Ex3_NEW - Time Series (M30085) 2002 Exercises 3 In these...

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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 non-stationary. 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.

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Ex3_NEW - Time Series (M30085) 2002 Exercises 3 In these...

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