please give the answer code in R $($explain your solution$)$

Consider my favourite $AR(2)$ model

$x_t=1\mathrm{.}5x_{t-1}-0\mathrm{.}75x_{t-2}+w_t$

where $w_{t}NID(0,1).$ Recall this is the same model we used in Assignment $4,$ Question

$2($b$).$ So expect some consistency with the results you obtained there.

Determine the theoretical auto$-$correlation function, $(h)$ for the above $AR(2)$ process.

To do this apply the formulae that were derived in the notes $($i$.$e$.$ the recursive calculation

of $(h).$ Use a "for loop" structure. For your final answer you should produce a table

of the theoretical auto$-$correlation values for lags $h=0,1,2,$dots,$15.$ As well, use $R$ to

make a plot of this theoretical auto$-$correlation function, $(h)$ for all lags from $0$ to $50$

$($in the plot command use type$="$h$").$ From the information in ACF, what is the period

of this $AR(2)$ process?

Next, generate and plot realizations from this $AR(2)$ model by representing it as a

bivariate AR$(1).$ Again, following the materials in class notes, being sure to first explain

and introduce the problem of converting a univariate $AR(2)$ to a bivariate $AR(1).$ For

simulation purposes, there is code provided on the website that generates realizations

from a bivariate random walk. Please make use of this code and modify it where

necessary to simulate a bivariate AR$(1).$ Annotate each line of the code to say what

it is doing, and also indicate exactly where you have modified it to adapt it to the

bivariate AR$(1)$ model. In your answer, show only the relevant time series plot, not all

the plots given for the $2$D random walk.