4005ass1(1).pdf - STAT 4005 Time Series Assignment 1 Due...

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STAT 4005 Time Series Assignment 1 Due date: Oct 9 Monday Let a t WN (0 2 ) 1. Does the quadratic trend T t = α + βt 2 pass through the moving average filter ( a - 1 ,a 0 1 ) = ( 1 3 , 1 3 , 1 3 )? 2. Suppose Z t = 8+4 t +2 X t , where X t is a zero-mean stationary series with autocovariance function γ k . (a) Find the mean and the autocovariance function of Z t . (b) Is Z t stationary? Why? (c) Find the mean and the autocovariance function of Δ Z t = (1 - B ) Z t . (d) Is Δ Z t stationary? Why? 3. Suppose that Z t = ( a t + a t - 1 + a t - 3 ) / 3 4. Consider the time series { Z t } satisfying Z t = 0 . 2 Z t - 1 + a t .
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