The majority of the world’s problem deal with directly or indirectly some kind of optimisation. Instance of optimisation of resources or utility function can be seen our daily life. Here I am talking about standard optimisation problem in statistics, maximum likelihood estimate. This blog is a small episode of my recent work. I used R for this optimisation exercise.
There are packages available for optimisation in R. The mostly used are: optim() and optimize() are in stats package. A dedicated function mle() available in stats4 package. This is very useful most of the mean part modeling(eg: glm). What we need for this optimisation is to prepare function for the (log)likelihood and gradient (or hessian). We can also specify the algorithm(methods) as any of the following: “Nelder-Mead”, “BFGS”, “CG”, “L-BFGS-B”, “SANN”, and “Brent”. This opimisation output give the necessary information for the model estimation.
The case I was doing is an extension of bivariate garch model. It includes more than 20 parameters. let me focus pure garch model, garch(1,1), as a prototype to explain the algorithm. Here the model equation is in the variance part. Also the parameter has constraint to ensure the positive variance. The model equation is given below.
This approach looks very silly for regression type problems. But in garch like process tweaking like this is very much require. I am still looking for the better way. Anyway the blogging helped me to relook at my approach again. Please let me know if you have any suggestions.