ROBUSTSTAR.RPF

ROBUSTSTAR.RPF shows test for STAR with outlier adjustments. The adjustment polynomial for downweighting data points in STAR linearity tests is from van Dijk, Franses and Lucas(1999).

This uses the same data set and basic model as in the TARMODELS.RPF example.

Full Program

*
* Weights are 1 below c1 standard errors, 0 above c2 standard errors and
* this polynomial in between.
*
procedure RobustPoly px
type vect *px
*
option real c1 2.576
option real c2 3.291
*
local rect a(6,6)
local vect b(6)
*
do j=1,6
   compute a(1,j)=%if(j<=2,0.0,(j-1)*(j-2)*c1^(j-3))
   compute a(2,j)=%if(j<=2,0.0,(j-1)*(j-2)*c2^(j-3))
   compute a(3,j)=%if(j<=1,0.0,(j-1)*c1^(j-2))
   compute a(4,j)=%if(j<=1,0.0,(j-1)*c2^(j-2))
   compute a(5,j)=c1^(j-1)
   compute a(6,j)=c2^(j-1)
end do j
compute b(1)=0.0,b(2)=0.0,b(3)=1.0,b(4)=0.0,b(5)=c1,b(6)=0.0
compute px=%solve(a,b)
end
*
******************************************************************
*
* This is applied to the lynx data contaminated by outliers
*
cal(a) 1821
open data lynx.dat
data(org=cols) 1821:1 1934:1 lynx
set x = log(lynx)/log(10)
diff(center) x / xc
*
* Pick contaminated points (randomly chosen with 10% probability)
*
seed 532343
set outliers = %ranflip(.1)
set xc = xc + %if(outliers,%ran(2.0),0.0)
*
* Get the weight transition polynomial at the default knots
*
@RobustPoly px
*
* Start with equal weights. Do 10 iterations on weighted least squares
* on the AR model.
*
set weight = 1.0
do iters=1,10
   linreg(weight=weight,noprint) xc
   # constant xc{1 to 11}
   compute sigma=sqrt(%seesq)
   set weight %regstart() %regend() = $
      stdu=abs(%resids)/sigma,%if(stdu<2.576,1.0,%if(stdu>3.291,0.0,%polyvalue(px,stdu)/stdu))
end do iters
*
* Apply the STAR test with the chosen weights to the contaminated data.
* Also apply the equally weighted STAR test.
*
@startest(p=11,d=1,weights=weight,title="Outlier-Adjusted STAR Test") xc
@startest(p=11,d=1) xc

Output

Outlier-Adjusted STAR Test

AR length 11

Delay 1

Test F-stat Signif

Linearity 4.0749113 0.0000

H01 1.7547539 0.0763

H02 5.6810400 0.0000

H03 2.1243022 0.0325

H12 4.2826145 0.0000

Test for STAR in series XC

AR length 11

Delay 1

Test F-stat Signif

Linearity 1.7517076 0.0306

H01 2.5343180 0.0085

H02 2.2361250 0.0218

H03 0.4827883 0.9065

H12 2.6005969 0.0014