Michael Weidman

Michelle-

These results are entirely consistent with how classification trees work. Simply rescaling each of the inputs by multiplying them with different coefficients should have no effect on the tree.

For exactly why this is, I'd recommend Breiman's book (which is referenced in the doc), but the short answer is that trees sort each predictor's observations and try a candidate split within each of the gaps. The tree will then select the split that gives the "best" splitting criterion (and that's an entirely different discussion). Scaling the predictor only serves to scale this process, but it doesn't fundamentally change the results.

As an example: suppose we have a simple set of obervations where the predictor has been measured at 1, 2, 4, and 10. The tree will try splits at 1.5, 3, and 7. Let's say that the "best" split is at 7.

Now we go ahead and rescale this input-- mulitply it by 100 or some other coefficient. Now, the tree tries splits at 150, 300, and 700, and it will still select the split at 700. Rescaling doesn't change anything.

Now, if we were to cleverly create _new_ predictors out of a well-chosen combination (linear or otherwise) of our existing predictors, then that certainly would change the tree's performance. For instance, make a 6th predictor in your X from Altman's coefficient's times your original X-- then you might get some interesting results.

Philip: On the top of this page we list the required products to run this code. R2010b of MATLAB should be fine as long as you have all of the needed toolboxes as well.

Within this package is a README file that provides step-by-step instructions on how to define the data sources (which is what seems to be going wrong in your error message above), how to get a copy of the MCR, and when you might need to recompile the code. I'm always looking for ways to improve those instructions, so let me know where you find them lacking.

Kostas: You're basically correct. PRBYZERO quotes clean prices; to worry about the partial coupon period, you'd need to use a dirty price convention or (equivalently) calculate the accrued interest. The ACCRFRAC function is useful in this case, as is the (more robust) BONDBYZERO function within Financial Derivatives Toolbox.

You're also correct that our choice of clean or dirty prices doesn't really affect the result as long as we're consistent: if present, the accrued interests from the original bond prices and the simulated bond prices just end up cancelling each other out.

Michelle-

These results are entirely consistent with how classification trees work. Simply rescaling each of the inputs by multiplying them with different coefficients should have no effect on the tree.

For exactly why this is, I'd recommend Breiman's book (which is referenced in the doc), but the short answer is that trees sort each predictor's observations and try a candidate split within each of the gaps. The tree will then select the split that gives the "best" splitting criterion (and that's an entirely different discussion). Scaling the predictor only serves to scale this process, but it doesn't fundamentally change the results.

As an example: suppose we have a simple set of obervations where the predictor has been measured at 1, 2, 4, and 10. The tree will try splits at 1.5, 3, and 7. Let's say that the "best" split is at 7.

Now we go ahead and rescale this input-- mulitply it by 100 or some other coefficient. Now, the tree tries splits at 150, 300, and 700, and it will still select the split at 700. Rescaling doesn't change anything.

Now, if we were to cleverly create _new_ predictors out of a well-chosen combination (linear or otherwise) of our existing predictors, then that certainly would change the tree's performance. For instance, make a 6th predictor in your X from Altman's coefficient's times your original X-- then you might get some interesting results.