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Unformatted text preview: Time Series (M30085) 2002 Exercises 3 In these questions, { t } is a discrete, purely random process, such that E ( t ) = 0, V AR ( t ) = 2 , COV ( t , t + ) = 0 for 6 = 0. 1. Find the ACF of the second order MA process given by X t = t + 0 . 7 t 1 . 2 t 2 2. Show that the ACF of the m th order MA process is given by X t = m k =0 t k / ( m + 1) is = ( m + 1 k ) / ( m + 1) k = 0 , 1 ,...,m k > m 3. Show that the infinite MA process { } defined by X t = t + C ( t 1 + t 2 + ... ) where C is a constant is nonstationary. Also show that the series of first differences { Y t } defined by Y t = X t X t 1 is a first order MA process and is stationary. Find the ACF of { Y t } 4. Find the ACF of the first order AR process defined by X t = 0 . 7( X t 1 ) = t . Plot for k = 6 , 5 ,..., 1 , , +1 ,..., +6 5. If X t = + t + t 1 , where is a constant, show that the ACF does not depend on ....
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This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.
 Spring '09
 jsdkasj

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