Issues with maximum likelihood estimation of realGARCH(1,1) in matlab - matlab

Question

I am having some trouble estimating the parameter for the log-linear realized Garch(1,1) model. The parameter values which I get from the optimisation are different from those derived in the paper and I'm not sure where I am going wrong. Any help would be great. The specification of the model from (Hansen et al. (2012)) is:
Realized GARCH specification
And the likelihood function is given by:
Log Likelihood
I am using the same data as used by Hansen and co-authors which can retrieved from the rugarch package with the command data(spyreal).
My matlab code is
function output = loglikRV(param, data)
r = data.SPY_OC;
RV = data.SPY_RK;
logRV = log(RV);
T = numel(RV); % time sample size
alpha0 = param(1);
alpha1 = param(2);
alpha2 = param(3);
omega0 = param(4);
omega1 = param(5);
omega2 = param(6);
omega3 = param(7);
sigmamu2 = param(8);
z = zeros(T,1);
logh = zeros(T,1);
u = zeros(T,1);
llhs = zeros(T,1);
logh(1) = 8.8296e-05;
u(1) = 0.005;
z(1) = 0.005;
llhs(1) = 0.005;
for i = 2:T
logh(i) = alpha0 + alpha1*logh(i-1) + alpha2*logRV(i-1);
z(i) = r(i) / sqrt(exp(logh(i)));
u(i) = logRV(i) - omega0 - omega1*logh(i) - omega2*z(i) - omega3*(z(i)^2 - 1);
llhs(i) = -(1/2)*(log(2*pi) + logh(i) + z(i)^2) - (1/2)*(log(2*pi) + log(sigmamu2) + u(1)^2 / sigmamu2);
end
output = sum(llhs(2:T-1));
return
And I am optimising this using the Matlab fmincon function with the code as shown below:
clear;close all;
RVfinal = readtable('spyreal.xlsx');
objfun = #(param)(-loglikRV(param,RVfinal)); % negative of the log-likelihood function
param0 = [0.07048753,0.43272574,0.52944743,-0.19368728,1.02540217,-0.06100213, 0.07437231, 0.38];
% constraints in the optimization
A = []; b = []; % no inequality constraints
Aeq=[]; beq=[]; % no equality constraints
% -- MLE Optimization using "fmincon" --
optim_options = optimset('Display','off','TolX',1e-4,'TolFun',1e-4);
[mymle,fval] = fmincon(objfun,param0,A,b,Aeq,beq,[],[],[],optim_options);
mymle
Thank You!