A series xt generated by the moving average process as: xt = µ + εt + θ1 εt−1, where εt are independently identically distributed random variables with E(εt) = 0, and V ar(εt) = σ2 . (a) Calculate the unconditional mean and the unconditional variance of xt (b) What is meant by saying that a process like xt is invertible? What condition would assure that xt is invertible? If θ = 0.75, does xt satisfy the invertibility condition? (c) What shapes of the ACF and PACF functions do you expect for xt ? Derive the first 4 autocorrelations for this process (τ1 up to τ4). (d) Write the equations for the 1, 2, 3 and 4 step ahead forecasts for xt .
A series xt generated by the moving average process as: xt = µ + εt + θ1 εt−1, where εt are independently identically distributed random variables with E(εt) = 0, and V ar(εt) = σ2 . (a) Calculate the unconditional mean and the unconditional variance of xt (b) What is meant by saying that a process like xt is invertible? What condition would assure that xt is invertible? If θ = 0.75, does xt satisfy the invertibility condition? (c) What shapes of the ACF and PACF functions do you expect for xt ? Derive the first 4 autocorrelations for this process (τ1 up to τ4). (d) Write the equations for the 1, 2, 3 and 4 step ahead forecasts for xt .
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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Hello, please help me to solve the question below.
A series xt generated by the moving average process as:
xt = µ + εt + θ1 εt−1,
where εt are independently identically distributed random variables with E(εt) = 0, and V ar(εt) = σ2
.
(a) Calculate the unconditional mean and the unconditional variance of xt
(b) What is meant by saying that a process like xt is invertible? What condition would assure that xt is invertible? If θ = 0.75, does xt satisfy the invertibility condition?
(c) What shapes of the ACF and PACF
(d) Write the equations for the 1, 2, 3 and 4 step ahead forecasts for xt .
.
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