2.9 Suppose Y, Bo + B₁t+ X, where (X,) is a zero-mean stationary series with auto- covariance function Y and ẞo and ẞ₁ are constants. (a) Show that (Y) is not stationary but that W, VY, Y,-Y-1 is stationary. (b) In general, show that if Y, μ, + X,, where (X,) is a zero-mean stationary series and u, is a polynomial in 7 of degree d, then V"Y, V(V"-Y) is sta- tionary for m ≥d and nonstationary for 0≤m
2.9 Suppose Y, Bo + B₁t+ X, where (X,) is a zero-mean stationary series with auto- covariance function Y and ẞo and ẞ₁ are constants. (a) Show that (Y) is not stationary but that W, VY, Y,-Y-1 is stationary. (b) In general, show that if Y, μ, + X,, where (X,) is a zero-mean stationary series and u, is a polynomial in 7 of degree d, then V"Y, V(V"-Y) is sta- tionary for m ≥d and nonstationary for 0≤m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer 2.9b
Transcribed Image Text:2.9 Suppose Y, Bo + B₁t+ X, where (X,) is a zero-mean stationary series with auto-
covariance function Y and ẞo and ẞ₁ are constants.
(a) Show that (Y) is not stationary but that W, VY, Y,-Y-1 is stationary.
(b) In general, show that if Y, μ, + X,, where (X,) is a zero-mean stationary
series and u, is a polynomial in 7 of degree d, then V"Y, V(V"-Y) is sta-
tionary for m ≥d and nonstationary for 0≤m<d.
=
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