Download the monthly time series consisting of returns on:

$30$ industry $($Food$,$ Beer, Smoke, etc$)$

$$Market$-$risk free $($M$-$r$)$

$$SMB $($Small minus big$)$

$$HML $($High minus low$)$

$$RF $($Riskfreerate$)$

$$Momentum

$$Form the correlation matrix between all these time series. For the four$-$factor model $($market$-$RF$,$ SMB$,$ HML$,$ and Momentum$),$ which factor correlates most highly with every industry? Which factor correlates negatively with every industry? Does RF $($Riskfreerate$)$ correlate highly with $30$ industry time series?

$$Form the auto$-$correlation function $($ACF$)$ for time$-$lag $1$ to time$-$lag $10$ with the four$-$factor time series $($market$-$RF$,$ SMB$,$ HML$,$ and Momentum$).$ Is there any AR$(1)$ model in the $4$ time series? Explain your observations.