Question

In: Statistics and Probability

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
⋮ ⋮
Dec-10 4.48


Source: Federal Reserve Bank of Dallas.

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 yˆty^t
2011 Jan
2011 Feb
2011 Mar

DATA:

Index Month Year Return
1 Jan 2006 3.13
2 Feb 2006 4.15
3 Mar 2006 3.18
4 Apr 2006 4.94
5 May 2006 4.34
6 Jun 2006 4.19
7 Jul 2006 5.12
8 Aug 2006 5.26
9 Sep 2006 3.81
10 Oct 2006 3.1
11 Nov 2006 3.87
12 Dec 2006 4.89
13 Jan 2007 3.94
14 Feb 2007 3.42
15 Mar 2007 4.13
16 Apr 2007 3.54
17 May 2007 4.58
18 Jun 2007 4.19
19 Jul 2007 4.62
20 Aug 2007 3.89
21 Sep 2007 3.62
22 Oct 2007 3.92
23 Nov 2007 4.46
24 Dec 2007 3.23
25 Jan 2008 4.78
26 Feb 2008 4.71
27 Mar 2008 5.05
28 Apr 2008 3.46
29 May 2008 3.15
30 Jun 2008 4.82
31 Jul 2008 3.87
32 Aug 2008 3.78
33 Sep 2008 3.22
34 Oct 2008 5.39
35 Nov 2008 4.78
36 Dec 2008 5.5
37 Jan 2009 4.8
38 Feb 2009 5.2
39 Mar 2009 3.82
40 Apr 2009 4.52
41 May 2009 3.53
42 Jun 2009 4.66
43 Jul 2009 5.46
44 Aug 2009 3.49
45 Sep 2009 3.75
46 Oct 2009 4.84
47 Nov 2009 4.83
48 Dec 2009 4.35
49 Jan 2010 4.63
50 Feb 2010 5.32
51 Mar 2010 4.75
52 Apr 2010 3.28
53 May 2010 4.8
54 Jun 2010 3.21
55 Jul 2010 4.4
56 Aug 2010 3.31
57 Sep 2010 4.81
58 Oct 2010 5.4
59 Nov 2010 3.54
60 Dec 2010 4.48

