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hw2 - The homework has to be stapled PSTAT 174/274...

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- The homework has to be stapled. PSTAT 174/274. Homework #2 Name: Due: 10/23/06 at the beginning of the discussion session Score: /10 Credit: People you worked with: Sources consulted(Reference): 1. (2 points) For an MA(1), x t = w t + θw t - 1 , show that | ρ x (1) | ≤ 1 / 2 for any number θ . For which values of θ does ρ x (1) attain its maximum and minimum? 2. (1 point each) Identify the following models as ARMA( p, q ) models (watch out for parameter re- dundancy), and determine whether they are causal and/or invertible: (a) x t = 0 . 80 x t - 1 - 0 . 15 x t - 2 + w t - 0 . 30 w t - 1 (b) x t = x t - 1 - 0 . 50 x t - 2 + w t - w t - 1 3. (2 points) For the AR(2) model given by x t = - 0 . 9 x t - 2 + w t , find the roots of the autoregressive polynomial and then sketch the ACF,
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