Question

Year	Month	Return	Year	Month	Return
2006	Jan	3.95	2008	Jul	3.29
2006	Feb	3.77	2008	Aug	4.62
2006	Mar	5.29	2008	Sep	4.81
2006	Apr	3.77	2008	Oct	5.16
2006	May	4.47	2008	Nov	3.69
2006	Jun	5.2	2008	Dec	5.15
2006	Jul	3.9	2009	Jan	5.29
2006	Aug	4.33	2009	Feb	3.19
2006	Sep	4.41	2009	Mar	3.89
2006	Oct	5.14	2009	Apr	4.48
2006	Nov	3.24	2009	May	5.27
2006	Dec	4.13	2009	Jun	3.93
2007	Jan	3.81	2009	Jul	4.67
2007	Feb	3.14	2009	Aug	5.23
2007	Mar	3.41	2009	Sep	5.06
2007	Apr	3.11	2009	Oct	5.39
2007	May	4.99	2009	Nov	4.41
2007	Jun	3.87	2009	Dec	3.91
2007	Jul	4.77	2010	Jan	3.44
2007	Aug	4.34	2010	Feb	4.77
2007	Sep	4.36	2010	Mar	3.62
2007	Oct	5.35	2010	Apr	4.9
2007	Nov	5.06	2010	May	3.68
2007	Dec	3.73	2010	Jun	4.81
2008	Jan	5.29	2010	Jul	4.36
2008	Feb	5.01	2010	Aug	3.84
2008	Mar	3.62	2010	Sep	4.82
2008	Apr	4.41	2010	Oct	3.56
2008	May	3.23	2010	Nov	4.8
2008	Jun	4.83	2010	Dec	4.62

Consider a portion of monthly return data (In %) on 20-year Treasury Bonds from 2006–2010 listed above.

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

Year	Month	y^t
2011	Jan
2011	Feb
2011	Mar

Answer 1

Given the monthly data, first define some relevant variables for the regression. We define seasonal monthly variables along with time variables. Here, we display some few data of the table

Year	Month	Return	M1	M2	M3	M4	M5	M6	M7	M8	M9	M10	M11
2006	Jan	3.95	1	0	0	0	0	0	0	0	0	0	0
2006	Feb	3.77	0	1	0	0	0	0	0	0	0	0	0
2006	Mar	5.29	0	0	1	0	0	0	0	0	0	0	0
2006	Apr	3.77	0	0	0	1	0	0	0	0	0	0	0
2006	May	4.47	0	0	0	0	1	0	0	0	0	0	0
2006	Jun	5.2	0	0	0	0	0	1	0	0	0	0	0

A linear trend model with seasonal dummy variables is

Using excel, we solve this data.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.398215
R Square	0.158576
Adjusted R Square	-0.05626
Standard Error	0.707313
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	12	4.431408	0.369284	0.738138	0.707499
Residual	47	23.51369	0.500291
Total	59	27.9451
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.2075	0.370918	11.34348	4.7E-15	3.461309	4.953691
t	0.002792	0.005381	0.518829	0.606315	-0.00803	0.013616
M1	0.078708	0.451242	0.174426	0.86228	-0.82907	0.986491
M2	-0.30408	0.450568	-0.67489	0.503053	-1.21051	0.602343
M3	-0.31688	0.449957	-0.70423	0.484762	-1.22207	0.588322
M4	-0.15167	0.44941	-0.33748	0.737258	-1.05576	0.75243
M5	0.039542	0.448927	0.08808	0.930187	-0.86358	0.942666
M6	0.23675	0.448507	0.527862	0.600078	-0.66553	1.13903
M7	-0.09604	0.448152	-0.21431	0.831236	-0.99761	0.805524
M8	0.175167	0.447861	0.391118	0.697477	-0.72581	1.076147
M9	0.392375	0.447635	0.876551	0.385189	-0.50815	1.2929
M10	0.617583	0.447473	1.380157	0.174068	-0.28262	1.517783
M11	-0.06521	0.447376	-0.14576	0.884736	-0.96521	0.834796

Putting the estimated value of regression coefficient, we get the estimated linear trend model.

Based on the estimated model, we compute the forecast for next three months.

Year	Month	y
2011	Jan	4.4565
2011	Feb	4.0765
2011	Mar	4.0665