H16 - H16 The discussion of bivariate processes is readily...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
H16 The discussion of bivariate processes is readily extended to the general multivariate case. If we have m processes, , each having zero mean, we define ,1 ,2 , { },{ }, . ..,{ } tt t XX X m m the covariance matrix at lag h by ( ) [ ( )], 1,. .., , 1,. .., ij hh i m j γ Γ= = = , where . For ,, () ij t h i t j hE X X + ⎡⎤ = ⎣⎦ ,( ii ij h ) = denotes the ACVF of , , ti X while for ij ) denotes the cross-covariance function between and . , X , tj X We assume that the m processes are jointly stationary , i.e. that for all ij ij h is a function of h only and does not depend on t . Each of the three main types of univariate models has its corresponding multivariate extension, which is obtained, essentially, by replacing the scalar parameters in the univariate model by matrix parameters. Let and be m -dimensional random vectors. , [ ,..., ]' t m = X , [ ,..., t m ZZ = Z A zero-mean, m -variate model is defined by ARMA( , ) pq (*) 11 ... ... p t p t t q −− = Φ ++ Φ + + Θ Θ X Z Z Z t q q where AR and MA coefficients, { and { } ( 1,. .., ) i ip Φ= } ( 1,. .., ) i i Θ = , are real matrices, and mm × is the multivariate white noise, i.e., with zero mean vector and uncorrelated values at different times
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.

Page1 / 2

H16 - H16 The discussion of bivariate processes is readily...

This preview shows document pages 1 - 2. Sign up to view the full document.

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