In order to achieve your desired result, I would advice you to use 'fitglme' function in order to successfully complete multi-objective optimization. This can be done as follows ->
1. You can first load the time series monthly data into MATLAB as a table using 'readtable' function. In case your data is in a different format, you will have restructure and pre-process the data into a table to get desired results.
2. Now, use 'fitglme' function as below-
% first you will have to define your fixed effects model (say as below example)
fixed_model = 'y ~ x1 + x2 ... + xn';
% then, you will have to define your intended random effects model (say as below example)
random_model = ~1+x1+x2+...+xn;
% now define name of your date (we use date as a parameter for time here)
TimeVar = 'date';
% now, create your desired formula using group variables for the panel data you inputed
Formula = [fixed_model ' (1|GroupVariable) + (' TimeVar '|GroupVariable)'];
% At last, you have to fit the mixed effects panel model using 'fitglme' function
panel_model = fitglme(T, Formula, 'Distribution', 'Normal', 'Link', 'Identity');
3. just do summary(panel_model) now to display the new table with panel mixed effect model incorporated.
The approach I have provided is a generic one, you can work on this framework after pre-processing your data table which is to be inputed according to above given format. But, 'fitglme' function should help you get your desired output.
I hope I was able to help you
