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Unformatted text preview: PSTAT 174 / 274  Midterm Consider GDP from 1983 1Q to 2002 4Q. Figure 1 shows the linear trend over time and you plotted the deterended time series with differentiation. G D P T im e Bilion $ 2 0 4 0 6 0 8 0 4000 6000 8000 10000 (a) D e tr e n d e d T im e S e r ie s w ith D iffe r e n tia tio n T im e Bilion $ 2 0 4 0 6 0 8 0 50 100 150 200 (b) Figure 1: GDP data from 1983 1Q to 2002 4Q 1. (30 points) You can consider the following model, x t = 1 + 2 t + w t , where 1 and 2 are known constants and w t is a white noise process with variance 2 . Prove that the first difference series x t = x t x t 1 is stationary by finding its mean and autocovariance function. 2. (30 points) Consider the following AR(1) time series model X t = 0 . 4 X t 1 + w t , w t i.i.d N (0 , 1225) . (a) Find and sketch the ACF, ( h ) . (b) Find and sketch the PACF, hh . 1 3. (10 points) You used differentiation to remove the linear trend and plotted ACF/PACF....
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.
 Spring '08
 MACKGALLOWAY

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