1 Consider the following ARIMA(0,1,1) process Et 119 where 0 0 1 and at is a strong white noise with mean zero and variance 1 1 Derive the Beveridge Nelson decomposition of Xt You should find that Xt (1 0) Es 0t (0o Xo) (1) Explain why the Beveridge Nelson decomposition is also know as trend cycle de composition s 1 20 1 2 Assume that Xo and so are constants Show that X, is not covariance stationary 10 1 3 Compute the h steps ahead forecast for Xt 10 1 4 Show that the forecast mean squared error can be written as 1 (h 1)(1 0) 0 10 For each sub question, please explain and comment on your derivations step by step The derivations should explicitly show the logical reasoning behind your solution List the premises and or the assumptions you are using, where necessary

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1. Consider the following ARIMA(0,1,1) process .. = Et + 119 where 0 0 <1 and {at} is a strong white noise with mean

1. Consider the following ARIMA(0,1,1) process .. = Et + 119 where 0 0

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11 Derivation of the BeveridgeNelson decomposition To derive the BeveridgeNelson decomposition of Xt we start with the ARIMA011 process equation Xt t t1 The first difference of Xt is equal to the curr... blur-text-image

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