4.18. Let { X, } be any stationary series with continuous spectral...

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4.18. Let { X, } be any stationary series with continuous spectral density f such that 0 f () < K and f () # 0. Let fn () denote the spectral density of the differenced series {(1 - B)"X1}. (a) Express fn(1) in terms of In - 1 () and hence evaluate fn(). (b) Show that 0 as n 00 for each he [0,Tt. (c) What does (b) suggest regarding the behaviour of the sample-paths of {(1 - B)"X, } for large values of n?

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