The Regression Output - Assignment Example

Question 3 Use the data set short bills.wf1. Limit the sample so that it begins in 2002. Regress the three-month treasury bill rate (tb3ms) on the lagged three-month rate and the twice lagged 6-month rate (tb6ms(-2)). Do the coefficients make much sense? (Okay, explain why they don’t.) Test, at the 1% level, for first-order serial correlation using the Breusch-Godfrey test. Now run the regression correcting for serial correlation by including AR(1) in the regression. Do the coefficients make sense now?

Correct for second-order serial correlation (add AR(1) and AR(2)). How about the coefficients now? The regression output looks like Dependent Variable: TB3MS Method: Least Squares Date: 09/17/12 Time: 15:24 Sample: 2002M01 2010M01 Included observations: 97 Variable Coefficient Std. Error t-Statistic Prob. C 0.063194 0.040434 1.562912 0.1214 TB3MS(-1) 1.346506 0.090650 14.85396 0.0000 TB6MS(-2) -0.357690 0.092599 -3.862769 0.0002 R-squared 0.985022 Mean dependent var 2.193814 Adjusted R-squared 0.984703 S.D.

dependent var 1.628331 S.E. of regression 0.201392 Akaike info criterion -0.336687 Sum squared resid 3.812524 Schwarz criterion -0.257057 Log likelihood 19.32931 Hannan-Quinn criteria. -0.304488 F-statistic 3090.922 Durbin-Watson stat 1.666622 Prob(F-statistic) 0.000000 Do the coefficients make much sense?From the above illustrations, the coefficients are sensible. For instance, an increase in six months rate can lead to a future reduction in three months rate, any coefficient bigger than 1 at intervals of three months rate may bring about a significant discharge.

Testing at the 1% level, for first-order serial correlation using the Breusch-Godfrey test we get the: If we test for one lag, it is discarded as shown by the test below. Breusch-Godfrey Serial Correlation LM Test: F-statistic 5.033116 Prob. F(1,93) 0.0272 Obs*R-squared 4.980075 Prob. Chi-Square(1) 0.0256 If we run the regression correcting for serial correlation by including AR (1) in the regression, the coefficients make sense and we get a dependent variable as indicated below. TB3MS Method: Least Squares Date: 09/17/12 Time: 15:28 Sample: 2002M01 2010M01 Included observations: 97 Convergence achieved after 5 iterations Variable Coefficient Std.

Error t-Statistic Prob. C 0.008697 0.090545 0.096051 0.9237 TB3MS(-1) 0.779682 0.169038 4.612475 0.0000 TB6MS(-2) 0.196326 0.157707 1.244879 0.2163 AR(1) 0.607484 0.134082 4.530678 0.0000 R-squared 0.986450 Mean dependent var 2.193814 Adjusted R-squared 0.986013 S.D. dependent var 1.628331 S.E. of regression 0.192581 Akaike info criterion -0.416241 Sum squared resid 3.449118 Schwarz criterion -0.310068 Log likelihood 24.18770 Hannan-Quinn critter. -0.373310 F-statistic 2256.760 Durbin-Watson stat 1.

978718 Prob(F-statistic) 0.000000 Inverted AR Roots .61 From the above illustration the coefficients make sense however if we Correct for second-order serial correlation (add AR(1) and AR(2)), the coefficient is more sensible from the approximations. We can say that they go hand in hand with the projections or the expectations.