ams316_hw2 - AMS316 HW2 Due Oct 19, 2009 1. Show that the...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMS316 HW2 Due Oct 19, 2009 1. Show that the acf of teh mth-order MA process given by m Xt = k =0 Zt−k /(m + 1) is ρ(k ) = (m + 1 − k )/(m + 1) k = 0, 1, . . . , m 0 k>m 2. Show that the infinite-order MA process {Xt } defined by Xt = Zt + C (Zt−1 + Zt−2 + . . . ) where C is a constant, is non-stationary. Also show that the series of first differences {Yt } defined by Yt = Xt − Xt−1 is a first-order MA process and is stationary. Find the ACF of {Yt }. 3. Find the values of λ1 and λ2 such that the 2nd-order AR process defined by Xt = λ1 Xt−1 + λ2 Xt−2 + Zt is stationary. If λ1 = 1/3, λ2 = 2/9, show that the ACF of Xt is given by ρ(k ) = 16 2 27 3 |k | + 1 5 − 21 3 |k | , k = 0, ±1, ±2, . . . 4. Show that the ACF of the stationary 2nd-order AR process Xt = is given by ρ(k ) = 1 1 Xt−1 + Xt−2 + Zt 12 12 1 32 − 77 4 |k | 45 1 77 3 |k | + , k = 0, ±1, ±2, . . . ...
View Full Document

Ask a homework question - tutors are online