Fit the ARIMA$(2,1,2)$ model

$(1-{}_{1}B-{}_2{B}^2)(1-B)x_t=c+(1+{}_{1}B+{}_2{B}^2)Z_t$

to the transport index sample data $(x_t{)}_t=1^{60}$ using the Arima function from the

forecast package and write down the fitted equation. Is there any evidence that theWithout using specialised $R$ functions such as arima.sim or the like, write code to

simulate a path $(hat(x{)}_t{)}_t=1^{60}$ of the fitted ARIMA model from $($c$).$ Generate the noise as

Gaussian RVs $($with appropriate variance$)$ using R function rnorm and use initial

values hat$(x{)}_1=x_1,$hat$(x{)}_2=x_2,$hat$(x{)}_3=x_3$ from the sample data. Provide a plot of a simulated