Bayesian Vector Autoregression in PyMC

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I recently wrote a PyMC Labs blogpost on Bayesian Vector Autoregression (BVAR) using PyMC (duh), which may be of interest to other PyMC-neers!

Feedback is more than welcome!

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Very cool! It would be nice if transformations were available to restrict the coefficient matrix to the stationary/invertible region of parameter space, as described for example here. From the results of that paper, forecast performance deteriorates as a function of the number of time series in the VAR without such a transformation.

I assume it would be possible to implement this using aeppl?

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That shouldn’t require aeppl, just defining priors in the way they mention in the paper.

Could be fun to try to get it working in PyMC, perhaps for pymc-experimental or a pymc-examples! Would that be something you would be interested in by any chance ^^?

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Yes, very interested! Since you’ve basically shown everything you need to set up the BVAR, I’ll put some time into it this weekend and see where I can get.

In the meantime, here’s a block to grab the data for your example that has a 100% HDI to go stale of 0%. Again, awesome blog post, thanks a lot for it!

# T10Y2YM is the 10-year yield minus the 3-month yield -- the best computations are the ones other people do for you!
from pandas_datareader.fred import FredReader

df_fred = (FredReader(symbols=['GDP', 'T10Y2YM'], start='1900-01-01', end=None)
          .read()
          .rename(columns={'T10Y2YM':'TSpread'}))
df_fred = df_fred.resample('Qs').last() # Last because interest rates are rates
df_fred['GDPGrowth'] = df_fred['GDP'].apply(np.log).diff().mul(400)
df_fred.dropna(how='any', axis=0, inplace=True)
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