Problems 1. Build simulations of length 100 of the following models. For each model, use the command set.seed(100) before you create random values, and let the white noise time series wt have standard deviation 5 (5 points each): a. A random walk. b. An AR(3) model xt = 0.9xt1 0.08xt2 + 0.024xt3 + wt. c. A quadratic model xt = 3 + 2t + 0.05 t 2 + wt. d. An exponential model with MA(2) error xt = e 0.04t + wt + 0.003wt1 + 0.00001wt2 e. A linear model with harmonic seasonal variation and white noise xt = 1.3t + 10 sin(2t/12) + 7 cos(4t/12) + 8.5 sin(10t/12) + wt f. An ARIMA(2,2,0) model with 2xt = 0.32xt1 + 0.122xt2 + wt 2. tree.rings.ts is a time series containing tree ring widths for a Bristecone pine from California. Fit the best ARMA(p,q) model with p 5, q 5 to the time series. Using other appropriate tools, show that the ARMA(p,q) model is a good fit for the time series (5 points). tree.rings.ts <- tsdl[[190]]