Nonparametric Estimation of Regime Switching Data

Methodology from simulated data without any modeling assumptions

This model was build for data that tends to fluctuate between different regimes but can be applied quite generally.
The data I used in this example is assumed to come from three regimes: 1-full generation, 2-partial generation, 3-little to no generation. The
%model works as follows:
1) I split the observable data into three partitions as determined by vector 'perc', (any number of partitions can be assigned here).
2) I compute an empirical markove chain based on the observable data and my partition space. For example I find the percentage of all observation in my dataset that are at full generation at time t and remain there at time t+1, this gives me p(1,1). I then find the percentage of all observations that are at full generation at time t and go the partial generation at time t+1, this gives me p(1,2)... I continue in this way until i have a 3x3 transition matrix for the data
3) I can now generate simulated states [1,2,3] from my empirical transition matrix, the next step is given I am in a particular state, to generate a sample from that state. I do this by computing empirical discrete probability distribution of each regime with a precision 'dt'.

This model can now be used to simulate the observed process dynamics, the results show that the sample paths as well has histograms match quite well. The general mechanism can be applied a wide array of dataset for nonparametric simulations.