Consider the following time series model for {v}_₁ Yt=yt-1 + Et + AE1-1, = where & is i.i.d with mean zero and variance o², for t= 1,..., T. Let yo 0. Demon- strate that y, is non-stationary unless = -1. In your answer, clearly provide the conditions for a covariance stationary process. Hint: Apply recursive substitution to express y in terms of current and lagged errors. (b) (3 marks) Briefly discuss the problem of applying the Dickey Fuller test when testing for a unit root when the model of a time series is given by: t = pxt-1+u, where the error term ut exhibits autocorrelation. Clearly state what the null, alternative hypothesis, and the test statistics are for your test.