/* PRG0: Program for Markov Testing */
/* omnibus testing M(0,0) */

/* 11-3-2003 */
new;

/* seed numbers */

iseed1=2555130;
iseed2=2660427;

/* N= sample size */
/* For applican of real data, N should be changed */

N=100;
Nu=30;
n0=100;
Iv0=2000;






ep=10^(-4);

ITRBmax=100;

ITR=1;
ITRmax=500;

/* U00 and V00 are grid points of (u,v) */
/* We use normal variates for (u,v) */

U00=rndns(1,0.5*Nu,iseed1);
u00=u00~-u00;
V00=rndns(1,0.5*Nu,iseed2);
v00=v00~-v00;


/* RANGE OF PRELIMINARY BANDWIDTH Pbar*/

Pmax=16;
Pmin=4; 

/* note: The total number of preliminary lags : 5 to 30 */

/* P0max is the maximum lag order to be integrated numerically. 
It can be set to N-1. But for the kernel with bounded support, 
it can be must less than N. This will speed up the computation */

P0max=50;
bandh=0;
/* GAUSSIAN KERNEL N(0,1) */

const2=1/sqrt(2*pi);
con1=pi;

proc GK(u);
    local Y;
    Y=const2*exp(-0.5*u.*u);
    retp(Y);
endp;
/*
/*higher order kernel*/
proc hk(u);
local y;
y= 0.5*(3-u.^2).*pdfn(u);
retp(y);
*/
/* KERNEL FUNCTIONS */



/* BARTLETT KERNEL */

proc Wbar(u);
    local Y;
    Y=(1-u).*(u.<=1);
    retp(Y);
endp;

/* DANIELL KERNEL */

proc Wdan(u);
    local Y;
    Y=sin(Con1*u)./(Con1*u);
    retp(Y);
endp;

/* PARZEN KERNEL */

proc Wpar(u);
    local X,Y;
    X=(Con1/6)*u;
    Y = (1-6.*X^2+6.*X^3).*(X.<=0.5) + (2.*(1-X)^3).*(X.>0.5).*(X.<=1.0);
    retp(Y);
endp;

/* QS KERNEL */

proc Wqs(u);
    local Y;
    Y=sqrt(5/3)*Con1*u;
    Y=(3./Y^2).*(sin(Y)./Y - cos(Y));
    retp(Y);
endp;

/*E kernel*/

proc ekernel(u);
     local Y;
     Y=0.75.*((1-u.*u).>=0).*(1-u.*u);
     retp(Y);
endp; 
/*nonparametric estimation*/


proc ccfm(x,u00);

local y,t,yreal,yimag,ccfreal,ccfimag,xnew,ymi,ymr,ccfrealsort,ccfimagsort;

yreal=cos(x*u00);
yimag=sin(x*u00);

xnew=zeros(n-1,1);
xnew=x[1:n-1,.];

ccfreal=zeros(n,nu);
ccfimag=zeros(n,nu);
ymr=yreal[2:n,.];
ymi=yimag[2:n,.];
ccfreal[1,.]=cos(x[1,1]*u00);
ccfimag[1,.]=sin(x[1,1]*u00);
t=1;
do until t==nu+1;

ccfrealsort=lpoly(ymr[.,t],xnew,bandh,xnew);
ccfimagsort=lpoly(ymi[.,t],xnew,bandh,xnew);

ccfreal[2:n,t]=ccfrealsort;
ccfimag[2:n,t]=ccfimagsort;

t=t+1;
endo;
y=x~ccfreal~ccfimag;
retp(y);
endp;
/*nonparamtric conditional distribution function*/ 
proc cdf(x,v0);

local y,cdfhat,xnew, temp,t;
y=zeros(n-1,iv0);

y=(x[2:n,.].<=v0);


xnew=zeros(n-1,1);
xnew=x[1:n-1,.];

cdfhat=zeros(n,iv0);
cdfhat[1,.]=(x[1,1].<=v0);

t=1;
do until t==iv0+1;

cdfhat[2:n,t]=lpoly(y[.,t],xnew,bandh,xnew);


t=t+1;
endo;





retp(cdfhat);
endp;

proc Kbar(n0,p0);
    local j,Y,c0;
    c0=cols(p0);
    Y=zeros(N0,c0);
    j=1;
    do until j==N0+1;
    Y[j,.]=Wbar(j./p0);
    j=j+1;
    endo;
    retp(Y);
endp;