Solutions

Expert Solution

for linear trend seasonal dummies for seasonal variation
Index Month Year Return(yt) period(t) x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
1 Jan 2006 3.13 1 1 0 0 0 0 0 0 0 0 0 0
2 Feb 2006 4.15 2 0 1 0 0 0 0 0 0 0 0 0
3 Mar 2006 3.18 3 0 0 1 0 0 0 0 0 0 0 0
4 Apr 2006 4.94 4 0 0 0 1 0 0 0 0 0 0 0
5 May 2006 4.34 5 0 0 0 0 1 0 0 0 0 0 0
6 Jun 2006 4.19 6 0 0 0 0 0 1 0 0 0 0 0
7 Jul 2006 5.12 7 0 0 0 0 0 0 1 0 0 0 0
8 Aug 2006 5.26 8 0 0 0 0 0 0 0 1 0 0 0
9 Sep 2006 3.81 9 0 0 0 0 0 0 0 0 1 0 0
10 Oct 2006 3.1 10 0 0 0 0 0 0 0 0 0 1 0
11 Nov 2006 3.87 11 0 0 0 0 0 0 0 0 0 0 1
12 Dec 2006 4.89 12 0 0 0 0 0 0 0 0 0 0 0
13 Jan 2007 3.94 13 1 0 0 0 0 0 0 0 0 0 0
14 Feb 2007 3.42 14 0 1 0 0 0 0 0 0 0 0 0
15 Mar 2007 4.13 15 0 0 1 0 0 0 0 0 0 0 0
16 Apr 2007 3.54 16 0 0 0 1 0 0 0 0 0 0 0
17 May 2007 4.58 17 0 0 0 0 1 0 0 0 0 0 0
18 Jun 2007 4.19 18 0 0 0 0 0 1 0 0 0 0 0
19 Jul 2007 4.62 19 0 0 0 0 0 0 1 0 0 0 0
20 Aug 2007 3.89 20 0 0 0 0 0 0 0 1 0 0 0
21 Sep 2007 3.62 21 0 0 0 0 0 0 0 0 1 0 0
22 Oct 2007 3.92 22 0 0 0 0 0 0 0 0 0 1 0
23 Nov 2007 4.46 23 0 0 0 0 0 0 0 0 0 0 1
24 Dec 2007 3.23 24 0 0 0 0 0 0 0 0 0 0 0
25 Jan 2008 4.78 25 1 0 0 0 0 0 0 0 0 0 0
26 Feb 2008 4.71 26 0 1 0 0 0 0 0 0 0 0 0
27 Mar 2008 5.05 27 0 0 1 0 0 0 0 0 0 0 0
28 Apr 2008 3.46 28 0 0 0 1 0 0 0 0 0 0 0
29 May 2008 3.15 29 0 0 0 0 1 0 0 0 0 0 0
30 Jun 2008 4.82 30 0 0 0 0 0 1 0 0 0 0 0
31 Jul 2008 3.87 31 0 0 0 0 0 0 1 0 0 0 0
32 Aug 2008 3.78 32 0 0 0 0 0 0 0 1 0 0 0
33 Sep 2008 3.22 33 0 0 0 0 0 0 0 0 1 0 0
34 Oct 2008 5.39 34 0 0 0 0 0 0 0 0 0 1 0
35 Nov 2008 4.78 35 0 0 0 0 0 0 0 0 0 0 1
36 Dec 2008 5.5 36 0 0 0 0 0 0 0 0 0 0 0
37 Jan 2009 4.8 37 1 0 0 0 0 0 0 0 0 0 0
38 Feb 2009 5.2 38 0 1 0 0 0 0 0 0 0 0 0
39 Mar 2009 3.82 39 0 0 1 0 0 0 0 0 0 0 0
40 Apr 2009 4.52 40 0 0 0 1 0 0 0 0 0 0 0
41 May 2009 3.53 41 0 0 0 0 1 0 0 0 0 0 0
42 Jun 2009 4.66 42 0 0 0 0 0 1 0 0 0 0 0
43 Jul 2009 5.46 43 0 0 0 0 0 0 1 0 0 0 0
44 Aug 2009 3.49 44 0 0 0 0 0 0 0 1 0 0 0
45 Sep 2009 3.75 45 0 0 0 0 0 0 0 0 1 0 0
46 Oct 2009 4.84 46 0 0 0 0 0 0 0 0 0 1 0
47 Nov 2009 4.83 47 0 0 0 0 0 0 0 0 0 0 1
48 Dec 2009 4.35 48 0 0 0 0 0 0 0 0 0 0 0
49 Jan 2010 4.63 49 1 0 0 0 0 0 0 0 0 0 0
50 Feb 2010 5.32 50 0 1 0 0 0 0 0 0 0 0 0
51 Mar 2010 4.75 51 0 0 1 0 0 0 0 0 0 0 0
52 Apr 2010 3.28 52 0 0 0 1 0 0 0 0 0 0 0
53 May 2010 4.8 53 0 0 0 0 1 0 0 0 0 0 0
54 Jun 2010 3.21 54 0 0 0 0 0 1 0 0 0 0 0
55 Jul 2010 4.4 55 0 0 0 0 0 0 1 0 0 0 0
56 Aug 2010 3.31 56 0 0 0 0 0 0 0 1 0 0 0
57 Sep 2010 4.81 57 0 0 0 0 0 0 0 0 1 0 0
58 Oct 2010 5.4 58 0 0 0 0 0 0 0 0 0 1 0
59 Nov 2010 3.54 59 0 0 0 0 0 0 0 0 0 0 1
60 Dec 2010 4.48 60 0 0 0 0 0 0 0 0 0 0 0

The regression output for above data taking return as dependent variable(y) and taking period(t) and seasonal dummies as independent variables is given below

Coefficients Standard Error t Stat P-value
Intercept 4.24975 0.383441215 11.08319 1.05E-14
period(t) 0.006673611 0.005562379 1.199776 0.236239
x1 -0.160590278 0.466477698 -0.34426 0.732185
x2 0.136736111 0.465780744 0.293563 0.770384
x3 -0.2439375 0.465149266 -0.52443 0.602445
x4 -0.488611111 0.464583533 -1.05172 0.298306
x5 -0.363284722 0.464083783 -0.7828 0.437671
x6 -0.235958333 0.463650232 -0.50891 0.613193
x7 0.237368056 0.463283063 0.512361 0.610798
x8 -0.517305556 0.462982436 -1.11733 0.269531
x9 -0.627979167 0.46274848 -1.35706 0.181243
x10 0.053347222 0.462581296 0.115325 0.908679
x11 -0.187326389 0.462480956 -0.40505 0.687281

The estimated equation is

Return(y)=4.24975 + 0.00667*period(t) - 0.16059*x1 + 0.13674*x2 -0.24394*x3 -0.48861*x4 - 0.363285*x5 - 0.235958*x6 + 0.237368*x7 - 0.51731*x8 - 0.6279792*x9 + 0.053347*x10 - 0.1873264*x11

The forecasts for first three months of 2011 is as below:

Year Month period(t) x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 Forecasted value from estimated equation(yt)
2011 Jan 61 1 0 0 0 0 0 0 0 0 0 0 4.50
2011 Feb 62 0 1 0 0 0 0 0 0 0 0 0 4.80
2011 Mar 63 0 0 1 0 0 0 0 0 0 0 0 4.43

orchestra answered 3 years ago
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