Consider the following three AR(2) (quadratic) problems of the form in each case, complete the following steps: i. Determine the coefficients  and  . ii. Simulate the data according to this model,...

Consider the following three AR(2) (quadratic) problems of the form

in each case, complete the following steps:

i. Determine the coefficients
 and
 .

ii. Simulate the data according to this model, with n = 800.

iii. Fit models A(1)…AR(4) to the data using the
 or ar.mle().

iv. Complete a table that uses AIC, BIC, and hypothesis testing to select the best model.

v. Verify, using pacf(), that the partial autocorrelation plot produces similar results to your table for the hypothesis testing part of the table. Explain what you are looking to in your table and the pacf () plot.