new;

@ simulates and estimates by GCOV noncausal Cauchy AR(1) with coef 0.8 @

nobs=300;



rho = 0.8;


mu = 0; @ location @
c = 1; @ scale @




@ Cauchy noncausal AR(1) - can change to t-student @
uu = rndu(nobs,1);

cou = c* tan(pi*(uu - 0.5)) + mu;


y = zeros(nobs,1);
y[1,1] = 0.1;

y[nobs,1] = 0.1;


i = 0;

do until i > (sobs-2);

k = nobs-i-1;
kak = nobs - i;

y[k,1] = rho*y[kak,1] + cou[k,1];

i = i+1;

endo;

@ cut off 50 first and 50 last @

y = trimr(y,50,50);



@ Estimation starts here @



library optmum;

optset;

proc fct(d);
local ps, eps, phi, i, term, vov, vc, corr, co, sco, epl, s1, s2, y11, y1l1, did, di, beps, te;


te=nobs-100;
eps=zeros(te,4);


y11 = trimr(y,1,0); y1l1=trimr(y,0,1);
 ps = y11 - d * y1l1; 

@ ps = y1l1 - d* y11; @


eps[.,1] = ps;
eps[.,2] = (eps[.,1])^2;
eps[.,3] = (eps[.,1])^3;
eps[.,4] = (eps[.,1])^4;

eps[.,1] = eps[.,1]-meanc(eps[.,1]);
eps[.,2] = eps[.,2]-meanc(eps[.,2]);

eps[.,3] = eps[.,3]-meanc(eps[.,3]);
eps[.,4] = eps[.,4]-meanc(eps[.,4]);


corr = zeros(4,4);

vc = vcx(eps);

did = diag(vc);
di = sqrt(did);
vov = di*di';


epl=eps;

i = 1;
do until i>10;

eps = trimr(eps,1,0);
epl=trimr(epl,0,1);


co = (eps'*epl)/nobs;

co = co./vov;

sco = co^2;

corr = corr+sco;
i = i+1;
endo;

s1 = sumc(corr);


s2 = sumc(s1);


retp(s2);

endp;



start = { 0.5 };

output file = nonmax.out reset;

{ d, f, g, ret } =optmum(&fct, start);


output file = nonT200.out on;

print d;



end;