Question

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

Date	Return
Jan-06	3.13
Feb-06	4.15
Mar-06	3.18
Apr-06	4.94
May-06	4.34
Jun-06	4.19
Jul-06	5.12
Aug-06	5.26
Sep-06	3.81
Oct-06	3.1
Nov-06	3.87
Dec-06	4.89
Jan-07	3.94
Feb-07	3.42
Mar-07	4.13
Apr-07	3.54
May-07	4.58
Jun-07	4.19
Jul-07	4.62
Aug-07	3.89
Sep-07	3.62
Oct-07	3.92
Nov-07	4.46
Dec-07	3.23
Jan-08	4.78
Feb-08	4.71
Mar-08	5.05
Apr-08	3.46
May-08	3.15
Jun-08	4.82
Jul-08	3.87
Aug-08	3.78
Sep-08	3.22
Oct-08	5.39
Nov-08	4.78
Dec-08	5.5
Jan-09	4.8
Feb-09	5.2
Mar-09	3.82
Apr-09	4.52
May-09	3.53
Jun-09	4.66
Jul-09	5.46
Aug-09	3.49
Sep-09	3.75
Oct-09	4.84
Nov-09	4.83
Dec-09	4.35
Jan-10	4.63
Feb-10	5.32
Mar-10	4.75
Apr-10	3.28
May-10	4.8
Jun-10	3.21
Jul-10	4.4
Aug-10	3.31
Sep-10	4.81
Oct-10	5.4
Nov-10	3.54
Dec-10	4.48

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	y^t
2011	January
2011	February
2011	March

Answer 1

Assuming monthly seasonal dummies, since there are 12 months there will be 11 dummy variables to avoid the dummy variable trap.

Like this, for all the years, set the dummy variable values.

Now, using the regression tool in data analysis toolpak of excel: -

The following is obtained.

So, the predicted returns equation is

y = 4.49 - 0.234(January) + 0.07(Feb) -0.304(Mar) +....and so on till november

For January =1 and other months=0

y = 4.49 - 0.234= 4.256

For February =1 and other months=0

y = 4.49 + 0.07 = 4.56

For January =1 and other months=0

y = 4.49 - 0.304= 4.186

So, the prediction for 2011 first quarter is like this: -

Year	Month	y^t (returns)
2011	January	4.256
2011	February	4.56
2011	March	4.186