TIME SERIES III

Question 1

(a) Let Xt be a zero-mean, unit-variance stationary process with autocorrelation k(rho) . Suppose that t is a non-constant function an

that t(standard deviation) is a positive-valued non-constant function. The observed series is formed as Yt = t + t Xt.

(i) Find the mean and covariance function for the Yt process

(ii) Is the process Yt stationary?

(b) Consider the model Yt = 5 + et - 0.7et-1 + 0.5et-2, where et * * IID N(0, J. ). (i) Find the autocovariance function for the Y process. (ii) Using b(i) or otherwise, determine $1, and $22- (c) Suppose that {Y} is generated according to Y = e + cet- + ce-2 + ce-3 + ... + ceo fort > 0, e "IID N(0, 62) and {VY} is the first difference of {Y} . (i) Determine {VY} (ii) Is {VY} stationary? Justify your answer. (ii) Identify {VY } as a specific ARIMA process specifying p, d, q, o and e