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*
* @TsayNLTest(options) x start end
*
* TsayNLTest does the Tsay Ori-F test for neglected non-linearities in an
* autoregression. Optionally, it can do the LST variant (which tests more
* specifically against STAR).
*
* Parameters:
*  x           Series to test
*  start end   Range over which to estimate autoregression.
*
* Options:
*  LAGS=number of lags to use [4]
*  LST/[NOLST] determines whether to use Tsay or LST variant.
*  [PRINT]/NOPRINT
*
* References:
*  Tsay(1996), "Nonlinearity Tests for Time Series", Biometrika, vol 73, 461-466.
*
*  Luukkonen, Saikkonen and Terasvirta(1988), "Testing Linearity against smooth
*  transition autoregressive models", Biometrika vol 75, 491-499.
*
* Revision Schedule:
*  06/2008 Written by Tom Doan, Estima
*
procedure TsayNLTest x start end
type series x
type integer start end
*
option integer lags  4
option switch  print 1
option switch  lst   1
*
local symm[series] m
local vect[series] l
local integer i j
local series u
*
dim m(lags,lags) l(lags)
*
if .not.%defined(x) {
   display "Syntax: @TsayNLTest(options) >>x<< start end"
   return
}
*
* Do the base autoregression
*
linreg(noprint) x start end u
# constant x{1 to lags}
*
* Set up the auxiliary variables. The M variables are for the Tsay Ori-F test. The
* L variables are the additional variables for the STAR test.
*
do i=1,lags
   set l(i) %regstart() %regend() = x{i}**3
   do j=1,i
      set m(i,j) %regstart() %regend() = x{i}*x{j}
   end do j
end do i
*
if lst==0 {
   linreg(noprint) x %regstart() %regend()
   # x{1 to lags} m
   exclude(print=print,title="Tsay Ori-F Test with "+lags+" lags")
   # m
}
else {
   linreg(noprint) x %regstart() %regend()
   # x{1 to lags} m l
   exclude(print=print,title="LST Test for STAR with "+lags+" lags")
   # m l
}
end

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open data "c:\rats\usecon.rat"
calendar(m) 1959
all 1993:2
data(format=rats) / fcm3 ftb3
set g3year = log(fcm3/fcm3{1})
set g3month = log(ftb3/ftb3{1})
set spread  = log(ftb3)-log(fcm3)
set sspread = (spread+spread{1}+spread{2})/3
compute sspread(1959:1)=spread(1959:1)
compute sspread(1959:2)=(spread(1959:1)+spread(1959:2))/2
*
rls(order=sspread{1}) g3year / rr3year
# constant g3year{1 to 7} g3month{1 to 7}
rls(order=sspread{1}) g3month / rr3month
# constant g3year{1 to 7} g3month{1 to 7}
*
linreg rr3year / wr3year
# constant g3year{1 to 7} g3month{1 to 7}
linreg rr3month / wr3month
# constant g3year{1 to 7} g3month{1 to 7}
*
ratio(mcorr=%nreg,degrees=30)
# rr3year rr3month
# wr3year wr3month

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*
* Replication file for Tsay (1998), "Testing and Modeling Multivariate Threshold
* Models", J. of American Statistical Assn, vol. 93, no. 443, 1188-1202.
*
* U.S. Interest Rates example. Data are similar, but not identical to those used
* in the paper.
*
open data usrates.xls
calendar(m) 1959
data(format=xls,org=columns) 1959:1 1993:2 fcm3 ftb3
set g3year  = log(fcm3/fcm3{1})
set g3month = log(ftb3/ftb3{1})
set spread  = log(ftb3)-log(fcm3)
set sspread = (spread+spread{1}+spread{2})/3
compute sspread(1959:1)=spread(1959:1)
compute sspread(1959:2)=(spread(1959:1)+spread(1959:2))/2
*
spgraph(vfields=3,footer="Figure 3. Time Plots of Growth Series of U.S. Monthly Interest Rates")
graph(vlabel="3-month")
# g3month
graph(vlabel="3-year")
# g3year
graph(vlabel="Spread")
# sspread
spgraph(done)
*
@VARLagSelect(lags=12,crit=aic)
# g3year g3month
*
compute p =7
compute k =2
*
do d=1,7
   dofor m0 = 50 100
      set thresh = sspread{d}
      *
      rls(noprint,order=thresh,condition=m0) g3year / rr3year
      # constant g3year{1 to p} g3month{1 to p}
      rls(noprint,order=thresh,condition=m0) g3month / rr3month
      # constant g3year{1 to p} g3month{1 to p}
      *
      * We need to exclude the conditioning observations, so we generate the
      * series of ranks of the threshold variable over the estimation range.
      *
      order(ranks=rr) thresh %regstart() %regend()
      *
      linreg(noprint,smpl=rr>m0) rr3year / wr3year
      # constant g3year{1 to p} g3month{1 to p}
      linreg(noprint,smpl=rr>m0) rr3month / wr3month
      # constant g3year{1 to p} g3month{1 to p}
      *
      ratio(mcorr=%nreg,degrees=k*%nreg,noprint)
      # rr3year rr3month
      # wr3year wr3month
      disp "D=" d "m0=" m0 @16 "C(d)=" *.## %cdstat @28 "P-value" #.##### %signif
   end dofor m0
end do d

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set thresh = sspread{1}
set rgrid 1 300 = -.30+(.35/300.0)*(t-1)
set aic   1 300 = 0.0
*
do i=1,300
   compute rtest=rgrid(i)
   sweep(group=thresh<rtest,var=hetero)
   # g3year g3month
   # constant g3year{1 to p} g3month{1 to p}
   compute aic(i)=-2.0*%logl+2.0*%nregsystem
end do i
*
scatter
# rgrid aic

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ext(noprint) aic 1 300
disp rgrid(%minent)