State Space Models in PyMC

[DanWeitzenfeld]

@jessegrabowski

The parameter estimates are quite different, though

This partly due to my priors. Try changing to:

sigma_trend = pm.InverseGamma('sigma_trend', mu=0.25, sd=.2)
sigma_mu = pm.InverseGamma('sigma_mu', mu=.8, sd=.25)

@jessegrabowski

Since I asked the “does this matter” question I’ve thought about it more, and I think it does. Using future information to estimate the parameters will certainly lead to model over-fitting and worse out of sample performance. I think it’s only called for in specific situations, such as missing value interpolation or time series decomposition, where we don’t necessarily want forecasts.

If you are using the kalman-smoothed estimate fit on data up to time T, and then using that to predict T+1, I don’t think it will lead to model over-fitting. If you are using the kalman-smoothed estimate fit on data up to time T to predict T-X, then yes, I agree it could lead to overfitting.

@jessegrabowski

Another answer, which is over-fit to my personal context, is that I am interested in estimating rational expectation models where the information set available to the decision makers in the model needs to be carefully controlled. To get valid parameter estimates in this context, I can’t allow any information about the future to seep in.

That is definitely a valid reason to avoid the kalman-smoothed estimate.

@jessegrabowski

I am curious if you think the GaussianRandomWalk setup can generalize to more complex models. The reason I avoided it in the first place is because I’m interested in a much larger family of models than just the local level model (which is known to be equivalent to a GRW). Can you represent an auto-regressive or moving-average process using clever application of the GRW process?

AR models yes, MA models require scan. See here and Brandon’s response