solutions10 - Matlab Solutions Time Series(2DD23 Week 10...

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Unformatted text preview: Matlab Solutions Time Series (2DD23) Week 10 Exercise 8.1 X t = Z 1 , t + β 11 Z 1 , t- 1 + β 12 Z 2 , t- 1 Y t = Z 2 , t + β 21 Z 1 , t- 1 + β 22 Z 2 , t- 1 γ XY ( ) = Cov ( X t , Y t ) = Cov ( Z 1 , t + β 11 Z 1 , t- 1 + β 12 Z 2 , t- 1 , Z 2 , t + β 21 Z 1 , t- 1 + β 22 Z 2 , t- 1 ) = Cov (β 11 Z 1 , t- 1 , β 21 Z 1 , t- 1 ) + Cov (β 12 Z 2 , t- 1 , β 22 Z 2 , t- 1 ) = β 11 β 21 Cov ( Z 1 , t- 1 , Z 1 , t- 1 ) + β 12 β 22 Cov ( Z 2 , t- 1 , Z 2 , t- 1 ) = (β 11 β 21 + β 12 β 22 )σ 2 Z γ XY ( 1 ) = Cov ( X t , Y t + 1 ) = Cov ( Z 1 , t + β 11 Z 1 , t- 1 + β 12 Z 2 , t- 1 , Z 2 , t + 1 + β 21 Z 1 , t + β 22 Z 2 , t ) = Cov ( Z 1 , t , β 21 Z 1 , t ) = β 21 Cov ( Z 1 , t , Z 1 , t ) = β 21 σ 2 Z γ XY (- 1 ) = Cov ( X t , Y t- 1 ) = Cov ( Z 1 , t + β 11 Z 1 , t- 1 + β 12 Z 2 , t- 1 , Z 2 , t- 1 + β 21 Z 1 , t- 2 + β 22 Z 2 , t- 2 ) = Cov (β 12 Z 2 , t- 1 , Z 2 , t- 1 ) = β 12 Cov ( Z 2 , t , Z 2 , t ) = β 12 σ 2 Z For k 6= - 1 , , 1 we have independence between...
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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.

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solutions10 - Matlab Solutions Time Series(2DD23 Week 10...

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