Problem 1. Answer the following questions: a) Write down the operator form of an ARIMA(2,1,D) process. Make sure to describe each component, for example, (36(8) = _____ b) Describe, in general terms, the behavior you would expect to see for the estimated ACF computed from the set of observation 1:1, - - - 1 :IST generated from the random walk model: 3.: = $34 + wt. Explain why. c) For an AR(1) model: act 2 0.53234 + wt, what is the denition of a partial auto-correlation between art and 33t_1'? d) For an AR(1) model: 2:: = 0.53:4 + wt, describe briey how will the PACF plot of this model look like? e) For an MA(1) model: 3:; = wt 0.811.134. Write it using the AR representation. E) Show that the autocovariance function of an ARU) series is given by _ 03\" _ 1 _ 9132 where d) is the parameter of the AR(1) process and w, M N(0, 012D). Hint: Using the fact that the MA representation is 1:: : (1 + $3 + $2132 + .. Juli. Wt)