chapt8

# chapt8 - Stat 153 19 Oct 2008 D R Brillinger Chapter 8...

This preview shows pages 1–9. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

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

Unformatted text preview: Stat 153 - 19 Oct 2008 D. R. Brillinger Chapter 8 - Bivariate processes 8.1 Cross-covariance and cross correlation time-side 8.2 Cross-covariance frequency-side Chapter 9 - Linear systems regression system - fixed input, stochastic output Some data Some more data Bivariate time series . random process: (X t , Y t ) , t = 0, ±1, ±2, ... data: (x 1 , y 1 ), ..., (x N , y N ) Typically leads to more specific conclusions "Ordinary" statistics correlation. (X,Y): μ X , μ Y , σ X , σ Y σ XY = E{(X - μ X )(Y - μ Y )} = σ YX joint distribution-1 ≤ ρ XY ≤ 1 ) 1 /( ) )( ( ) /( ˆ 2--- = = ∑ n y y x x s s s s i i xy yy xx xy ρ MSE linear prediction min E{(Y - βX) 2 } = σ Y 2 (1- ρ 2 ) β = σ YX σ XX-1 min E{(X - αY) 2 } = σ X 2 (1- ρ 2 ) α = σ XY σ YY-1 ρ 2 measures goodness of prediction γ XY (k) = cov{X t , Y t+k } = γ YX (-k) Cross-covariance function , stationary case Cross-correlation function ρ XY (k) = corr{X t , Y t+k } | ρ XY (k)| ≤ 1 X t = Σ a u Z t-u...
View Full Document

{[ snackBarMessage ]}

### Page1 / 22

chapt8 - Stat 153 19 Oct 2008 D R Brillinger Chapter 8...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online