Re: Maxi/minimization stupid question - CIR stochastic process

[Michael Creel]

I don't know anything about this model, but here's some code to minimize the
function. I just made up some data.
#--------------------------------------------------------
1;
function out= MaxLikehood( data, dt, params )

        N=length(data);
        alpha = params (1); theta = params (2); sigma = params (3);
        c = (2* alpha )/(( sigma ^2)*(1 - exp(- alpha *dt )));
        q = ((2* alpha * theta )/( sigma ^2)) -1;
        u = c* exp(- alpha *dt )* data (1:N -1);
        v = c* data (2:N);
        out = -(N -1)* log(c)+ sum(u+v- log(v./u)*q /2 -...
        log( besseli (q ,2* sqrt (u.*v) ,1)) - abs( real (2* sqrt(u.*v ))));

endfunction

data = rand(100,1);
dt = 0.01;
params = [1;1;1];
MaxLikehood(data, dt,params)
control = {-1;1;1;3};  # maxiters, verbosity, conv. reg., arg_to_min
[theta, obj_value, convergence] = bfgsmin("MaxLikehood", {data, dt, params},
control);
#--------------------------------------------------------


If I run this, I get 
octave:1> junk
ans =  1569.7
bfgsmin: Hessian reset

bfgsmin final results: 88 iterations

function value: 22.22

STRONG CONVERGENCE
Function conv 1  Param conv 1  Gradient conv 1

used numeric gradient
          param    gradient (n)          change
     1463.33090        -0.00000         0.00000
        0.55726         0.00000        -0.00000
       25.37338        -0.00000         0.00000
octave:2> 

So, the final function value is less than the starting value, which is a
good sign. bfgsmin is in the optim package at Octave Forge. Hope this helps.
Cheers, Michael
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