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

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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 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. 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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Sure lets go through each subquestion step by step 11 Derive the BeveridgeNelson decomposition of X1 To derive the BeveridgeNelson decomposition we st... View the full answer