1.13 Consider the two series Xt = Wt Yt = Wt – 0wr-1+ ut, where wi and Uz are independent white noise series with variances o? and o?, respectively, and 0 is an unspecified constant. (a) Express the ACF, py(h), for h = 0,±1,±2,... of the series yt as a function of o?, o?, and 0. (b) Determine the CCF, pæy(h) relating xt and yt. (c) Show that xt and yt are jointly stationary.
1.13 Consider the two series Xt = Wt Yt = Wt – 0wr-1+ ut, where wi and Uz are independent white noise series with variances o? and o?, respectively, and 0 is an unspecified constant. (a) Express the ACF, py(h), for h = 0,±1,±2,... of the series yt as a function of o?, o?, and 0. (b) Determine the CCF, pæy(h) relating xt and yt. (c) Show that xt and yt are jointly stationary.
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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
Transcribed Image Text:1.13 Consider the two series
Xt = Wt
Yt = Wt – 0wr-1+ ut,
where wi and Uz are independent white noise series with variances o? and o?,
respectively, and 0 is an unspecified constant.
(a) Express the ACF, py(h), for h = 0,±1,±2,... of the series yt as a function
of o?, o?, and 0.
(b) Determine the CCF, pæy(h) relating xt and yt.
(c) Show that xt and yt are jointly stationary.
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