Unformatted text preview: { Z t } and { Y t } are independent stationary process, then the process W t = 2 Z t + Y t . is stationary. 4. Let { a t } be white noise with V ar ( a t ) = σ 2 a and let c be a constant with  c  < 1. The series { Z t } is then constructed as follows: Z 1 = a 1 ; Z t = cZ t1 + a t for t > 1 (a) Show that E ( Z t ) = 0. (b) Show that V ar ( Z t ) = σ 2 a (1 + c 2 + c 4 + ... + c 2 t2 ). (c) Show that Corr ( Z t ,Z tk ) = c k [ V ar ( Z tk ) V ar ( Z t ) ] 1 / 2 for k > ....
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 Spring '08
 WU,KaHo
 Statistics, Autocorrelation, Stationary process, Autocovariance, zt

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