Suppose we observe x1, · · · , x100, and obtain the sample autocovariances ˆγ(0) = 1382.2, γˆ(1) = 1114.4, γˆ(2) = 591.73 and ˆγ(3) = 96.216. Find the Yule-walker estimates of φ1, φ2, and σ 2 w in the model xt = φ1xt−1 + φ2xt−2 + wt , where wt is Gaussian white noise with variance σ 2 w. Also find 95% confidence intervals for φ1 and φ2. You may use R to help with matrix calculations.