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Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x=B₁xt-1 + 0.25x1-2 - 0.10x1-3+ ₂+ 8 + where var(u) 6². 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 U t = a) Determine the values of B₁, dand 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 $11, P22, Þ33 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: x=B₁xt-1 + 0.25x1-2 - 0.10x1-3+ ₂+ 8 + where var(u) 6². 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 U t = a) Determine the values of B₁, dand 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 $11, P22, Þ33 and Þ44 the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.

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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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.
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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