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1. Consider the data generating process Y₂ = c + Ø ₂Y₁-2+ & where & is a white noise process. Assuming 0 <0₂<1, answer the following: a. Derive the expected value of this process. b. c. Derive the variance of this process. Derive the covariance of this process for j=1,2,.... Note that j represents the number of periods between Y, and Y₁-j. d. Derive the autocorrelation function of this process j=1,2,...... e. Plot the autocorrelation function with the information you derived above.

1. Consider the data generating process Y₂ = c + Ø ₂Y₁-2+ & where & is a white noise process. Assuming 0 <0₂<1, answer the following: a. Derive the expected value of this process. b. c. Derive the variance of this process. Derive the covariance of this process for j=1,2,.... Note that j represents the number of periods between Y, and Y₁-j. d. Derive the autocorrelation function of this process j=1,2,...... e. Plot the autocorrelation function with the information you derived above.

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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1. Consider the data generating process Y₁ = c + Ø₂Yt-2+ &t where & is a white noise process. Assuming 0 <0₂<1, answer the following: a. Derive the expected value of this process. b. Derive the variance of this process. C. Derive the covariance of this process for j=1,2,.... Note that j represents the number of periods between Y, and Yt-j. d. Derive the autocorrelation function of this process j=1,2,..... e. Plot the autocorrelation function with the information you derived above.
Transcribed Image Text:1. Consider the data generating process Y₁ = c + Ø₂Yt-2+ &t where & is a white noise process. Assuming 0 <0₂<1, answer the following: a. Derive the expected value of this process. b. Derive the variance of this process. C. Derive the covariance of this process for j=1,2,.... Note that j represents the number of periods between Y, and Yt-j. d. Derive the autocorrelation function of this process j=1,2,..... e. Plot the autocorrelation function with the information you derived above.
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