Cublic Spline

[e1983]

Does anyone know if it is possible to use cubic spline data interpolation in RATS?

[TomDoan]

Does anyone know if it is possible to use cubic spline data interpolation in RATS?

The Durbin and Koopman examples DURKP136.RPF and DURKP172.RPF do cubic splines. Both of those have "knots" at every observation. For fewer knots, you can use the following:

Code: Select all

compute nk = 3           ;* number of spline knots

*** Compute Break Points
declare vector[integer] nks(nk+1)
 compute nks(1) = 1
 do i = 1, nk
  compute frac = (float(i))/(float(nk+1))
  compute nks(i+1) = fix(frac*(float(nlast-nfirst+1)))
 end do i
declare vector[series] splreg(nk+4)
set splreg(1) = 1.
set splreg(2) = (t-nfirst+1)
set splreg(3) = (t-nfirst+1)*(t-nfirst+1)

do ik = 1,nk+1
 set t1 = splreg(2)(t) - nks(ik)
 set splreg(ik+3) = 0.5*t1(t)*t1(t)*t1(t)
 set splreg(ik+3) = splreg(ik+3)*(splreg(2)(t)>nks(ik))
end do ik

*** Detrend series using cubic splines: USER CHOOSES HERE
linreg(noprint) y / yr
# splreg(1) to splreg(nk+4)
linreg(noprint) rl_rs / rlrs
# splreg(1) to splreg(nk+4)
set y = yr
set rl = rlrs + rs

[e1983]

Thanks so much Tom. Do you know of any examples in RATS that uses cubic splines to interpolate a yield curve?

[TomDoan]

This does a cubic spline approximation to the discount function, as described in McCulloch(1971), "Measuring the Term Structure of Interest Rates", Journal of Business, vol 44, pp 19-31.

bondspline.rpf

Program file

(2.64 KiB) Downloaded 91 times

bonds.xls

Data file

(31.5 KiB) Downloaded 85 times

[e1983]

thanks Tom.