Unformatted text preview: γ X ( τ ) and autocorrelation function (acf) ρ X ( τ ). Show by the deﬁnition of acvf and acf that, γ X ( τ ) = γ X (τ ) for τ = 1 , 2 ,... and ρ X (0) = 1. 5. Write down the deﬁnition of the secondorder (or weakly) stationary process. 6. Consider the purely random processes { Z t } , where Z t are independent and identically distributed random variables with mean 0 and variance σ 2 Z . (a) Compute its autocovariance function γ Z ( τ ) and autocorrelation function ρ Z ( τ ) for τ = 0 , 1 , 2 ,... . (b) Is this process weakly statioanry? 7. Consider the MA(1) process: X t = Z t + θZ t1 where  θ  < 1 and Z t are independent and identically distributed random variables with mean 0 and variance σ 2 Z . (a) Compute its autocovariance function γ Z ( τ ) and autocorrelation function ρ Z ( τ ) for τ = 0 , 1 , 2 ,... . (b) Is this process weakly statioanry?...
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 Fall '09
 Stochastic process, Autocorrelation, Stationary process, Xt, Autocovariance, autocorrelation function

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