I am trying to learning pyro to build a hierarchical time series forecasting model .

My target: predict `product_in_different_store`

for future 14 days salecount .

For example ,

- I have 4 levels hierarchy structure
`category 1/ category 2 / product_in_different_city/ product_in_different_store`

. - The exogenous features are bound to bottom level
`product_in_different_store`

and middle level`product_in_different_city`

- Many
`product_in_different_store`

may have different distribution : normal , poisson , negative-binomial , zero-inflated-poisson or zero-inflated-negative-binomial

My motivation:

- Train ARIMA/Prophet on each
`product_in_different_store`

or`product_in_different_city with one-hot encode store features`

doesn’t perform well , because each single product timeseries is lack of exogenous features , some features may be only happend once(but may apreared many times in different product) , hard to estimate best coefficient . So I am looking into hierarchy model . - I can’t look so many product ( 4 cities , avg 30+ stores each city, about 8000+ product each store ) , seems many product only on selling in very short time ( less than 28 days , have blank period or stock out period ) . It is hard to choose one distribution for all of them .

My question:

- Could we choose distribution dynamicly in trainning ?
- Could you provide an example for hierarchical multivariate time series ? I have saw some hierarchy model only bind features to top level , how do I bound different feature to different levels ?