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Unformatted text preview: Time Series Analysis Problem Sheet 1 If you wish hand in solutions to questions 1 and 3 on Thursday 23rd October at the 10.00 lecture. These solutions do not count for credit. 1. (Revision). Suppose β > 0. Define S n = n X i =0 β i . Show that S n = 1- β n +1 1- β . Let S ∞ = lim n →∞ S n . Determine the values of β for which S ∞ is finite and derive a formula for S ∞ when this is so. 2. Suppose the linear filter given by y t = S m ( x t ) = s X r =- q a r x t + r is a moving average filter. (a) From your lecture notes write down the definition of Res( x t ) and show that it may be written as Res( x t ) = s X r =- q b r x t + r (b) show that: i. ∑ s r =- q b r = 0; ii. b = 1- a ; iii. b r =- a r for r 6 = 0. 3. Sixteen successive observations on a stationary time series are as follows: x t = (1 . 2 , . 8 , 1 . 3 , . 5 , 1 . 2 , . 9 , . 8 , 1 . 5 , . 6 , 1 . 1 , 1 . 1 , . 9 , . 5 , 1 . 2 , . 8 , 1 . 6) (a) Produce a time series plot of the data....
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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