Question: Condition distribution varianles a (7 marks) A natural estimator for the unknown mean u of a weakly stationary time series { X } is given

Condition distribution varianles

a (7 marks) A natural estimator for the unknown mean u of a weakly stationary time series { X } is given by X = = [X1 + X2 + . .. + Xx], n where n is the sample size. Show that E[X ] = /, Var [X= 1 7 (h) , n h=-(n-1) where y(h) is the autocovariance function of {X}. Hint: n Var = Cov Ex, = EE Cov (Xx, X; ). j=1 =li=11. Let wt, -co 0|X1 + X3 = 0)

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