T12 - STA4005B Time Series (2007-2008) Tutorial 12 (15/4,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: STA4005B Time Series (2007-2008) Tutorial 12 (15/4, 16/4) (Time & Venue: T9, BMS LT; W5, MMW 704) Correlation function between forecast errors The l step and l+j step ahead forecast errors are respectively et (l ) = a t +l + ψ 1 at +l −1 + ψ 2 at +l − 2 + L + ψ l −1 at +1 et (l + j ) = a t + l + j + ψ 1 a t + l + j −1 + ψ 2 a t + l + j − 2 + L + ψ j a t + l + ψ j +1 a t + l −1 + L + ψ l + j −1 a t +1 The correlation function between l step and l+j step ahead forecast error is l −1 corr[et (l ), et (l + j )] = ∑ψ ψ i =0 i i+ j ∑ψ ∑ψ m =0 where ψ 0 = 1 l + j −1 l −1 2 m n =0 2 n Example 1 Find the correlation between 2-step and 3-step ahead forecast error at time t for the MA(2) process such that Z t = at + θ 1 a t −1 + θ 2 at − 2 Example 2 Find the auto-covariance function of the process Z t = (1 − 0.6 B + 0.9 B 2 )(1 − 0.5 B 12 ) a t . Revision Exercise: Consider the process Z t = 3 + 0.7 Z t −1 + at 2 where σ a = 4 . Let Z 200 = 10 , Z 199 = 12 and Z 198 = 11 . ˆ ˆ a) Find Z 200 (1) and Z 200 (4) . b) Calculate the 95% prediction interval of Z 201 and the 95% prediction interval of Z 204 . Note that if X ~ N (0,1) , then P ( X ≤ 1.96) = 0.975 . ˆ c) Let e (k ) = Z − Z (k ) be the k-step ahead forecast error. Find Cov[e (k ), e (m)] . t t +k t t t ...
View Full Document

This note was uploaded on 11/02/2011 for the course STAT 4005 taught by Professor Wu,kaho during the Spring '08 term at CUHK.

Page1 / 3

T12 - STA4005B Time Series (2007-2008) Tutorial 12 (15/4,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online