Let us consider a process consisting of a linear trend with an additional, serially correlated noise...

 

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Let us consider a process consisting of a linear trend with an additional, serially correlated noise Bo+Bit + wt + Wt-1; t = = xt = 0, 1, 2, . . . , where {w} is a white noise with zero mean and variance o², and ßo and ß₁ are some fixed constants. (a) Prove that {x} is not stationary. (b) Take the first difference yt = √xt = xt - Xt−1, t = 1,2,.... Is {yt} stationary? Explain. If so, compute the mean and autocorrelation function. Let us consider a process consisting of a linear trend with an additional, serially correlated noise Bo+Bit + wt + Wt-1; t = = xt = 0, 1, 2, . . . , where {w} is a white noise with zero mean and variance o², and ßo and ß₁ are some fixed constants. (a) Prove that {x} is not stationary. (b) Take the first difference yt = √xt = xt - Xt−1, t = 1,2,.... Is {yt} stationary? Explain. If so, compute the mean and autocorrelation function.

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Lets address each part of the question a Proving that xt is not stationary For a process to be stationary its mean and variance should be constant ove... View the full answer