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Consider a process consisting of a linear trend with an additive noise term consisting of independent random variables wt with zero means and variances σ2 w, that is, xt = β0 + β1t + wt, where β0, β1 are fixed constants. (a) Prove xt is nonstationary. (b) Prove that the first difference series ∇xt = xt − xt−1 is stationary by finding its mean and autocovariance function. (c) Repeat part (b) if wt is replaced by a general stationary process, say yt, with mean function µy and autocovariance function γy(h)

Consider a process consisting of a linear trend with an additive noise term consisting of independent random variables wt with zero means and variances σ2 w, that is, xt = β0 + β1t + wt, where β0, β1 are fixed constants. (a) Prove xt is nonstationary. (b) Prove that the first difference series ∇xt = xt − xt−1 is stationary by finding its mean and autocovariance function. (c) Repeat part (b) if wt is replaced by a general stationary process, say yt, with mean function µy and autocovariance function γy(h)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider a process consisting of a linear trend with an additive noise term
consisting of independent random variables wt with zero means and variances
σ2
w, that is,
xt = β0 + β1t + wt,
where β0, β1 are fixed constants.
(a) Prove xt is nonstationary.
(b) Prove that the first difference series ∇xt = xt − xt−1 is stationary by
finding its mean and autocovariance function.
(c) Repeat part (b) if wt is replaced by a general stationary process, say yt,
with mean function µy and autocovariance function γy(h)

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