In: Statistics and Probability
Consider a portion of monthly return data (In %) on 20-year Treasury Bonds from 2006–2010.
Date | Return |
Jan-06 | 5.12 |
Feb-06 | 4.14 |
⋮ | ⋮ |
Dec-10 | 5.47 |
Date | Return |
ene-06 | 5.12 |
feb-06 | 4.14 |
mar-06 | 4.68 |
abr-06 | 5.25 |
may-06 | 5.35 |
jun-06 | 3.64 |
jul-06 | 4.68 |
ago-06 | 4.65 |
sep-06 | 3.55 |
oct-06 | 3.55 |
nov-06 | 4.3 |
dic-06 | 3.54 |
ene-07 | 3.8 |
feb-07 | 3.98 |
mar-07 | 4.33 |
abr-07 | 4.69 |
may-07 | 5.37 |
jun-07 | 4.74 |
jul-07 | 5.17 |
ago-07 | 3.22 |
sep-07 | 4.97 |
oct-07 | 5.13 |
nov-07 | 3.35 |
dic-07 | 3.86 |
ene-08 | 4.06 |
feb-08 | 4.64 |
mar-08 | 4.83 |
abr-08 | 5.06 |
may-08 | 5.46 |
jun-08 | 5.22 |
jul-08 | 4.29 |
ago-08 | 4.79 |
sep-08 | 5.45 |
oct-08 | 4.85 |
nov-08 | 3.54 |
dic-08 | 4.9 |
ene-09 | 3.6 |
feb-09 | 4.48 |
mar-09 | 3.51 |
abr-09 | 3.72 |
may-09 | 4.24 |
jun-09 | 4.36 |
jul-09 | 5.17 |
ago-09 | 3.25 |
sep-09 | 4.74 |
oct-09 | 5.03 |
nov-09 | 5.44 |
dic-09 | 3.55 |
ene-10 | 4.21 |
feb-10 | 5.27 |
mar-10 | 5.07 |
abr-10 | 3.7 |
may-10 | 4.65 |
jun-10 | 4.21 |
jul-10 | 4.38 |
ago-10 | 4.29 |
sep-10 | 4.93 |
oct-10 | 4.48 |
nov-10 | 3.32 |
dic-10 | 5.47 |
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 |
Soln
We will be calculating the seasonality of each Month (ie Jan – Dec) and use it to predict Revenue for 2011 (Jan – Dec)
Steps:
Table 1
Table 2
Season |
2006 |
2007 |
2008 |
2009 |
2010 |
Mean |
X ADJ Factor |
SEASONAL INDEX |
Cumulative Indx |
2011 Return (Predicted) |
Regression Equation: Y = a + bX |
|||||
Jan |
97.2% |
97.5% |
87.2% |
92.1% |
93.5% |
1.00 |
0.93 |
61 |
4.18 |
n |
60 |
|||||
Feb |
98.1% |
103.2% |
112.7% |
116.0% |
107.5% |
1.00 |
1.07 |
62 |
4.80 |
b |
0.0005 |
|||||
Mar |
97.0% |
98.5% |
100.2% |
89.8% |
109.8% |
99.0% |
1.00 |
0.99 |
63 |
4.42 |
a |
4.4392 |
||||
Apr |
109.5% |
100.1% |
99.8% |
93.6% |
81.5% |
96.9% |
1.00 |
0.97 |
64 |
4.33 |
||||||
May |
113.1% |
109.9% |
107.6% |
101.8% |
107.6% |
108.0% |
1.00 |
1.08 |
65 |
4.82 |
∑ XY |
8,159 |
||||
Jun |
78.2% |
98.6% |
105.0% |
101.1% |
97.7% |
96.1% |
1.00 |
0.96 |
66 |
4.29 |
∑ X2 |
73,810 |
||||
Jul |
107.5% |
113.0% |
86.9% |
119.7% |
99.2% |
105.2% |
1.00 |
1.05 |
67 |
4.70 |
∑ X |
1,830 |
||||
Aug |
112.9% |
70.4% |
97.9% |
72.8% |
95.6% |
89.9% |
1.00 |
0.90 |
68 |
4.02 |
∑ Y |
267 |
||||
Sep |
87.4% |
113.1% |
114.7% |
103.5% |
112.4% |
106.2% |
1.00 |
1.06 |
69 |
4.75 |
||||||
Oct |
91.6% |
120.8% |
103.8% |
108.1% |
101.8% |
105.2% |
1.00 |
1.05 |
70 |
4.70 |
||||||
Nov |
114.2% |
79.5% |
79.5% |
117.7% |
97.7% |
1.00 |
0.98 |
71 |
4.37 |
|||||||
Dec |
91.9% |
95.6% |
117.3% |
77.4% |
95.6% |
1.00 |
0.95 |
72 |
4.27 |
|||||||
Total |
1200.9% |
|||||||||||||||
Final Predicted Values:
Season |
2011 Return (Predicted) |
Jan |
4.18 |
Feb |
4.80 |
Mar |
4.42 |
Apr |
4.33 |
May |
4.82 |
Jun |
4.29 |
Jul |
4.70 |
Aug |
4.02 |
Sep |
4.75 |
Oct |
4.70 |
Nov |
4.37 |
Dec |
4.27 |
PS: If Images are not visible, Right click on image and select open image in new tab option.