From a sample of 50 consecutive observations from a stationary process, the table below gives values for the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF): Lag ACF PACF 1 0.854 0.854 2 0.820 0.371 3 0.762 0.085 The sample variance of the observations is 1.253. a. Suggest, giving reasons, an appropriate model based on this information b. State two conditions that must be met for two time series processes X and Y to be Cointegrated. [3] c. State the circumstances in which it is reasonable to expect that two time series are cointegrated [2] Consider the ARCH(1) process X = +o+ (X--) where e, are independent normal random variables with variance 1 and mean 0. Show that, for s = 1, 2,..., 1-1, X, and X-, are: d. Uncorrelated e. Not independent. [5] [6] [4]