# hw3 - X t deﬁned by X t = Z t C Z t-1 Z t-2 where C is a...

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

AMS316 HW3 (Due Oct 24, 2011) In the following equations, { Z t } is a discrete-time, purely random pro- cess such that E ( Z t ) = 0, Var( Z t ) = σ 2 Z , and successive values of Z t are independent so that Cov( Z t ,Z t + k ) = 0, k 6 = 0. 3.1 Show that the ac.f of the second-order MA process X t = Z t + 0 . 7 Z t - 1 - 0 . 2 Z t - 2 is given by ρ ( k ) = 1 , k = 0 0 . 37 , k = ± 1 - 0 . 13 , k = ± 2 0 , otherwise 3.2 Consider the MA( m ) process, with equal weights 1 m +1 at all lags (so it is a real moving average), given by X t = m X k =0 Z t - k m + 1 Show that the ac.f of this process is ρ ( k ) = ± m +1 - k m +1 , k = 0 ,...,m 0 k > m 3.3 Consider the inﬁnite-order MA process
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X t , deﬁned by X t = Z t + C ( Z t-1 + Z t-2 + ... ) where C is a constant. Show that the process is non-stationary. Also show that the series of the ﬁrst diﬀerences Y t deﬁned by Y t = X t-X t-1 is a ﬁrst-order MA process and is stationary. Find the ac.f of Y t . 3.5 If X t = μ + Z t + βZ t-1 , where μ is a constant, show that the ac.f does not depend on μ . 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