Question: Suppose that {Yt } is stationary with autocovariance function k. Show that for any fixed positive integer n and any constants c1, c2,..., cn, the

Suppose that {Yt } is stationary with autocovariance function k.

Show that for any fixed positive integer n and any constants c1, c2,..., cn, the process {Wt } defined by is stationary.

Mean{Wt} E{Wt} = c1E(Yt)+c2E(Yt)++cnE(Yt)

= E(Yt)(c1+c2++cn)

HOW DO I SOLVE:

Cov{Wt} =Cov(c1Yt+c2Yt1++cnYtk,c1Ytk+c2Ytk1++cnYtkn)

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