Lets say that you have panel data, of daily consumption of product p1 of 10000 individuals. The panel data is on a daily basis for only one month, this means that $t=1,...,30$. The question is how do it ? What kind of model I to use and why.My answer iss to have a two-level model: $y_{i,t}=\beta_{i}x_{i,t}+\epsilon_{i,t}$$\beta_{i}=\gamma_{i}z_{i} + \eta_{i}$where $x_{i,t}$ would contain my time variant variables and $z_{i}$ will contain all my time invariant variables. My argument was, that by modeling it like this, I believe that I take control of the time dependency between the $y_{i,t}$ and $y_{i,t-1}$ by letting the $\epsilon_{i,t}$ also depend on time and also I capture the heterogeneity of the consumers. Where $\epsilon_{it}\sim N(0,\Sigma_{\epsilon})$ and $\eta_{i}\sim N(0,\sigma_{ \eta _{i}}^2)$ What do you think ?
Forecasting daily usage of a prouct
predictive modeling;bigdata;regression;time series;hierarchical data format