Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x₁ = ₁x₁-1 + 0.25x1-2 - 0.10x1-3+ 8 + u, where var(u) = o². Suppose that the autocorrelation function, p(h), at lag h = 1 takes on the values p(1) = 0.50. In addition var(x,) = 10 and E[x₂] = µ = 25 a) Determine the values of ß₁, § and ♂² . b) Compute and plot a graph of o(h), the auotocovariance function of the process at lag h, for h = 0, 1, 2, 3, 4. c) Find the values of $11, Ø22, Ø33 and Þ44 - the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.
Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x₁ = ₁x₁-1 + 0.25x1-2 - 0.10x1-3+ 8 + u, where var(u) = o². Suppose that the autocorrelation function, p(h), at lag h = 1 takes on the values p(1) = 0.50. In addition var(x,) = 10 and E[x₂] = µ = 25 a) Determine the values of ß₁, § and ♂² . b) Compute and plot a graph of o(h), the auotocovariance function of the process at lag h, for h = 0, 1, 2, 3, 4. c) Find the values of $11, Ø22, Ø33 and Þ44 - the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.
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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![Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation:
x₁= B₁xt-1 + 0.25x₁-2 - 0.10x1-3+ 8+u, where var(u,) = o².
Suppose that the autocorrelation function, p(h), at lag h = 1 takes on the values
p(1) = 0.50. In addition var(x,) = 10 and E[x₂] = µ=25
a) Determine the values of ₁, and o².
b) Compute and plot a graph of o(h), the auotocovariance function of the process
at lag h, for h = 0, 1, 2, 3, 4.
c) Find the values of Ø11, Þ22, Þ33 and Þ44
the values of the partial
autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2F67ee9fd8-5667-409b-b205-44ac8ddfb5fe%2F7smfbu9_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation:
x₁= B₁xt-1 + 0.25x₁-2 - 0.10x1-3+ 8+u, where var(u,) = o².
Suppose that the autocorrelation function, p(h), at lag h = 1 takes on the values
p(1) = 0.50. In addition var(x,) = 10 and E[x₂] = µ=25
a) Determine the values of ₁, and o².
b) Compute and plot a graph of o(h), the auotocovariance function of the process
at lag h, for h = 0, 1, 2, 3, 4.
c) Find the values of Ø11, Þ22, Þ33 and Þ44
the values of the partial
autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.
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