Stochastic Volatility with PyMCStateSpace

Questions v5
2

Yes you can do this. All statespace matrices except x0 and P0 are allowed to have a time dimension on the far left. There is some discussion about how this works here.

To take advantage of this, you will need to register sigma_eta with a time dimension. You don’t know how long that is going to be until you see the data, so put None like this:

        sigma_eta = self.make_and_register_variable('sigma_eta', shape=(None, self.k_posdef,))

To allocate this into state_cov, you will need to make it into a stack of covariance matrices. You can do this with pt.diag, but you need to vectorize it:

        self.ssm['state_cov'] = pt.vectorize(pt.diag, '(a)->(a,b)')(sigma_eta)

Finally, add the dimension TIME_DIM to sigma_eta. If you’re feeling fancy you can also update the info to note that it needs to be time-varying.

Two final comments:

  1. The statespace model itself doesn’t know anything about the time dynamics, so you have to give sigma_eta a prior that encode that information (via pm.GaussianRandomWalk or whatever)
  2. Small quibble with names: your parameter is called sigma_eta, but it’s being put directly into the covariance matrix, so it’s actually sigma_eta_squared. This is important if you are doing a replication study/communicating your results.
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