proc Kdan(n0,p0);
    local j,Y,c0;
    c0=cols(p0);
    Y=zeros(n0,c0);
    j=1;
    do until j==n0+1;
    Y[j,.]=Wdan(j./p0);
    j=j+1;
    endo;
    retp(Y);
endp;

proc Kpar(n0,p0);
    local j,Y,c0;
    c0=cols(p0);
    Y=zeros(n0,c0);
    j=1;
    do until j==n0+1;
    Y[j,.]=Wpar(j./p0);
    j=j+1;
    endo;
    retp(Y);
endp;

proc Kqs(n0,p0);
    local j,Y,c0;
    c0=cols(p0);
    Y=zeros(n0,c0);
    j=1;
    do until j==n0+1;
    Y[j,.]=Wqs(j./p0);
    j=j+1;
    endo;
    retp(Y);
endp;

/* JUST USE THE BARTLETT KERNEL FOR AUTOMATIC P */
/* P00 is the preliminary bandwidth vector */

P00=zeros(1,Pmax);
j=1;
do until j==Pmax+1;
P00[1,j]=Pmin+j;
j=j+1;
endo;


Bar=Kbar(P0max,P00);
Bar2=Bar^2;


itr=1;
do until ITR==ITRmax+1;

/*simiulate regime swching**/

itrb=0;

e=rndns(N+N0,1,iseed1);

s=rndns(n+n0,1,iseed1);
y=s;



t=1;
do until t==N+N0+1;

if t==1;
ru=rndu(1,1);
if (ru<0.6);
s[t]=0;
y[t]=e[1];
else;
s[t]=1;
y[t]=e[1];
endif;

else;
ru=rndu(1,1);
if (s[t-1]==0);
if(ru<0.6);
s[t]=1;
y[t]=-0.3*y[t-1]+e[t];
else;
s[t]=0;
y[t]=0.7*y[t-1]+e[t];
endif;
else;
if(ru<0.6);
s[t]=0;
y[t]=0.7*y[t-1]+e[t];
else;
s[t]=1;
y[t]=-0.3*y[t-1]+e[t];
endif;
endif;
endif;
t=t+1;
endo;


y=y[(n0+1):(n0+n),.];
/*scale y on support [0,1]*/
/***
y=1/(1+exp(-y));
***/
/*y=(y-minc(y))/(maxc(y)-minc(y));*/
step=(maxc(y)-minc(y))/iv0;
V0_sm=seqa(minc(y),step,iv0)';
do until itrb==itrbmax+1;
if itrb==0;
x=y;
bandh=stdc(x)*n^(-1/5);



/* Iv0 x 1 cdf estimates */



g0_cdf_sm=cdf(x,v0_sm);



/*normalization*/

g0_cdf_sm=(g0_cdf_sm-minc(g0_cdf_sm)')./(maxc(g0_cdf_sm)'-minc(g0_cdf_sm)');

/* Below are for BOOTSTRAP Residuals */

else;


/* Generate U[0,1] randam variables */

X=zeros(N,1);

IB=rndus(N,1,iseed2);

i=1;
do until i==N+1;

Y=1000*(g0_cdf_sm[i,.]-IB[i]); 
Y=abs(Y);
Iy=indexcat(Y',minc(Y'));

 X[i,1]=v0_sm[1,Iy[1]];


i=i+1;
endo;
/* FOR BOOTSTRAP: corresponding to "If B0 >= 1" */
endif; 



/* SCALE {X} ON SUPPORT [0,1] */

/*X=(X-minc(X))/(maxc(X)-minc(X));*/

/***simulate MA(1)***/
/**
yy=zeros(500+n,1);
estep=zeros(2,1);
estep[1,1]=rndns(1,1,iseed1);
simindex=1;
ap=0.5;
do until simindex==500+n+1;
estep[2,1]=rndns(1,1,iseed1);
yy[simindex,1]=estep[2,1]+ap*estep[1,1];
estep[1,1]=estep[2,1];
simindex=simindex+1;
endo;
x=yy[501:(500+n),.];
***/
/*y=rndns(N,1,iseed1);

