1. Let {Wt}tez ~WN(0, 0) and define the time series {X+} tez by X = W...

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1. Let {Wt}tez ~WN(0, 0) and define the time series {X+} tez by X = W + OW-1, t Z, where is a real constant. (a) Compute the mean function of {X}tez. (b) Compute the variance function of {X}tez. [5] [5] (c) Compute the autocovariance function of {X+}tEZ. [5] (d) For |e| < 1, show that {Wt}tez can be represented in terms of Xt, Xt1, .. 1 Hint: For a complex number z with |z| < 1, we have that 1 Z = zi. j=0 [5] 1. Let {Wt}tez ~WN(0, 0) and define the time series {X+} tez by X = W + OW-1, t Z, where is a real constant. (a) Compute the mean function of {X}tez. (b) Compute the variance function of {X}tez. [5] [5] (c) Compute the autocovariance function of {X+}tEZ. [5] (d) For |e| < 1, show that {Wt}tez can be represented in terms of Xt, Xt1, .. 1 Hint: For a complex number z with |z| < 1, we have that 1 Z = zi. j=0 [5]