Assume that we are in December 2009 and try to make forecasts of the five year interest rate at the end of January 2010. For this question, you just need to fill out the blank space provided (if any) for each question - no further materials should be submitted.
1) First, download the interest rate data file (Assignment 2_Winter 2011_interest rate forecasting data.xls) from the Assignment Folder at the course website. The data should go from January 1972 until July 2010. In this file, interest rates are in percentage points. For example, in cell C2, you will see: 3.763708 - this means the 3 month interest rate as of end of January 1972 is 3.763708%. This is just a preparation, you don't have to report anything here.
2) Second, construct the level, slope and curvature factors as follows:
Level = 3 month rate
Slope = 10 year rate - 3 month rate
Curvature = (3 month rate + 10 year rate) - 2 × 2 year rate
Since we are at the end of 2009, remember to limit your construction of these factors up to December 2009. Again, this is just a preparation, you don't have to report anything here.
3) Regress the contemporaneous 5 year rate over the same period (from January 1972 to December 2009) on these three factors to determine how the 5 year rate can be approximated by Level, Slope, and Curvature. Report the regression coefficients and the regression R^{2 }statistics. That is, report a, b, c, and d in the simple linear regression equation below:
5 year rate = a + b × Level + c × Slope + d × Curvature + error
and the R^{2 }statistics of this regression.
To answer this question, fill in the blank spaces below:
5 year rate = ________ + _______ × Level + _______ × Slope + _______ × Curvature
R^{2 }statistic = _______.
4) Use the estimated coefficients from part 3) above, a, b, c, and d, to construct the approximate 5 year interest rate as: a + b × Level + c × Slope + d × Curvature. Plot below this approximate series together with the actual 5 year interest rate series in the data to see how close these two series match up.
5) Regress one month ahead Level factor on the current values of Level, Slope and Curvature factors and report the regression coefficients. That is, report a, b, c, and d in the following regression equation:
Level _{one month down the road }= a + b × Level + c × Slope + d × Curvature+ error
Note that a, b, c, and d here are different from those in parts 3) and 4) above. Given the values of Level, Slope, and Curvature in December 2009, what would be your prediction of the Level factor at the end of January 2010?
To answer this question, fill in the blank spaces below:
Level _{one month down the road }= _______ + _______ × Level + _______ × Slope + _______ × Curvature
Prediction of the Level factor at end of Jan 2010 = _______.
6.) Repeat part 5) above for the Slope factor. To answer this question, fill in the blank spaces below:
Slope _{one month ahead }= _______ + _______ × Level + _______ × Slope + _______ × Curvature
Prediction of the Slope factor at the end of January 2010 = _______.
7) Repeat part 5) above for the Curvature factor. To answer this question, fill in the blank spaces below:
Curvature _{one month down the road }= _______ + _______ × Level + _______ × Slope + _______ × Curvature
Prediction of the Curvature factor at end of January 2010 = _______.
8) Given the prediction of the Level factor obtained from part 5), the prediction of the Slope factor obtained from part 6), and the prediction of the Curvature factor obtained from part 7), what would be your prediction of the 5 year interest rate at the end of January 2010? To answer this question, fill in the blank spaces below:
Prediction of the 5 year interest rate at the end of January 2010 = ______.