X=Y;
x=x/stdc(x);*/
stdy=stdc(x);
meany=meanc(x);
U00=rndns(1,0.5*Nu,iseed1).*stdy+meany;
u00=u00~-u00;
V00=rndns(1,0.5*Nu,iseed2).*stdy+meany;
v00=v00~-v00;


bandh=stdc(x)*N^(-1/5);
ccf=ccfm(x,u00);
x=ccf[.,1];
realccf=ccf[.,2:(Nu+1)];
imagccf=ccf[.,(Nu+2):(2*Nu+1)];
/*use true*/
/*realccf=ones(n,1)*exp(-u00.^2/2);
imagccf=zeros(n,nu);*/
imagccf2=-imagccf;
realccf2=realccf;


/* THIS IS THE ORIGINAL RANDOM VARIABLE X(t) */

/* t=j+1 to N */
proc X1(j);
    local Z;
    Z=X[j+1:N,.];
    retp(Z);
endp;

/* t=1 to N-j */
proc X2(j);
    local Z;
    Z=X[1:N-j,.];
    retp(Z);
endp;


/* Data CCF */

proc CX1(u,j);
local Z1,Z2,r,q;
r=rows(u);
Z1=X1(j);
/*
Z2=Z1[.,1].*u[1,.];
q=2; do until q==r+1;
Z2=Z2+Z1[.,q].*u[q,.];
q=q+1; endo;*/
z2=z1*u;
Z2=cos(Z2);
retp(Z2);
endp;

proc CX2(u,j);
local Z1,Z2,r,q;
r=rows(u);
Z1=X2(j);
/*Z2=Z1[.,1].*u[1,.];
q=2; do until q==r+1;
Z2=Z2+Z1[.,q].*u[q,.];
q=q+1; endo;*/
z2=z1*u;
Z2=cos(Z2);
retp(Z2);
endp;


proc SX1(u,j);
local Z1,Z2,r,q;
r=rows(u);
Z1=X1(j);
/*Z2=Z1[.,1].*u[1,.];
q=2; do until q==r+1;
Z2=Z2+Z1[.,q].*u[q,.];
q=q+1; endo;*/
z2=z1*u;
Z2=sin(Z2);
retp(Z2);
endp;


proc SX2(u,j);
local Z1,Z2,r,q;
r=rows(u);
Z1=X2(j);
/*Z2=Z1[.,1].*u[1,.];
q=2;do until q==r+1;
Z2=Z2+Z1[.,q].*u[q,.];
q=q+1;endo;*/
z2=z1*u;
Z2=sin(Z2);
retp(Z2);
endp;




proc Re_CCF1(u,j);
    local Z;
    Z=realccf[j+1:N,.];
    retp(Z);
endp;

/*I add this for u00[.,q]*/
proc Re_CCFq1(u,j,q);
    local Z;
    Z=realccf[j+1:N,q];
    retp(Z);
endp;

/* t=1 to N-j */
proc Re_CCF2(u,j);
    local Z;
    Z=realccf[1:N-j,.];
    retp(Z);
endp;

/*for -u00*/
proc Re_CCF3(u,j);
    local Z;
    Z=realccf2[1:N-j,.];
    retp(Z);
endp;

proc IM_CCF1(u,j);
    local Z;
    Z=imagccf[j+1:N,.];
    retp(Z);
endp;

proc IM_CCFq1(u,j,q);
    local Z;
    Z=imagccf[j+1:N,q];
    retp(Z);
endp;

/* t=1 to N-j */
proc IM_CCF2(u,j);
    local Z;
    Z=imagccf[1:N-j,.];
    retp(Z);
endp;

/*for -u00*/
proc IM_CCF3(u,j);
    local Z;
    Z=imagccf2[1:N-j,.];
    retp(Z);
endp;

/* exp(u*X(t))- Model CCF */

proc CM1(u,j);
local Z;
Z=CX1(u,j)-Re_CCF1(u,j);
retp(Z);
endp;

/*I add this for u00[.,q]*/
proc CMq1(u,j,q);
local Z;
Z=CX1(u,j)-Re_CCFq1(u,j,q);
retp(Z);
endp;


proc CM2(u,j);
local Z;
Z=CX2(u,j)-Re_CCF2(u,j);
retp(Z);
endp;

/*for -u00*/
proc CM3(u,j);
local z;
z=cx2(u,j)-Re_CCF3(u,j);
retp(Z);
endp;


proc SM1(u,j);
local Z;
Z=SX1(u,j)-Im_CCF1(u,j);
retp(Z);
endp;

