(a) Is this model causal? Explain your answer. (b) Its autocorrelation function obeys the linear difference equation p(h)-0.7p(h-1) +0.1p(h-2) = 0, h≥ 1. Using this equation, find the values of p(0) and p(1). (c) The general solution of the linear difference equation in (b) is of the form p(h) = k₁r7h + k₂r₂¹, h≥ 1, where r₁ and r2 are the roots of the characteristic polynomial from the AR(2) process above, and k₁ and k₂ are constants. Find p(h) by computing the values for these quantities, with initial condition k₁ + k₂ = 1.
(a) Is this model causal? Explain your answer. (b) Its autocorrelation function obeys the linear difference equation p(h)-0.7p(h-1) +0.1p(h-2) = 0, h≥ 1. Using this equation, find the values of p(0) and p(1). (c) The general solution of the linear difference equation in (b) is of the form p(h) = k₁r7h + k₂r₂¹, h≥ 1, where r₁ and r2 are the roots of the characteristic polynomial from the AR(2) process above, and k₁ and k₂ are constants. Find p(h) by computing the values for these quantities, with initial condition k₁ + k₂ = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Consider the AR(2) process
Xt = 0.7
Xt-1-0.1 Xt-2 + Zt,
Transcribed Image Text:where {Z} is a white noise process with mean 0 and variance 4.
(a) Is this model causal? Explain your answer.
(b) Its autocorrelation function obeys the linear difference equation
p(h)-0.7p(h-1) + 0.1 p(h− 2) = 0, h ≥ 1.
Using this equation, find the values of p(0) and p(1).
(c) The general solution of the linear difference equation in (b) is of the form
-h
p(h) = k₁r7¹ +k₂r₂h, h≥1,
where r₁ and r2 are the roots of the characteristic polynomial from the AR(2) process
above, and k₁ and k₂ are constants. Find p(h) by computing the values for these
quantities, with initial condition k₁ + k₂ = 1.
(d) Find the partial autocorrelation function for all lag values h ≥ 1 for this model.
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