Q II. For each ARMA model below, show how an unit shock (i.e.,1) to X at t (i.e., et =1) affects Xt+i, for i=0,1,2,3,.... manually and draw a plot for it. The plot would show the impact of an unit shock at t on Xt+i (y axis) against different i (x axis). You can do this by converting ARMA to MA representation and see how an unit value (i.e.,1) of white noise at i-period before (i.e., et-i ) affects Xt. We call the plot impulse response function graph. Do this manually (i.e., do not use a software). You confirm your results with Matlab. (First specify each model using ARIMA command. Then use Impulse command. For the second ARMA model, Matlab will complain that the model is unstable and will not give you the impulse response. So, use the command to check just 1st and 3rd ARMA models. Do not submit the Matlab results.)

Xt = 0.7Xt-1 + et , where et ~ iid. N(0.1)

Xt =Xt-1 + et , where et ~ iid. N(0.1)

Xt = et + 0.3et-1 + 0.1et-2, where et ~ iid. N(0.1)