1.1. (a) generate n = 100 observations from the autoregression xt = −.9xt−2 + wt with σw = 1, using the method described in example 1.9. next, apply the moving average filter vt = (xt + xt−1 + xt−2 + xt−3)/4 to xt , the data you generated. now plot xt as a line and superimpose vt as a dashed line. (b) repeat (a) but with xt = 2 cos(2πt/4) + wt , where wt ∼ iid n(0, 1). (c) repeat (a) but where xt is the log of the johnson & johnson data discussed in example 1.1. (d) what is seasonal adjustment (you can do an internet search)? (e) state your conclusions (in other words, what did you learn from this exercise).