Download daily SPY data $($trading symbol $\text{'}$SPY$\text{'})$ from February $1,1993$ to February

$29,2024$ in $R.$ Please answer the following questions:

$($a$).$ Does the log return follow a unit root process? Specify your reason.

$($b$).$ Does the log return follow a white noise process if you just consider the first $20$ lags of

autocorrelations? Specify your reason.

$($c$).$ Calculate the ACF of log return and print the first $5$ lags;

$($d$).$ Calculate the PACF of log return and print the first $5$ lags;

$($e$).$ Identify and estimate an ARMA model to fit the log return and write down the estimated

model; $($Round your estimates to the fourth decimal place$)$

$($f$).$ Suppose that you are standing at the last trading day. Forecast the log return for the

next $5$ days and print out your forecast.