'Gregory-Hansen Cointegration Test
'Reference: Gregory, A. W. and Hansen, B. E. (1996). "Residual-Based Tests for Cointegration in Models with Regime Shifts", Journal of Econometrics, Vol. 70, pp. 99-126.
    
    group independents
    independents.add x
    

call greghansen(y,x,3,"aic",6)

' ----------------------------------------------------------------------------------------------------
' Arguments
'-----------------------------------------------------------------------------------------------------
'series Y                 ' dependent variable
'group G                 ' group of independent variable(s) (including single series)
'scalar Model         ' 2 = Level Shift, 3 = Level Shift with Trend, 4 = Regime Shift
'scalar Maxlag       ' Maximum number of lags for unit root testing
'string %Criterion  ' Selection criteria for unit root testing (i.e. aic / sic / hqc)
' ----------------------------------------------------------------------------------------------------

subroutine greghansen(series Y, group G, scalar Model, string %Criterion, scalar Maxlag)
smpl @all
!trim = 0.15
!maxlag = Maxlag

!n = @obs(y)
!nindep = G.@count

!lower = @round(@obs(Y)*!trim)
!upper = @round(@obs(Y)*(1-!trim))
matrix(!upper-!lower+1,4) GHtest

equation ghc

Table GHZ
GHZ(1,1) =  "THE GREGORY-HANSEN"
GHZ(2,1) = "COINTEGRATION TEST"
if Model=2 then GHZ(3,1) = "MODEL 2: Level Shift" 
else if Model =3 then GHZ(3,1) = "MODEL 3: Level Shift with Trend"
   else if Model = 4 then GHZ(3,1) = "MODEL 4: Regime Shift"
   endif
endif
endif
GHZ(5,1) = "ADF Procedure"
GHZ(7,1) = "t-stat"
GHZ(8,1) = "Lag"
GHZ(9,1) = "Break"
GHZ(11,1) = "Phillips Procedure"
GHZ(13,1) = "Za-stat"
GHZ(14,1) = "Za-break"
GHZ(15,1) = "Zt-stat"
GHZ(16,1) = "Zt-break"

for !ref = 2 to 4
  GHZ.setwidth(!ref) 15
next

GHZ.setlines(a4:b4) +d
GHZ.setlines(a6:b6) +d
GHZ.setlines(a10:b10) +d
GHZ.setlines(a12:b12) +d

for !i = !lower to !upper 

  if Model=2 then 
   'MODEL 2 - C: LEVEL SHIFT MODEL
     ghc.ls Y c G (@trend>!i-2)
     ghc.makeresid res
     uroot(adf, none, info={%criterion}, maxlag=!maxlag, save=level) res
     GHtest(!i-!lower+1,1) = level(3,1)
     GHtest(!i-!lower+1,2) = level(2,1)
     call phillips(res)   
     GHtest(!i-!lower+1,3) = !Za
     GHtest(!i-!lower+1,4) = !Zt
  
   else if Model=3 then
   'MODEL 3 - C/T: LEVEL SHIFT WITH TREND MODEL
     ghc.ls Y c @trend G (@trend>!i-2)
     ghc.makeresid res
     uroot(adf, none, info={%criterion}, maxlag=!maxlag, save=level) res
     GHtest(!i-!lower+1,1) = level(3,1)
     GHtest(!i-!lower+1,2) = level(2,1)
     call phillips(res)   
     GHtest(!i-!lower+1,3) = !Za
     GHtest(!i-!lower+1,4) = !Zt
    
   else if Model = 4 then
   'MODEL 4 - C/S: REGIME SHIFT MODEL
       for !g = 1 to !nindep
         G.add (@trend>!i-2)*G(!g)
       next
     ghc.ls Y c (@trend>!i-2) G
     ghc.makeresid res
     uroot(adf, none, info={%criterion}, maxlag=!maxlag, save=level) res
     GHtest(!i-!lower+1,1) = level(3,1)
     GHtest(!i-!lower+1,2) = level(2,1)
     call phillips(res)   
     GHtest(!i-!lower+1,3) = !Za
     GHtest(!i-!lower+1,4) = !Zt 
       for !g = G.@count to !nindep+1 step -1
        %name = G.@seriesname(!g)
         G.drop {%name}
       next
     endif
    endif
   endif
next
     vector min_t_lag = @cmin(GHtest)
     vector break = @cimin(GHtest)

     GHZ(7,2) = min_t_lag(1)
     GHZ(8,2) = GHtest(break(1),2)
     GHZ(13,2) = min_t_lag(3)
     GHZ(15,2) = min_t_lag(4)

    if @datestr(@now,"F") = "?" then
     GHZ(9,2) = break(1) + !lower - 2
     GHZ(14,2) = break(3) + !lower - 2
     GHZ(16,2) = break(4) + !lower - 2
    else
     GHZ(9,2) = @otod(break(1) + !lower - 2)
     GHZ(14,2) = @otod(break(3) + !lower - 2)
     GHZ(16,2) = @otod(break(4) + !lower - 2)
    endif

     show GHZ

delete res level GHtest break min_t_lag
endsub


subroutine phillips(series y) 'MATLAB code of this routine is available at Bruce E. Hansen's website: http://www.ssc.wisc.edu/~bhansen/progs/joe_96.html
!n = @obs(y)
equation eq1.ls y y(-1)
!be = eq1.@coefs(1)
series ue = y - !be*y(-1)



'Bandwidth selection
!nu = @obs(ue)
equation eq2.ls ue ue(-1)
!bu = eq2.@coefs(1)
series uu = ue - !bu*ue(-1)
!su = @sumsq(uu)/@obs(uu)
!a2 = (4*!bu^2*!su/(1-!bu)^8)/(!su/(1-!bu)^4)
!bw =1.3221*((!a2*!nu)^0.2)
     
!pi = @acos(-1)
!j=1
!lemda = 0
     while !j <= !bw
        series temp = ue*ue(-!j)
        !gama =  @sum(temp)/!nu
        !w=(75/(6*!pi*!j/!bw)^2)*(@sin(1.2*!pi*!j/!bw)/(1.2*!pi*!j/!bw)-@cos(1.2*!pi*!j/!bw))
        !lemda=!lemda+!w*!gama
        !j=!j+1
     wend
     
series temp = y*y(-1) - !lemda
!p = @sum(temp)/@sumsq(y(-1))
!Za = !n*(!p-1)
!Zt = (!p-1)/@sqrt((2*!lemda + @sumsq(ue)/!nu)/(@sumsq(y(-1))))
smpl @all
delete eq1 eq2 ue uu temp
endsub