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

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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): X , Y , X , Y XY = E{(X - X )(Y - Y )} = YX joint distribution-1 XY 1 ) 1 /( ) )( ( ) /( 2--- = = n y y x x s s s s i i xy yy xx xy MSE linear prediction min E{(Y - X) 2 } = Y 2 (1- 2 ) = YX XX-1 min E{(X - Y) 2 } = X 2 (1- 2 ) = XY YY-1 2 measures goodness of prediction XY (k) = cov{X t , Y t+k } = YX (-k) Cross-covariance function , stationary case Cross-correlation function XY (k) = corr{X t , Y t+k } | XY (k)| 1 X t = a u Z t-u...
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chapt8 - Stat 153 - 19 Oct 2008 D. R. Brillinger Chapter 8...

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