hw4 - AMS316 HW4 (Due Nov 16, 2011) 1. Find the ac.f of the...

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Unformatted text preview: AMS316 HW4 (Due Nov 16, 2011) 1. Find the ac.f of the first-order AR process defined by Xt - = 0.7(Xt-1 - ) + Zt Plot (k) for k = -6, -5, ..., 0, +1, ..., +6 (Remark: You can plot in Excel for convenience, if you want). 2. Assume the AR(2) process Xt = 1 Xt-1 + 2 Xt-2 + Zt is stationary. If 1 = 1/3, 2 = 2/9, show that the ac.f of Xt is given by |k| |k| 5 1 16 2 + - , k = 0, 1, 2, ... (k) = 21 3 21 3 3. Show that the ac.f of the stationary second-order AR process Xt = is given by 45 (k) = 77 1 3 |k| 1 1 Xt-1 + Xt-2 + Zt 12 12 32 + 77 1 - 4 |k| k = 0, 1, 2, ... 4. For each of the following models: (a) Xt = 0.3Xt-1 + Zt ; (b) Xt = Zt - 1.3Zt-1 + 0.4Zt-2 ; (c) Xt = 0.5Xt-1 + Zt - 1.3Zt-1 + 0.4Zt-2 . Express the model using B notation and determine whether the model is stationary and/or invertible. 1 ...
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This note was uploaded on 02/28/2012 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

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