/*I add this for u00[.,q]*/
proc SMq1(u,j,q);
local Z;
Z=SX1(u,j)-Im_CCFq1(u,j,q);
retp(Z);
endp;

proc SM2(u,j);
local Z;
Z=SX2(u,j)-Im_CCF2(u,j);
retp(Z);
endp;

proc SM3(u,j);
local Z;
Z=SX2(u,j)-Im_CCF3(u,j);
retp(Z);
endp;

proc Re_xxsgm(u,v,j);
local a1,b1,a2,b2,Z;
a1=CX1(u,j); a1=a1-meanc(a1)'; 
b1=SX1(u,j); b1=b1-meanc(b1)';
a2=CX2(v,j); a2=a2-meanc(a2)';
b2=SX2(v,j); b2=b2-meanc(b2)';
Z=meanc(a1.*a2-b1.*b2);
retp(Z);
endp;

proc Im_xxsgm(u,v,j);
local a1,b1,a2,b2,Z;
a1=CX1(u,j); a1=a1-meanc(a1)'; 
b1=SX1(u,j); b1=b1-meanc(b1)';
a2=CX2(v,j); a2=a2-meanc(a2)';
b2=SX2(v,j); b2=b2-meanc(b2)';
Z=meanc(a1.*b2+b1.*a2);
retp(Z);
endp;


proc Re_mmsgm(u,v,j);
local a1,a2,b1,b2,Z;
a1=CM1(u,j);a1=a1-meanc(a1)';
b1=SM1(u,j);b1=b1-meanc(b1)';
a2=CM3(v,j);a2=a2-meanc(a2)';
b2=SM3(v,j);b2=b2-meanc(b2)';
Z=meanc(a1.*a2-b1.*b2);
retp(Z);
endp;

proc Im_mmsgm(u,v,j);
local a1,a2,b1,b2,Z;
a1=CM1(u,j);a1=a1-meanc(a1)';
b1=SM1(u,j);b1=b1-meanc(b1)';
a2=CM3(v,j);a2=a2-meanc(a2)';
b2=SM3(v,j);b2=b2-meanc(b2)';
Z=meanc(a1.*b2+b1.*a2);
retp(Z);
endp;


/* Below is used to determine lag order that from data */

/* COMPUTE THE INTEGRALS */
/* WRSXX will be used to select lag orders for M(0,0) */ 

WRSMM=zeros(1,P0max+1);
WRSXX=zeros(1,P0max+1);
WISMM=WRSMM;
WISXX=WRSXX;

j=0;
do until j==P0max+1;

/* For lag dedetrmination */

/* Compute the integral of real Sigma_mm(u,-u).*G(u) and Sigma_xx(v,-v,j).*GK(v)*/


WRSMM[1,j+1]=meanc(Re_MMsgm(U00,-U00,j));
WRSXX[1,j+1]=meanc(Re_XXsgm(V00,-V00,j));

/*
WISMM[1,j+1]=meanc(Im_MMsgm(U00,-U00,j));
WISXX[1,j+1]=meanc(Im_XXsgm(V00,-V00,j));
*/

/* NOTE: I have Checked INTQUAD1(&WIXsgm, V1) is indeed zero */

j=j+1;
endo;


/* TEST FOR MARTINGALE DIFFERENCE */
/* TEST 1: Based on Cov( exp(u'X(t))-CCF(u), exp(ivX(t-j)) */

/* MS1: M(0,0) */

/* Smx00s(u,v,j) */

proc Smx00s(u,v,j);
    local a1,a2,b1,b2, RZ,IZ;
    a1=CM1(u,j);a1=a1-meanc(a1)';
    b1=SM1(u,j);b1=b1-meanc(b1)';
    a2=CX2(v,j);a2=a2-meanc(a2)';
    b2=SX2(v,j);b2=b2-meanc(b2)';
    RZ=meanc(a1.*a2-b1.*b2);
    IZ=meanc(a1.*b2+b1.*a2);
    retp(RZ.*RZ+IZ.*IZ);
endp;


MS1=zeros(1,P0max);
M1_1=MS1;
M1_2=MS1;

j=0;
do until j==P0Max+1;


if j==0;

M1_10 = (1-j/N)*WRSmm[1,j+1].*WRSxx[1,j+1];

else;

