I found a reference which answered my question: https://arxiv.org/pdf/1405.3738.pdf. 

The model is quite complicated, here is the state space representation:

[![enter image description here][1]][1]

So, let's say I have L different products I'm studying across 1,..,T time periods.

$Y_{l,t} \sim z*\delta_0 + (1-z)NB(exp(\widetilde{\eta}_{l,t}),alpha_l)$ is the distribution for product l at time t

$\widetilde{\eta}_{l,t} = \eta_{l,t} + X_{l,t}\theta_l$ this is the Log of the mean of product l sales at time t, guaranteeing that it is positive.

$\eta_{l,t} = \mu_l + \phi_l(\eta_{l,t-1}-\mu) + \epsilon_{l,t}$

$\epsilon_{l,t} \sim N(0,\frac{1}{\tau_l})$

The other priors and hyperpriors are in the next images:

[![enter image description here][2]][2]
[![enter image description here][3]][3]



P.S. Now I'm trying to write the JAGS code and any help would be much appreciated!

  [1]: https://i.sstatic.net/Zhdz7.png
  [2]: https://i.sstatic.net/BDrVO.png
  [3]: https://i.sstatic.net/NpMB5.png