Simulation and Inference for Stochastic Processes

General Usage
1

Is there any package that allows me to do simulation and inference for stochastic processes?

For example, if I need to estimate parameters for Merton (1976) jump diffusion model using stock return data, which package should I use? I am looking for something similar to yuima:
https://yuimaproject.com/

2

It depends on the kind of inference you want to perform, you have to be more specific (eg ML, MAP, Bayesian, indirect inference, …). There are packages to help doing these, but you have to understand the relevant methodology (eg for MAP, you have to be able to code a likelihood, then use on of the optimization packages). I am not aware of a pre-packaged black box approach.

3

That is what I am doing now, when I do it in optimization ways, I am not sure how to find the p value and the choice of initial guess affect results a lot. That’s why I want a black box that could handle this.

4

DifferentialEquations.jl. Simulating jump diffusions:

http://docs.juliadiffeq.org/latest/tutorials/jump_diffusion.html

Estimation:

http://docs.juliadiffeq.org/latest/analysis/parameter_estimation.html#Parameter-Estimation-for-Stochastic-Differential-Equations-and-Monte-Carlo-1