Quarter
4	3	2	1	Year
79.8	92.1	88.8	77.4	1986
80.1	92.4	89.1	77.5	1987
178.1	162.4	185.2	74.7	1988
138.7	160.6	158.4	129.1	1989
132.9	151.7	149.8	127.2	1990
123.5	141.3	136.8	103.0	1991
123.7	138.6	136.1	107.3	1992
138.2	156.1	144.4	106.1	1993
141.8	158.5	149.8	111.8	1994
151.8	170.4	158.0	119.1	1995
169.5	189.3	178.2	127.4	1996
181.4	199.2	187.2	151.4	1997
300.7	341.4	317.7	224.9	1998
326.7	370.0	333.4	244.9	1999

Q1: Southdown, Inc., the nations third largest cement producer, is pushing ahead with a waste fuel burning program. The cost for Southdown will total about $37 million. For this reason, it is extremely important for the company to have an accurate forecast of revenues for the first quarter of 2000. The data are presented in the table next page. Solve

1. Refer to part iii. Examine the residual autocorrelations. Are you happy with simple

   exponential smoothing for this example? Explain. (Use a chi-square value of 30 as your

   reference for the LBQ test.)

2. Now apply double exponential smoothing using the optimal ARIMA constants.

3. Examine the residual autocorrelations. Are you happy with double exponential smoothing for this example? Explain. (Use a chi-square value of 30 as your reference for the LBQ test.)

4. Finally, apply winters method using a smoothing constant of 0.4, a trend constant of 0.1, and a seasonality constant of 0.3.

5. Examine the residual autocorrelations. Are you happy with Winters method for this example? Explain. (Use a chi-square value of 30 as your reference for the LBQ test.)

6. Which of the methods applied gives the best fit? Explain.