Math Problem Statement
A stationary coupled multivariate time series is defined by x t = λ y t − 1 + σ z t y t = λ x t − 1 + σ w t where λ and σ are constants, and z t and w t are independent, uncorrelated standard Gaussian random variables. That is, w t , z t ∼ N ( 0 , 1 ) E [ z t w s ] = 0 ∀ t , s E [ z t z s ] = E [ w t w s ] = δ t s now What are the lag- l cross-covariances Cov ( x t , y t − l ) ? Express your answer in terms of λ , σ , l . Your answer will depend on the parity of l . Fill in the answer accordingly below: For even l , Cov ( x t , y t − l ) =? give me an answer no steps
Solution
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Math Problem Analysis
Mathematical Concepts
Time Series Analysis
Covariance
Gaussian Random Variables
Formulas
Covariance formula for lagged variables
Theorems
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Suitable Grade Level
Graduate Level
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