Diebold Li (2006) AR process

Hi there,

I have a question about the paper by Diebold and Li (2006). They estimated a time-series of three factors subsequently they want to forecast these parameters to forecast the yield curve. I have exactly the same estimated factors, however, when I want to forecast the factors I get different results. They say they model the factor B[t+h] = c + y*B[t] by a simple regression. However, when you perform this regression on simply the previous B, you will only get an estimate of for y and the constant c is always zero right?

Here is the paper

http://www.ssc.upenn.edu/~fdiebold/papers/paper49/Diebold-Li.pdf

Kind regards,

Michael

Answer 1

[the cyclist]

Why would c be zero? Wouldn't the autoregression of B be something like

B = [1 1 2 3 5 8 13 21 34]';
regressCoeffs = regress(B(2:end)',[ones(8,1) B(1:end-1)']);

c = regressCoeffs(1);
y = regressCoeffs(2);

where I have obviously just put in some nonsense data.

[Michael]

Well on page 15 they say they simply perform a regression of B[t+h] = c + y*B[t] so I interpreted it first as, in a 1 periode ahead estimation, to use mldivide on the last observation and the one to last observation, that way no coefficient for the constant is estimated. I also tried to estimate and forecast in Eviews but this also did not give me the right results. But I will try this.

[the cyclist]

You need to estimate not just the relationship of the last observation to the next-to-last, but rather all observations (except the first one) to the one just prior. So, you are doing the estimate of the coefficients c and y that best fit

B(2) = c + y*B(1)
B(3) = c + y*B(2)
B(4) = c + y*B(3)

etc.

Or maybe I misunderstand.

[Michael]

I had tried that aswell, but that also gave me not the right outputs. I also found a mistake in my code which caused some deviance and now I have fixed that I almost have the correct output. I need to multiply the coefficients with the last datapoints and multiply that by estimated factor loadings to get estimates of my independent variable. Then I compare the deviance from the true values of the independent values and I get slightly different results. But I think I can live with that. Thank you for your input.