Monte Carlo simulation with random poisson draws and fixed exogenous variables

Hello

I have a question concerning Monte Carlo simulation in matlab. I've created a function calling an estimate function, that does a MLE of my model. Now I want to simulate it to evaluate the perfomance of my MLE. My model is a poisson proces and I want the number of replications to be N=1000 and my sample size to be T.

lambda_t = delta+sigma_1*y_t-1+beta_1*lambda_t-1+gamma*x_t-1

First of all y_t must be drawn from a poisson distribution as it can't take negative values - see below. Second of all I have a series for x_t which I want to use - thus fixing x_t with the values I've actually observed. The sample size of x_t is 360.

Let's say I want to carry out the simulation with delta=0.1; sigma=0.3; beta=0; gamma=0.5;

I use this script:

konk=importdata('konk.txt');
y=poissrnd(konk); %this makes y a poisson random draw from konk
opi=importdata('opi.txt');
X=opi;

theta0=[0.1;0.3;0;0.5]; %here I set delta=0.1, sigma=0.3, beta=0 and gamma=0.5    
lb=-Inf*ones(4,1); %I am not sure if a lower bound is necessary
opt=optimset('Algorithm','interior-point');

outputMC(y,X,theta0,lb,opt,1,1,1) 
%this function calls my MLE-function which uses fmincon. This is the one I want to simulate with the above paramater values, and 1000 replications. 1 is the lags of y and lambda respectively while the last 1 is output sheet in excel.

Am I on the right track? I need to simulate this instead of estimating it.

If you lack information to help solve my question please tell me and I will try to provide it.

Thanks in advance