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Let {e} be a zero mean white noise process. Suppose that the observed process is Y₁ = et + Oet - 1, where 0 is either 3 or 1/3. (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of 0 and that the autocorrelation functions are the same for 0 = 3 and 0 = 1/3. For simplicity, suppose that the process mean is known to be zero and the

Let {e} be a zero mean white noise process. Suppose that the observed process is Y₁ = et + Oet - 1, where 0 is either 3 or 1/3. (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of 0 and that the autocorrelation functions are the same for 0 = 3 and 0 = 1/3. For simplicity, suppose that the process mean is known to be zero and the

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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Let {e} be a zero mean white noise process. Suppose that the observed process is 0e₁-1, where 0 is either 3 or 1/3. Y₁ = e₁ + et Oet (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of 0 and that the autocorrelation functions are the same for 0 = 3 and 0 1/3. For simplicity, suppose that the process mean is known to be zero and the variance of Y, is known to be 1. You observe the series {Y} for t = 1, 2,..., n and suppose that you can produce good estimates of the autocorrelations Pk. Do you think that you could determine which value of 0 is correct (3 or 1/3) based on the estimate of pk? Why or why not? t
Transcribed Image Text:Let {e} be a zero mean white noise process. Suppose that the observed process is 0e₁-1, where 0 is either 3 or 1/3. Y₁ = e₁ + et Oet (a) Find the autocorrelation function for {Y} both when 0 = 3 and when 0 = 1/3. (b) You should have discovered that the time series is stationary regardless of the value of 0 and that the autocorrelation functions are the same for 0 = 3 and 0 1/3. For simplicity, suppose that the process mean is known to be zero and the variance of Y, is known to be 1. You observe the series {Y} for t = 1, 2,..., n and suppose that you can produce good estimates of the autocorrelations Pk. Do you think that you could determine which value of 0 is correct (3 or 1/3) based on the estimate of pk? Why or why not? t
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