Forecasting panel data and time series

Question

I have a panel data set of lets say 1000 observations, so

 i=1,2,...,1000 

. The data set runs in daily basis for a month, so

t=1,2,...,31.

I want to estimate individual specific in R:

    y_i10=αi+βi∗yi9+γi∗yi8+...+δi∗yi1+ϵit

and then produce density forecasts for the next 21 days, that is produce density forecasts for

yi11,yi12 etc

My questions are:

1. Can I do this with plm package ? I am aware how to estimate with plm package but I do not know how to produce the forecasts.

2. Would it be easier (and correct) if I consider each observation as a separate time series, and use arima(9,0,0) for each one of them, and then get the density forecasts ? If so, how can I get the density forecasts ?

3. In (2.) , how can I include individual specific effects that are constant over time ?

Thanks a lot