Gregory-Hansen Cointegration Test
Posted: Sun Jun 14, 2009 9:45 am
Attached is a subroutine to carry out Gregory-Hansen procedure for testing cointegration in the case of level, trend and regime shifts. Building the procedure in EViews is a joint work of myself and tcfoon. We urge you to see the original study for details. Comments are welcomed and the usual disclaimer applies.
Code: Select all
'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.
call greghansen(y,x,2,"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