statsmodels - SARIMAX model in PyMC3

Question

I would like to write down the following SARIMAX model (2,0,0) (2,0,0,12) in PyMC3 to perform bayesian estimation of its coefficients but I cannot figure out how to start with the seasonal part Has anyone tries something like this?

with pm.Model() as ar2:
    theta = pm.Normal("theta", 0.0, 1.0, shape=2)
    sigma = pm.HalfNormal("sigma", 3)
    likelihood = pm.AR("y", theta, sigma=sigma, observed=data)

    trace = pm.sample(
        1000,
        tune=2000,
        random_seed=13,
    )
    idata = az.from_pymc3(trace)

question from:https://stackoverflow.com/questions/65891813/sarimax-model-in-pymc3

Answer 1

Although it would be best (e.g. best performance) if you can get an answer that uses PyMC3 exclusively, in case that does not exist yet, there is an alternative way to do this that uses the SARIMAX model in Statsmodels in combination with PyMC3.

There are too many details to repeat a full answer here, but basically you wrap the log-likelihood and gradient methods associated with a Statsmodels SARIMAX model. Here is a link to an example Jupyter notebook that shows how to do this:

https://www.statsmodels.org/stable/examples/notebooks/generated/statespace_sarimax_pymc3.html