Explain the process of selecting the order $p$ of an AR model using the Partial Autocorrelation Function $($PACF$)$ plot. What indicates the significance of lags in the PACF plot?

$1$

Based on figure $(1),$ indicate the order $p$ of a hypothetical AR model. Which lags should at least be included in the AR specification and why?:

Describe the different types of panel data models. Make sure to write down and understand the general specification for each type.

What is the meaning of ${}_i$ in the fixed effects specification? Give an example.

Suppose that you have monthly data on several financial assets funds, from $2020$ to $2024.$ The variables available for each fund are: monthly return, bonds composition $(\%),$ stocks composition $(\%),$ number of fund managers, number of financial analyst, average manager salary, average financial analyst salary. Write down the corresponding fixed effects specification if you want to estimate the monthly return of a fund, based on the other available variables, assuming i represents a particular fund, while $t$ represents a particular month.