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

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)


Cov{Wt} =Cov(c1Yt+c2Yt−1+⋯+cnYt−k,c1Yt−k+c2Yt−k−1+⋯+cnYt−k−n)  

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