Latent State Variable Plots

[donskerclass]

Specifically for the Stochastic Volatility Second order model (ie, the output of estimate_rbc_sv_2_joint.jl), write the following code to make plots of the latent state variables x.

• Write code to make time series plots of the latent variables (specifically z and ν) in the same format as the existing plots of the epsilons, ie with mean and intervals over time.

Outline of approach:

• This basically requires taking the MCMC output, and writing code so that for each draw of parameters and shocks, it solves the model and produces the simulations with noise= in QuadraticStateSpaceProblem set to the saved shocks.
• This is slightly different than either the estimation code in estimate_rbc_sv_2_joint.jl (which computes the likelihood) or the data generation code in generate_fake_data_rbc_sv.jl, which does not take in shocks and so I think generates new ones by default.
• It might be possible to do this using the EnsembleProblem method (see Jesse's code example), which does generally what I want, but if it's hard to make that use the saved data and parameter values, you can just write a loop.

Asides on potential implementation improvements, not required:

• If you can write this code as a generic function that produces the corresponding output given MCMC output from an arbitrary DSSM model solved at second order int he same format, great, but no rush on that.
• This should be naively parallelizable, but it's not likely to be slow enough that you should worry about that

[jlperla]

Closing as we are unlikely to add this.