For a detailed background of the problem I am solving, please click here. In summary, the aggregate losses of 34 companies across a country were gathered. These losses were sampled spatially across a country and then the losses of each year were recorded. Hence giving us a data set of aggregate losses for 34 companies for 9 years. For each year, a t-distribution was fit to show a spatial variation of losses. It was established in this problem that the t - distribution (estimated by the investigator) is evolving or changing with time.
That said, the questions are as follows-
Given the data (data), can I model the said evolution of probability density as a stochastic process? If yes, then what are some standard techniques? Also, if such a model is viable, will it help in creating better forecasts (with a one-step-ahead horizon)?
I am quite used to modelling processes as differential equations (DE). How different is the modelling of a stochastic process compared to first principal modelling (DE-based modelling) of a deterministic process?
Is a state-space approach feasible? If yes, can you point me to resources that can help me estimate state-space matrices for the said process?
