I. Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x=1x-1 +0.25x+-2 - 0.10x+-3+ 8+ш where var(u) = σ². δ 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[x] = µ = 25 a) Determine the values of ẞ1, 8 and σ². b) Compute and plot a graph of σ(h), the auotocovariance function of the process at lag h, for h = 0, 1, 2, 3, 4. c) Find the values of 11, 22, 33 and 44 - the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively. d) Find the values of 01, 02, 03, 04 where: 00 x=μ+ (with 00 = 1) i=0

I. Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x=1x-1 +0.25x+-2 - 0.10x+-3+ 8+ш where var(u) = σ². δ 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[x] = µ = 25 a) Determine the values of ẞ1, 8 and σ². b) Compute and plot a graph of σ(h), the auotocovariance function of the process at lag h, for h = 0, 1, 2, 3, 4. c) Find the values of 11, 22, 33 and 44 - the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively. d) Find the values of 01, 02, 03, 04 where: 00 x=μ+ (with 00 = 1) i=0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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