[R-SIG-Finance] What does mean MidTau in Nelson-Siegel's model?

[Joshua Ulrich]

On Wed, May 9, 2012 at 1:17 PM, Minerva Mora <mimode_14 at hotmail.com> wrote:
> Hi!
>
> I apologize for my english.
> I'm working with the YieldCurve package in the estimation of the
> Nelson-Siegel parameters. In this model, the arguments are: rate, maturity
> and MidTau.
>
> I don´t have problem with the rate and maturity, but i can´t understand the
> MidTau, because the argument is: MidTau ------> vector which indicates
> medium term maturity to maximize the beta_2 factor
>
> My questions are:
> 1) What does mean medium term maturity int the MidTau? What does is this
> argument for?

MidTau is the maturity at which the Nelson Siegel estimated yield
curve will have the greatest amount of curvature.

> 2) How many datas in the vector are good to obtain a good estimation? If i
> have 77 datas of maturity. I asked this beacuse i sow in my several testing
> that the results of the parameters changes if a put more datas or if i
> remove datas from this vector, but sometimes the results doesn´t change.

I would guess that there are outliers on the dates where changing the
amount of data you use causes changes in the estimated parameters.
Also note that the model is over-specified for certain curves (if the
yield curve is approximately linear, for example), which would cause
the estimates to be very sensitive to changes in data.

> 3)If my maturity datas are since 0.03 months to 323 months, Which is the
> best or the theorical month data to start in the vector of the midTau?
>
This depends on the range of maturities at which the greatest amount
of curvature occurs.  If you look at YieldCurve::Nelson.Siegel, you'll
see this code:

    a1 <- mean(c(MidTau[1], MidTau[2]))
    a2 <- mean(c(MidTau[1], MidTau[3]))
    a3 <- mean(c(MidTau[2], MidTau[3]))
    lambdaValues <- c(MidTau, a1, a2, a3)

The optimization will then try all those lambdaValues and use the one
that provides the best fit.  So you need to look at the data you are
using for estimation and determine an appropriate range for MidTau.
Note that you must provide at least 3 values for MidTau, but you can
use as many values as you would like (more values will also mean
longer optimization times).

Best,
--
Joshua Ulrich  |  FOSS Trading: www.fosstrading.com

R/Finance 2012: Applied Finance with R
www.RinFinance.com