Please note all the data in this assignment is provided in an Excel file attached in the Assignment tab.

1. (20 points)

Consider the quarterly electricity production for years 1-4:

Year	1	2	3	4
Q1	99	120	139	160
Q2	88	108	127	148
Q3	93	111	131	150
Q4	111	130	152	170

1. Estimate the trend using a centered moving average.
2. Using an additive decomposition, calculate the seasonal component.
3. Explain how you handled the end points.

1. (20 points)

The data in the table below represent the monthly sales of a product for years 1 through 5.

Year	1	2	3	4	5
January	742	741	896	951	1030
February	697	700	793	861	1032
March	776	774	885	938	1126
April	898	932	1055	1109	1285
May	1030	1099	1204	1274	1468
June	1107	1223	1326	1422	1637
July	1165	1290	1303	1486	1611
August	1216	1349	1436	1555	1608
September	1208	1341	1473	1604	1528
October	1131	1296	1453	1600	1420
November	971	1066	1170	1403	1119
December	783	901	1023	1209	1013

1. Plot the time series of sales. Can you identify seasonal fluctuations and/or a trend?
2. Use a multiplicative decomposition to calculate the trend-cycle and monthly seasonal indices.
3. Do the results support the graphical interpretation from part (1)?

1. (30 points)

The following data reflect sales of product A for the period January 2011 through April 2012:

2011	2012
Jan	19	Jan	82
Feb	15	Feb	17
Mar	39	Mar	26
Apr	102	Apr	29
May	90
Jun	29
Jul	90
Aug	46
Sep	30
Oct	66
Nov	80
Dec	89

Management wants to use both moving averages and exponential smoothing as methods for forecasting sales. Answer the following questions:

1. What will the forecast be for May 2012 using a 3-, 5-, 7-, 9-, and 11- month moving average?
2. What will the forecast be for May 2012 for exponential smoothing with values of 0.1, 0.3, 0.5, 0.7, and 0.9?
3. Assuming that the past pattern will continue into the future, what k and values should management select in order to minimize the errors?

1. (30 points)

The following shows the daily sales for paperback and hardcover books.

Day	Paperbacks	Hardcovers	Day	Paperbacks	Hardcovers
1	199	139	16	243	240
2	172	128	17	225	189
3	111	172	18	167	222
4	209	139	19	237	158
5	161	191	20	202	178
6	119	168	21	186	217
7	195	170	22	176	261
8	195	145	23	232	238
9	131	184	24	195	240
10	183	135	25	190	214
11	143	218	26	182	200
12	141	198	27	222	201
13	168	230	28	217	283
14	201	222	29	188	220
15	155	206	30	247	259

The goal is to forecast the next four days' sales for paperback and hardcover books.

a. Use single exponential smoothing and compute the measures of forecast accuracy over the test periods 11-30. Hint: Try different alpha values and save the error measures for each in your Excel file. Then you can pick the best.

b. Repeat using the method of linear exponential smoothing (Holt's method). Hint: Use different alpha and beta values and pick the best. For simplicity, keep alpha at .3 but try different betas.

c. Compare the error statistics and discuss the merits of the two forecasting methods for these data sets.

d. Compare the forecasts for the two methods and discuss their relative merits.