3. Let {Y} be the first order autoregressive (AR(1)) process and define X = = Y...

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3. Let {Y} be the first order autoregressive (AR(1)) process and define X = = Y p. Yt - = (Y-1) Et, || < 1, Et ~ iid (0,02), (a) Find MA() representation of Xt. (b) Using the MA(0) representation in (a), compute the impulse response function axt IRF 'j at-j* = (c) Let Xt be the time series of US GDP, and t_; be some unexpected news (say, a sudden drop of the federal fund rate) from time t - j. What will be the economic interpretation of the IRF; above? What happens to this IRF; if j gets larger and larger (j )? (d) Compute Var (Xt), Cov (Xt, Xt-1) and Corr (Xt, Xt-1). 3. Let {Y} be the first order autoregressive (AR(1)) process and define X = = Y p. Yt - = (Y-1) Et, || < 1, Et ~ iid (0,02), (a) Find MA() representation of Xt. (b) Using the MA(0) representation in (a), compute the impulse response function axt IRF 'j at-j* = (c) Let Xt be the time series of US GDP, and t_; be some unexpected news (say, a sudden drop of the federal fund rate) from time t - j. What will be the economic interpretation of the IRF; above? What happens to this IRF; if j gets larger and larger (j )? (d) Compute Var (Xt), Cov (Xt, Xt-1) and Corr (Xt, Xt-1).