This one is for statistical inference questions

Suppose we have a data set (X1, . .. , Xn) that is a realization from an AR(1) model Xt = 1Xt-1+ Zt, Zt ~ WN(0, o?). A student Bob fails to pick up the correct model. Instead, he overfits the data to an AR(2) process Xt = $1Xt-1+ $2Xt-2 + Zt, Zt ~ WN(0, o?) and obtains the Yule-Walker estimators ($1, $2) of ($1, $2) as the solution of 1 p(1) p(1) [p (1 ) 1 p (2 ) where p(2)'s are the sample acf's of the data. What is the asymptotic distribution of $1? Note: The asymptotic distribution contains the population parameters that should be derived under the true model. Hint: Treat the AR(1) model as AR(2) with 02 = 0 and apply the asymptotic results of Y-W estimators of AR(p) with p = 2