Question

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

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

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