hw5 - MA ∞ model(d Evaluate the first three AR...

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

View Full Document Right Arrow Icon
AMS316 HW5 (Due Nov 30, 2011) 1. Following the procedure I have done in class, show that the ACFs of the ARMA (1 , 1) model, X t = αX t - 1 + Z t + βZ t - 1 , | α | < 1 , | β | < 1 , is given by ρ (1) = (1 + αβ )( α + β ) / ( 1 + β 2 + 2 αβ ) ρ ( k ) = αρ ( k - 1) ,k = 2 , 3 ,... 2. For the model (1 - B )(1 - 0 . 2 B ) X t = (1 - 0 . 5 B ) Z t : (a) Classify the model as an ARIMA ( p,d,q ) process(i.e. find p,d,q). (b) Determine whether the process is stationary and invertible. (c) Evaluate the first three MA coefficients of the model when ex- pressed as
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA ( ∞ ) model. (d) Evaluate the first three AR coefficients of the model when ex-pressed as AR ( ∞ ) model. 3. Show that AR(2) process X t = X t-1 + cX t-2 + Z t is stationary provided-1 < c < 0. Find the autocorrelation function when c =-3 / 16. 4. Show that the AR (3)process X t = X t-1 + cX t-2-cX t-3 + Z t is non-stationary for all values of c. 1...
View Full Document

This note was uploaded on 02/28/2012 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

Ask a homework question - tutors are online