MS1[1,j]= (1-j/N)*meanc(Smx00s(U00,V00,j));

M1_2[1,j] = j*j*MS1[1,j];
M1_1[1,j] = (1-j/N)*WRSmm[1,j+1]*WRSxx[1,j+1];

endif;

j=j+1;
endo;


MS1=N*MS1;

M1_1=2*M1_1*Bar2+M1_10;
M1_2=2*M1_2*Bar2;

MM1=N*2*M1_2./M1_1;

P1_1=1.1447142*MM1^(1/3);
P1_2=1.4017333*MM1^0.2;
P1_3=1.3934819*MM1^0.2;
P1_4=1.4223747*MM1^0.2;


lnn=ln(n);

P1_1=(P1_1.>lnn).*P1_1+(P1_1.<=lnn).*lnn;
P1_2=(P1_2.>lnn).*P1_2+(P1_2.<=lnn).*lnn;
P1_3=(P1_3.>lnn).*P1_3+(P1_3.<=lnn).*lnn;
P1_4=(P1_4.>lnn).*P1_4+(P1_4.<=lnn).*lnn;





/* THIS IS 1 by 4*Pmax vector */

P0=P1_1~P1_2~P1_3~P1_4;

/*p0=p00~p00~p00~p00;*/
/* PART II */
/* COMPUTE TEST STATISTICS */

N1=P0max;

Ka=Kbar(n1,P1_1)~Kdan(n1,P1_2)~Kpar(n1,P1_3)~Kqs(n1,P1_4);
/*ka=kbar(n1,p00)~kdan(n1,p00)~kpar(n1,p00)~kqs(n1,p00);*/



Ka2=Ka.*Ka;
Ka4=Ka2.*Ka2;
Cka=sumc(Ka2);
Cka=Cka';
Dka=sumc(Ka4);
Dka=Dka';


/* means/variance of M(0,0) */

/* For M(0,0) */

C00=zeros(P0max,1);

D00=zeros(P0max,P0max);

/* This helps to reduce computational cost */

Pdim=CEIL(maxc(P0'))+1;

proc C00j(u,v,j);
local a1,b1,a2,b2,Z1,Z2,Z;
a1=CM1(u,j); a1=a1-meanc(a1)';
b1=SM1(u,j); b1=b1-meanc(b1)';
a2=CX2(v,j); a2=a2-meanc(a2)';
b2=SX2(v,j); b2=b2-meanc(b2)'; 
Z1=a1.*a1+b1.*b1;
Z2=a2.*a2+b2.*b2;
Z=Z1.*Z2;
Z=meanc(Z);
retp(Z);
endp;

proc D00JL(u1,v1,u2,v2,j,L,q);
local a1,b1,a2,b2,a3,b3,a4,b4, Z0, Z,RZ, IZ, R12,I12,R34,I34, r,p;
a1=CM1(u1,j); a1=a1-meanc(a1)';
b1=SM1(u1,j); b1=b1-meanc(b1)';
a2=CMq1(u2,j,q); a2=a2-meanc(a2)';
b2=SMq1(u2,j,q); b2=b2-meanc(b2)';
a3=CX2(v1,j); a3=a3-meanc(a3)';
b3=SX2(v1,j); b3=b3-meanc(b3)';
Z0=X[j-L+1:N-L,.];
r=rows(v2);
/*Z=Z0[.,1].*v2[1,.];
p=2; do until p==r+1;
Z=Z+Z0[.,p].*v2[p,.];
p=p+1; endo;*/
z=z0*v2;
a4=cos(Z); a4=a4-meanc(a4)';
b4=sin(Z); b4=b4-meanc(b4)';
R12=a1.*a2-b1.*b2;
I12=a1.*b2+b1.*a2;
R34=a3.*a4-b3.*b4;
I34=a3.*b4+b3.*a4;
RZ=meanc(R12.*R34-I12.*I34);
IZ=meanc(R12.*I34+I12.*R34);
retp(RZ.*RZ+IZ.*IZ);
endp;


j=1;
do until j==Pdim+1;


C00[j,1]=meanc(C00j(U00,V00,j));


L=1;
do until L==j+1;

D00tmp=zeros(Nu,1);
q=1;
do until q==Nu+1;
D00tmp[q,1]=meanc(D00jL(U00,V00,U00[.,q],V00[.,q],j,L,q));
q=q+1;
endo;

