answer the question

1. Answer the following questions and explain your reasoning: a) (i) Discuss the methodology proposed by Box and Jenkins in determining appropriate models for univariate time series data. In particular, rst stating what the parameters p and q represent in the ARMAQJ, q) model. Comment on the methods Box and Jenkins suggested for determining the values of p and q in practice. [7 marks] (ii) Discuss new developments in the identication stage of estimating an ARMA model since Box and Jenkins proposed their approach in 1976. [5 marks] b) Suppose that the AR(1) model y, = py,_1 + u, is weakly stationary, where u, is white noise with mean zero and variance 0'2, i.e. u, m WN(0,0'2). Derive the conditional variance of y, (var[y, |1,_1]), where [,4 is the information set at time t - l, and the unconditional variance of y, (varly). Comment on the relationship between the conditional and unconditional variance and explain the intuition behind the relationship. r11 ___ __I._1