Stochastic volatility model demo

Hi! I am working through the stochastic volatility model notebook (link below).

It is pointed out that the model specification is not ideal because the priors (sample_prior_predictive) plot grossly over-estimate the fluctuations in the observations. I took that to mean that the observed fluctuations (on the order of ± 1e-2) are much smaller than the T distribution. However, after the fit, the poster_predictive is now within shouting distance of the observations. While that is good, it is unclear to me what has happened. I considered the nu parameter in the T distribution, but at nu = ~10, it’s close to Guassian, and would in any case span the same scale as the normal distribution.

Related to the above, what would be the most straightforward approach to dealing with the scaling problem?

Thanks in advance for everyone’s insight!

Best wishes,