D00[j,L]=meanc(D00tmp);
D00[L,j]=D00[j,L];


L=L+1;
endo;

j=j+1;
endo;

W00m=Ka2'D00*Ka2;

Wdim=rows(W00m);
W00=zeros(1,Wdim);


j=1;
do until j==Wdim+1;

W00[1,j]=W00m[j,j];

j=j+1;
endo;


/* TEST FOR MARTINGALE DIFFERENCE Mxx(0,0) */

MS1=MS1*Ka2;
MS1=(MS1-C00'Ka2)./sqrt(2*W00);


MS=MS1;
if ITRb==0;
/*original test statistics*/


statis=ms;
elseif itrb==1;
data0=MS;
else; 
data0=data0|MS;
endif;



ITRb=ITRb+1;
endo;

/*compute bootstrap p-values*/
pv1=(statis-data0).<0;
pv1=meanc(pv1);
pv1=pv1';
pv1;

/*asymptotic p value*/
asympv=cdfnc(statis);
output file=c:\users\Public\Documents\p100markov_switching_100.dat on;
itr~pv1~asympv~statis;
output off;


/* INDEX for lag Pbar*/

Pbar0=zeros(Pmax,1);
j=1;
do until j==Pmax+1;
Pbar0[j,1]=Pmin+j;
j=j+1;
endo;

j=1;
do until j==1+1;
if j==1;
Ipbar=Pbar0;
Itest=ones(Pmax,1)*j;
else;
Ipbar=Ipbar|Pbar0;
Itest=Itest|ones(Pmax,1)*j;
endif;
j=j+1;
endo;


/* Results based on BARTLETT KERNEL */

j=1;
do until j==1+1;
if j==1;
data1=data0[1:itrbmax,(j-1)*4*Pmax+0*Pmax+1:(j-1)*4*Pmax+0*Pmax+Pmax];
else;
data1=data1~data0[1:itrbmax,(j-1)*4*Pmax+0*Pmax+1:(j-1)*4*Pmax+0*Pmax+Pmax];
endif;
j=j+1;
endo;

/* sort data to compute ecv */

j=1;
do until j==cols(data1)+1;
data1[.,j]=sortc(data1[.,j],1);
j=j+1;
endo;

Bar_ecv=data1[90,.]~data1[95,.]~data1[99,.];

CDim=cols(data1);
if itr==1;
BAR_rej=zeros(itrmax,3*cdim);
par_rej=zeros(itrmax,3*cdim);
bar_rej2=zeros(itrmax,cdim);
par_rej2=zeros(itrmax,cdim);
endif;

/* Test statistics values */

/* rejections based on asymptotic critical values */
statisb=statis[.,1:pmax];
statisp=statis[.,2*pmax+1:2*pmax+pmax];

bar_rej2[itr,.]=meanc((statisb-data1).<0)';
BAR_REJ[itr,.]=(statisb.>BAR_ECV[1,1:CDim])~(statisb.>BAR_ECV[1,CDim+1:2*CDim])~(statisb.>BAR_ECV[1,2*CDim+1:3*CDim]);


/* Results based on PARZEN KERNEL */

j=1;
do until j==1+1;
if j==1;
data2=data0[1:itrbmax,(j-1)*4*Pmax+2*Pmax+1:(j-1)*4*Pmax+2*Pmax+Pmax];
else;
data2=data2~data0[1:itrbmax,(j-1)*4*Pmax+2*Pmax+1:(j-1)*4*Pmax+2*Pmax+Pmax];
endif;
j=j+1;
endo;
par_rej2[itr,.]=meanc((statisp-data2).<0)';
/* sort data to compute ecv */

j=1;
do until j==cols(data2)+1;
data2[.,j]=sortc(data2[.,j],1);
j=j+1;
endo;

Par_ecv=data2[90,.]~data2[95,.]~data2[99,.];


/* Statistics Values */
pAR_REJ[itr,.]=(statisp.>pAR_ECV[1,1:CDim])~(statisp.>pAR_ECV[1,CDim+1:2*CDim])~(statisp.>pAR_ECV[1,2*CDim+1:3*CDim]);
bar_rej[itr,.];
par_rej[itr,.];
itr=itr+1;
endo;
bar_rejmean=meanc(bar_rej);
par_rejmean=meanc(par_rej);

