Problem in likelihood convergence

Good evening to everyone, I coded an entire model in Matlab about multivariate time series and I adopted as optimization solver fmincon (because of stationarity conditions) and I used as algortihm the interior point. I write a one step likelihood of the type:

lt=−1/2*[ln|St|+ tr(St^(−1)*Rt)], where St and Rt are matrices that changes for every observation (row) , from 1 to 4683, from which I have to estimate 82 parameters. Whent I use fmincon optimization solver, it happens that the sum of likelihood (sum of lt) goes drastically down and it determines error in the last two parameters estimation end I also get an exitflag of 0. Could anyone suggest me an approach to deal with this issue? Thank you in advance.

[Alessandra Costa]

Or every suggestion to understand why this happens.

[Matt J]

Why do you perceive that there is an issue? fmincon is a function minimizer, so if your obective "goes drastrically down", then fmincon is doing its job.

[Alessandra Costa]

Yes, I know how it works, I think this could be a problem since after a certain number of iterations, when likelihood drecreases a lot from an iteration to another, likelihood doesn't reach the optimal solution I expected, while before the solution was optimal (in the case of stability of likelihood)

[Alessandra Costa]

I setted up the display option for fmincon to 'iter' and I noted that first-order optimality reported start to increase after a certain number of iterations

[John D'Errico]

Are you trying to use a minimizer to solve a MAXIMUM likelihood problem? fmincon is a minimizer. You may be going in the wrong direction. You want to minimize the negative log likelihood.

[Alessandra Costa]

Yes, I used the minus(-) sign before the function name when I call fmincon

[Alessandra Costa]

I verified what happens during estimation; initially it works very well (parameters are optimals) and the log likelihood decreases as expected, then it starts to grow and at the end of iterations, the likelihood has the same minimum value reached before it started to increase, but with lower parameters that are not acceptable.

[Matt J]

I suggest you post your code, along with a .mat file of input data necessary to run it.

[Alessandra Costa]

Ok, I'll post them as Matlab finishes to estimate. Thank you

[Alessandra Costa]

The main file is mainscript, the likelihood used in fmincon is in lik.m and the other matlab file containes a function inside the lik. The excel file containes data for rvseries, required as input in the code.

[Alessandra Costa]

The problems are relative to the last two parameters, alpha and beta, for which the expected values are around 0.1 and 0.8.

[Alessandra Costa]

Does anyone have suggestion about the code?

[Matt J]

Did you attach it? I don't see it.

[Alessandra Costa]

Yes, I attached here two days ago.