Question

# Year Month Return Year Month Return 2006     Jan 3.95 2008     Jul 3.29 2006     Feb 3.77 2008...

 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

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

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