/*output file=c:\Markov\ar5_200.out on;
bar_rejmean;
par_rejmean;
output off;*/

/*****************************

/*****************
USE THIS for DATA UNDER THE ALTERNATIVE MODELS (e.g., A1(3)) 
******************/


/* compute p-values */

/* INDEX for lag Pbar*/

Pbar0=zeros(Pmax,1);
j=1;
do until j==Pmax+1;
Pbar0[j,1]=Pmin+j;
j=j+1;
endo;

j=1;
do until j==1+1;
if j==1;
Ipbar=Pbar0;
Itest=ones(Pmax,1)*j;
else;
Ipbar=Ipbar|Pbar0;
Itest=Itest|ones(Pmax,1)*j;
endif;
j=j+1;
endo;


/* Results based on BARTLETT KERNEL */

j=1;
do until j==1+1;
if j==1;
data1=data0[.,1+1+(j-1)*4*Pmax+0*Pmax+1:1+1+(j-1)*4*Pmax+0*Pmax+Pmax];
else;
data1=data1~data0[.,1+1+(j-1)*4*Pmax+0*Pmax+1:1+1+(j-1)*4*Pmax+0*Pmax+Pmax];
endif;
j=j+1;
endo;



/* Test statistics values */

/* rejections based on asymptotic critical values */

pvalue1=cdfnc(data1);

BAR_ACVREJ=meanc(pvalue1.<0.10)~meanc(pvalue1.<0.05)~meanc(pvalue1.<0.01);

/* rejection using ecv */

/* Here 2 = Bartlett and Parzen, 3 = 10%, 5% and 1% levels */


CDim=cols(data1);

/*load ECV[1,2*3*CDim]=c:\diagonalk\hlp0_ecv500.out;*/

/*********
BAR_ECV=ECV[1,0*CDim+1:3*CDim];
PAR_ECV=ECV[1,3*CDim+1:2*3*CDim];

BAR_ECVREJ=meanc(data1.>BAR_ECV[1,1:CDim])~meanc(data1.>BAR_ECV[1,CDim+1:2*CDim])~meanc(data1.>BAR_ECV[1,2*CDim+1:3*CDim]);
************/
/* Results based on PARZEN KERNEL */

j=1;
do until j==1+1;
if j==1;
data2=data0[.,1+1+(j-1)*4*Pmax+2*Pmax+1:1+1+(j-1)*4*Pmax+2*Pmax+Pmax];
else;
data2=data2~data0[.,1+1+(j-1)*4*Pmax+2*Pmax+1:1+1+(j-1)*4*Pmax+2*Pmax+Pmax];
endif;
j=j+1;
endo;

/* compute ecv */

j=1;
do until j==cols(data2)+1;
data2[.,j]=sortc(data2[.,j],1);
j=j+1;
endo;

/*Par_ecv=data2[900,.]~data2[950,.]~data2[990,.];*/


/* Statistics Values */

pvalue2=cdfnc(data2);

PAR_ACVREJ=meanc(pvalue2.<0.10)~meanc(pvalue2.<0.05)~meanc(pvalue2.<0.01);

/*PAR_ECVREJ=meanc(data2.>PAR_ECV[1,1:CDim])~meanc(data2.>PAR_ECV[1,CDim+1:2*CDim])~meanc(data2.>PAR_ECV[1,2*CDim+1:3*CDim]);*/

output file=c:\Markov\ibmtest_y.out on;
Itest~Ipbar~BAR_ACVREJ~PAR_ACVREJ;
output off;
output file=c:\Markov\ibmtest_statistics_y.out on;
data1~data2;
output off;

*************************************/



proc lpoly(y,x,h,targmat);
local m,k,yhat,n,l,cont,kernarg,ki,estden,estreg;

n=rows(y);
targmat=targmat';
m=n;
k=cols(x);


yhat=zeros(m,1);
/* START OF MAIN LOOP */

    cont=1;
  do while cont==1;
   kernarg=(x-targmat)/h;
  ki=0.5*(3-kernarg.^2).*pdfn(kernarg);
estden=sumc(ki);
estreg=sumc(ki.*y);
         if abs(estden) > (10^(-20));
       yhat=estreg./estden;
cont=0;
else;
h=h*1.1;
cont=1;
endif;
endo;

retp(yhat);
 endp;