Question 3: Consider an AR(1) process: Xt aXt-1 + Et (a) Check the stationarity conditions for the AR(1) process. (b) Derive the autocorrelation function for this process. Sketch the cor- relogram which would arise in each of the following situations: (i) a = 0 (ii) 0 < a < 1 (iii) -1 < a < 0 (iv) a = 1 (v) a > 1 (vi) a < -1 In which of these situations is the series stationary? If a series is sta- tionary, what obvious feature do we expect the correlogram to have? What In which of these situations is the series stationary? If a series is sta- tionary, what obvious feature do we expect the correlogram to have? What 3 1 names are normally used for these series defined by (i) and (iv)?