Suppose we have a time-series $x(t_i)$ at discrete times $t_i$ and we want to estimate the parameters of an underlying SDE corresponding to this time-series:  $$dx_t = f(x_t,\theta)dt + \sigma(x_t,\theta)dB_t$$ I have read that there exists a lot of different numerical methods to approach this problem, but I have not found a comprehensive and comparative survey about this problem.

1.What is the best method (according to the type of data/model) ?

2.Is there a Python or Matlab toolbox doing the job ? I have had a look at SDE_toolbox for Matlab (http://sourceforge.net/projects/sdetoolbox/?source=dlp) but it is not clear to me how to use it, so it would be appreciated to provide an example.

I think it can be useful to have an overview of this topic since it may be interesting for many people.

  Thank you.

Suppose we have a time-series $x(t_i)$ at discrete times $t_i$ and we want to estimate the parameters of an underlying SDE corresponding to this time-series: 

$$dx_t = f(x_t,\theta)dt + \sigma(x_t,\theta)dB_t$$

I have read that there exists a lot of different numerical methods to approach this problem, but I have not found a comprehensive and comparative survey about this problem.

1. What is the best method (according to the type of data/model) ?

2. Is there a Python or Matlab toolbox doing the job ? I have had a look at SDE Toolbox for Matlab but it is not clear to me how to use it, so it would be appreciated to provide an example.

I think it can be useful to have an overview of this topic since it may be interesting for many people. Thank you.