Compute the Method of Moments estimators for the parameters (1, 2) R 2 of the AR(2) process: Yt = 1Yt1 + 2Yt2 + et where et W N(0, 2 e ) are iid random variables for every t Z.

Consider the AR(1) model Yt = (Yt1 ) + et , where R is constant in time and et W N(0, 2 e ) are iid random variables for every t Z. Let Sc(, ) be the corresponding conditional sum of square function. Find the Least Square estimates (, ).

Consider an AR(1) model with et N(0, 2 e ) iid and parameters , . Write the corresponding likelihood function.

Consider an AR(1) model with et N(0, 2 e ) iid and parameters , known and 2 e unknown. Prove that the Maximum Likelihood estimator of 2 e takes the form 2 e = S(, )/n .

Consider an MA(1) model with parameter . Compute the Method of Moment estimator for . Is this a good estimator of . Why?