Homework Help is Here – Start Your Trial Now!
Math
Statistics
3. Consider the following process, Xt = 0.7Xt-1-0.1Xt-2+Zt +20Zt-1-0² Z₁-2, where {Z} is a white noise with mean zero and variance o². (a) Is {X} stationary? Justify your answer. (b) Find the range of such that {X} is invertible. (c) Suppose that is in the range found in (b) so that Z₁ can be expressed as Z₁ = Σ TjX₁-j. j=0 i. Find the values of 0, 1 and 2 in terms of 0. ii. Write down a recursive formula of 7; for j≥ 3 in terms of 0. (d) Let = 0. Given that Var (X) = 0.5, calculate the variance of Zt, 0². (e) Given the observations X2022 = 1.6 and X2021 = 0.9, find the one-step, two-step and three-step ahead forecasts at t = 2022, when 0 = 0. Moreover, calculate the variance of these three forecast errors in terms of o².

3. Consider the following process, Xt = 0.7Xt-1-0.1Xt-2+Zt +20Zt-1-0² Z₁-2, where {Z} is a white noise with mean zero and variance o². (a) Is {X} stationary? Justify your answer. (b) Find the range of such that {X} is invertible. (c) Suppose that is in the range found in (b) so that Z₁ can be expressed as Z₁ = Σ TjX₁-j. j=0 i. Find the values of 0, 1 and 2 in terms of 0. ii. Write down a recursive formula of 7; for j≥ 3 in terms of 0. (d) Let = 0. Given that Var (X) = 0.5, calculate the variance of Zt, 0². (e) Given the observations X2022 = 1.6 and X2021 = 0.9, find the one-step, two-step and three-step ahead forecasts at t = 2022, when 0 = 0. Moreover, calculate the variance of these three forecast errors in terms of o².

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
See similar textbooks
icon
Related questions
Question
3. Consider the following process, Xt = 0.7 Xt-1-0.1 X-2 +Z₁ +20 Z-1-0² Zt-2, where {Z} is a white noise with mean zero and variance o². (a) Is {X} stationary? Justify your answer. (b) Find the range of such that {X} is invertible. (c) Suppose that is in the range found in (b) so that Zt can be expressed as Z₁ = Σ TjXt-j. j=0 i. Find the values of To, T₁ and ₂ in terms of 0. ii. Write down a recursive formula of ₁ for j≥ 3 in terms of 0. (d) Let 0 = 0. Given that Var (X₂) = 0.5, calculate the variance of Zt, 0². (e) Given the observations X2022 = 1.6 and X2021 = 0.9, find the one-step, two-step and three-step ahead forecasts at t = 2022, when 0 = 0. Moreover, calculate the variance of these three forecast errors in terms of o². 1 1
Transcribed Image Text:3. Consider the following process, Xt = 0.7 Xt-1-0.1 X-2 +Z₁ +20 Z-1-0² Zt-2, where {Z} is a white noise with mean zero and variance o². (a) Is {X} stationary? Justify your answer. (b) Find the range of such that {X} is invertible. (c) Suppose that is in the range found in (b) so that Zt can be expressed as Z₁ = Σ TjXt-j. j=0 i. Find the values of To, T₁ and ₂ in terms of 0. ii. Write down a recursive formula of ₁ for j≥ 3 in terms of 0. (d) Let 0 = 0. Given that Var (X₂) = 0.5, calculate the variance of Zt, 0². (e) Given the observations X2022 = 1.6 and X2021 = 0.9, find the one-step, two-step and three-step ahead forecasts at t = 2022, when 0 = 0. Moreover, calculate the variance of these three forecast errors in terms of o². 1 1
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS