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Unformatted text preview: Time Series Analysis Problem Sheet 4 Hand in solutions to questions 3, 4 and 5 on Tuesday 2nd December at the 12.00 lecture. LATE solutions will NOT be accepted unless you have very good reasons supported by evidence. You will also need to at least read the definition given in question 2. Your solutions to this sheet COUNT TOWARDS ASSESSMENT. 1. Find the spectral density functions of the following processes: (a) X t = Z t + Z t 1 + Z t 2 (b) X t = Z t + 0 . 5 Z t 1 . 3 Z t 2 2. The normalized spectral density function f * ( ) for a process X is obtained from the spectral density function f ( ) by f * ( ) = f ( ) 2 X . Assume that the secondorder MA process X t = + Z t + 0 . 8 Z t 1 + 0 . 5 Z t 2 is second order stationary, where is a constant. Find the acv.f. and ac.f. of { X t } and show that its normalized spectral density function is given by f * ( ) =  1 (1 + 1 . 27 cos( ) + 0 . 53 cos(2 )) (0 < < ) ....
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 Spring '09
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