= cieo, Let {e} be a zero-mean, unit-variance white noise process. Consider a process {Y} which starts at time t = 0, and is defined recursively as follows: Let Yo Y₁ = c₂Yo + e₁, and Y₁ = 0₁ Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process). a) Show that the process has zero mean. 1 b) For values of 01,02 in the stationarity region for an AR(2) process, show how to choose C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that of a stationary AR(2) process with parameters 01, 02. c) Once the process {Y} has been generated, show how one can transform in into a new process which has any desired mean and variance. (Remark. This gives a method for simu- lating stationary AR (2) processes.)
= cieo, Let {e} be a zero-mean, unit-variance white noise process. Consider a process {Y} which starts at time t = 0, and is defined recursively as follows: Let Yo Y₁ = c₂Yo + e₁, and Y₁ = 0₁ Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process). a) Show that the process has zero mean. 1 b) For values of 01,02 in the stationarity region for an AR(2) process, show how to choose C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that of a stationary AR(2) process with parameters 01, 02. c) Once the process {Y} has been generated, show how one can transform in into a new process which has any desired mean and variance. (Remark. This gives a method for simu- lating stationary AR (2) processes.)
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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Transcribed Image Text:Let {e} be a zero-mean, unit-variance white noise process. Consider a process
{Y} which starts at time t = 0, and is defined recursively as follows: Let Yo
= cieo,
Y₁ = c₂Yo + e₁, and Y₁ = ¢₁Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process).
a) Show that the process has zero mean.
1
b) For values of 01, 02 in the stationarity region for an AR (2) process, show how to choose
C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that
of a stationary AR(2) process with parameters 01, 02.
c) Once the process {Y} has been generated, show how one can transform in into a new
process which has any desired mean and variance. (Remark. This gives a method for simu-
lating stationary AR(2) processes.)
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