Question

Consider a monthly return data on 20-year Treasury Bonds from 2006–2010.

Year	Month	Return	Year	Month	Return
2006	Jan	5.39	2008	Jul	4.94
2006	Feb	4.83	2008	Aug	3.90
2006	Mar	5.41	2008	Sep	4.72
2006	Apr	4.64	2008	Oct	4.58
2006	May	4.05	2008	Nov	4.83
2006	Jun	3.41	2008	Dec	4.17
2006	Jul	3.92	2009	Jan	4.68
2006	Aug	3.46	2009	Feb	4.35
2006	Sep	5.06	2009	Mar	4.10
2006	Oct	5.44	2009	Apr	4.98
2006	Nov	4.96	2009	May	5.22
2006	Dec	4.17	2009	Jun	4.79
2007	Jan	3.48	2009	Jul	5.00
2007	Feb	4.70	2009	Aug	3.58
2007	Mar	4.38	2009	Sep	4.34
2007	Apr	3.82	2009	Oct	3.15
2007	May	4.19	2009	Nov	5.48
2007	Jun	4.35	2009	Dec	4.28
2007	Jul	3.83	2010	Jan	4.35
2007	Aug	5.42	2010	Feb	3.24
2007	Sep	3.29	2010	Mar	3.27
2007	Oct	4.00	2010	Apr	4.72
2007	Nov	3.42	2010	May	5.00
2007	Dec	3.24	2010	Jun	4.82
2008	Jan	5.21	2010	Jul	3.59
2008	Feb	4.84	2010	Aug	4.52
2008	Mar	4.59	2010	Sep	4.44
2008	Apr	3.82	2010	Oct	4.59
2008	May	3.61	2010	Nov	4.62
2008	Jun	4.34	2010	Dec	3.74

Estimate a linear trend model with seasonal dummy variables to make forecasts for the first three months of 2011. (Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Year	Month	y-forecast
2011	Jan
2011	Feb
2011	Mar

Answer 1

Centered Moving Average and Deseasonalization
				Centered
				Moving	Ratio to	Seasonal	Return
t	Year	Month	Return	Average	CMA	Indexes	Deseasonalized
1	1	1	5.39			1.022	5.272
2	1	2	4.83			0.985	4.904
3	1	3	5.41			0.939	5.760
4	1	4	4.64			0.998	4.652
5	1	5	4.05			1.040	3.894
6	1	6	3.41			1.060	3.216
7	1	7	3.92	4.482	0.875	1.008	3.890
8	1	8	3.46	4.397	0.787	0.944	3.665
9	1	9	5.06	4.349	1.164	1.006	5.029
10	1	10	5.44	4.272	1.274	0.999	5.444
11	1	11	4.96	4.243	1.169	1.084	4.577
12	1	12	4.17	4.288	0.972	0.915	4.559
13	2	1	3.48	4.324	0.805	1.022	3.404
14	2	2	4.70	4.402	1.068	0.985	4.772
15	2	3	4.38	4.410	0.993	0.939	4.663
16	2	4	3.82	4.276	0.893	0.998	3.829
17	2	5	4.19	4.152	1.009	1.040	4.029
18	2	6	4.35	4.049	1.074	1.060	4.102
19	2	7	3.83	4.082	0.938	1.008	3.801
20	2	8	5.42	4.160	1.303	0.944	5.741
21	2	9	3.29	4.175	0.788	1.006	3.270
22	2	10	4.00	4.183	0.956	0.999	4.003
23	2	11	3.42	4.159	0.822	1.084	3.156
24	2	12	3.24	4.135	0.784	0.915	3.542
25	3	1	5.21	4.180	1.246	1.022	5.096
26	3	2	4.84	4.163	1.163	0.985	4.914
27	3	3	4.59	4.160	1.103	0.939	4.887
28	3	4	3.82	4.243	0.900	0.998	3.829
29	3	5	3.61	4.326	0.834	1.040	3.471
30	3	6	4.34	4.424	0.981	1.060	4.093
31	3	7	4.94	4.440	1.113	1.008	4.903
32	3	8	3.90	4.398	0.887	0.944	4.131
33	3	9	4.72	4.357	1.083	1.006	4.691
34	3	10	4.58	4.385	1.044	0.999	4.583
35	3	11	4.83	4.500	1.073	1.084	4.457
36	3	12	4.17	4.586	0.909	0.915	4.559
37	4	1	4.68	4.608	1.016	1.022	4.578
38	4	2	4.35	4.597	0.946	0.985	4.417
39	4	3	4.10	4.568	0.898	0.939	4.365
40	4	4	4.98	4.492	1.109	0.998	4.992
41	4	5	5.22	4.460	1.171	1.040	5.019
42	4	6	4.79	4.491	1.067	1.060	4.517
43	4	7	5.00	4.482	1.116	1.008	4.962
44	4	8	3.58	4.422	0.810	0.944	3.792
45	4	9	4.34	4.341	1.000	1.006	4.314
46	4	10	3.15	4.296	0.733	0.999	3.152
47	4	11	5.48	4.276	1.282	1.084	5.057
48	4	12	4.28	4.268	1.003	0.915	4.679
49	5	1	4.35	4.210	1.033	1.022	4.255
50	5	2	3.24	4.191	0.773	0.985	3.290
51	5	3	3.27	4.234	0.772	0.939	3.481
52	5	4	4.72	4.298	1.098	0.998	4.732
53	5	5	5.00	4.323	1.157	1.040	4.807
54	5	6	4.82	4.264	1.130	1.060	4.546
55	5	7	3.59			1.008	3.563
56	5	8	4.52			0.944	4.788
57	5	9	4.44			1.006	4.413
58	5	10	4.59			0.999	4.593
59	5	11	4.62			1.084	4.263
60	5	12	3.74			0.915	4.089

The deseasonalized trend equation is y = 4.4331 - 0.0025x
Forecasts for 2011:
Month	Predicted y	Index	Forecast
Jan	4.2806	1.022	4.38
Feb	4.2781	0.985	4.21
Mar	4.2756	0.939	4.02