hwk2 - X t = 0 . 5 X t-1 + Z t . 4. Compute the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Time Series Analysis Problem Sheet 2 Hand in solutions to questions 3, 4 and 6 on Thursday 6th November at the 10.00 lecture. LATE solutions will NOT be accepted unless you have very good reasons supported by evidence. Your solutions to this sheet COUNT TOWARDS ASSESSMENT . 1. Find the mean, variance and autocovariance function of the following MA(2) process X ( t ) = Z t + 0 . 2 Z t - 1 - 0 . 4 Z t - 2 , where Z t is a purely random process with zero mean and σ 2 Z = 1. 2. Define the MA( m ) process by X t = m X i =0 a - i Z t - i , where a (0 , 1) is a constant and Z t is a purely random process with zero mean and σ 2 Z = 1. Compute the autocovariance function of X t . Check your answer is correct for k = m where γ ( m ) = a - m . 3. Compute the autocovariance function of the following autoregressive process:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X t = 0 . 5 X t-1 + Z t . 4. Compute the autocorrelation function of the following autoregressive process: X t = 1 3 X t-1 + 2 9 X t-2 + Z t . 5. Suppose the stationary process { X t } has autocovariance function X ( k ). Dene a new sta-tionary process { Y t } by Y t = X t-X t-1 . Find the autocovariance function of { Y t } in terms of X ( k ) and obtain Y ( k ) when X ( k ) = | k | . 6. Show that the autocorrelation function of the mixed ARMA(1,1) model X t = X t-1 + Z t + Z t-1 is given by (1) = (1 + )( + ) 1 + 2 + 2 ( k ) = ( k-1) for k = 2 , 3 , 4 , . . . 1...
View Full Document

This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.

Ask a homework question - tutors are online