2 #1 32.7 (4.40) 5.24 (2.46) -0.335 (2.59) 0.360252 #2 50.6 (13.4) -11.5 (2.15) 0.343 (0.06) 0.346762 #3 36.0 (6.48) -11.7 (3.09) 0.621 (0.16) 5.38 (3.53) -0.345 (3.74) 0.728076 A. Test for seasonality at the α = 5% level of statistical significance. H 0 : _______________ H 1 : _______________ Test statistic = __________ 5% critical value(s) = _________________ { Accept Reject } H 0 and conclude that there { is is not } seasonality in the data. B. Assuming there IS seasonality, compute ex ante forecast for periods t = 16 (1 st trimester) and t = 17 (2 nd trimester).
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Ec 178 Old Exams - Ec 178 RECENT EXAMS Midterm Winter 2006...

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