Question

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

Date	Return
Jan-06	5.39
Feb-06	4.83
Mar-06	5.41
Apr-06	4.64
May-06	4.05
Jun-06	3.41
Jul-06	3.92
Aug-06	3.46
Sep-06	5.06
Oct-06	5.44
Nov-06	4.96
Dec-06	4.17
Jan-07	3.48
Feb-07	4.7
Mar-07	4.38
Apr-07	3.82
May-07	4.19
Jun-07	4.35
Jul-07	3.83
Aug-07	5.42
Sep-07	3.29
Oct-07	4
Nov-07	3.42
Dec-07	3.24
Jan-08	5.21
Feb-08	4.84
Mar-08	4.59
Apr-08	3.82
May-08	3.61
Jun-08	4.34
Jul-08	4.94
Aug-08	3.9
Sep-08	4.72
Oct-08	4.58
Nov-08	4.83
Dec-08	4.17
Jan-09	4.68
Feb-09	4.35
Mar-09	4.1
Apr-09	4.98
May-09	5.22
Jun-09	4.79
Jul-09	5
Aug-09	3.58
Sep-09	4.34
Oct-09	3.15
Nov-09	5.48
Dec-09	4.28
Jan-10	4.35
Feb-10	3.24
Mar-10	3.27
Apr-10	4.72
May-10	5
Jun-10	4.82
Jul-10	3.59
Aug-10	4.52
Sep-10	4.44
Oct-10	4.59
Nov-10	4.62
Dec-10	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 at least 4 decimal places and final answers to 2 decimal places.)

Year

Month

yˆt

2011	Jan
2011	Feb
2011	Mar

Answer 1

Let's breakdown the periods into the corresponding year and months as follows (showing a part below):

Year	Month	Return
2006	1	5.39
2006	2	4.83
2006	3	5.41
2006	4	4.64
2006	5	4.05
2006	6	3.41
2006	7	3.92
2006	8	3.46
2006	9	5.06
2006	10	5.44
2006	11	4.96
2006	12	4.17

...............................................

Now, carrying out regression in Excel with Return as the response variable and Year, Month as predictor variables (go to Data tab -> Data Analysis -> Regression, and choose Return as Y-column and Year, Month as X-columns), we get the following output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.121061158
R Square	0.014655804
Adjusted R Square	-0.019917677
Standard Error	0.656504176
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	2	0.365402512	0.182701256	0.423903055	0.656533573
Residual	57	24.56687082	0.430997734
Total	59	24.93227333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	35.45209091	120.340294	0.294598673	0.769370754	-205.5251913	276.4293731
Year	-0.015416667	0.059930358	-0.257243027	0.797917543	-0.135425138	0.104591805
Month	-0.021706294	0.024551864	-0.884099618	0.380356471	-0.070870554	0.027457966

Hence, the regression model obtained is: Return = 35.452 - 0.0154 * Year - 0.0217 * Month

Using this regression equation, the forecasts for the first 3 months of 2011 are:

Year	Month	Yt
2011	Jan	4.46
2011	Feb	4.44
2011	Mar	4.42