Given the first-order autoregressive model (AR(1)) is as follows:

(Formula look at pic)

(1) Please give the log-likelihood two numbers of the above expression.

(2) Please derive the parameter maximum likelihood estimation expression of the above model.

(3) Please derive the variance expression formula for the parameter estimation of the Shangda model.

(4) Please prove that the parameter estimator formula obtained by the maximum likelihood method and the least squares method is consistent.

yt=yt1+ut,utN(0,2) yt=yt1+ut,utN(0,2)